Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery ApplicationsClick to copy article linkArticle link copied!
- Nick S. BluntNick S. BluntRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Nick S. Blunt
- Joan CampsJoan CampsRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Joan Camps
- Ophelia CrawfordOphelia CrawfordRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Ophelia Crawford
- Róbert IzsákRóbert IzsákRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Róbert Izsák
- Sebastian LeonticaSebastian LeonticaRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Sebastian Leontica
- Arjun MiraniArjun MiraniRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Arjun Mirani
- Alexandra E. MoylettAlexandra E. MoylettRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Alexandra E. Moylett
- Sam A. ScivierSam A. ScivierRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Sam A. Scivier
- Christoph SünderhaufChristoph SünderhaufRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Christoph Sünderhauf
- Patrick SchopfPatrick SchopfAstex Pharmaceuticals, 436 Cambridge Science Park, Cambridge CB4 0QA, United KingdomMore by Patrick Schopf
- Jacob M. TaylorJacob M. TaylorRiverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomMore by Jacob M. Taylor
- Nicole Holzmann*Nicole Holzmann*Email: [email protected]Riverlane, St. Andrews House, 59 St. Andrews Street, Cambridge CB2 3BZ, United KingdomAstex Pharmaceuticals, 436 Cambridge Science Park, Cambridge CB4 0QA, United KingdomMore by Nicole Holzmann
Abstract
Computational chemistry is an essential tool in the pharmaceutical industry. Quantum computing is a fast evolving technology that promises to completely shift the computational capabilities in many areas of chemical research by bringing into reach currently impossible calculations. This perspective illustrates the near-future applicability of quantum computation of molecules to pharmaceutical problems. We briefly summarize and compare the scaling properties of state-of-the-art quantum algorithms and provide novel estimates of the quantum computational cost of simulating progressively larger embedding regions of a pharmaceutically relevant covalent protein–drug complex involving the drug Ibrutinib. Carrying out these calculations requires an error-corrected quantum architecture that we describe. Our estimates showcase that recent developments on quantum phase estimation algorithms have dramatically reduced the quantum resources needed to run fully quantum calculations in active spaces of around 50 orbitals and electrons, from estimated over 1000 years using the Trotterization approach to just a few days with sparse qubitization, painting a picture of fast and exciting progress in this nascent field.
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License Summary*
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1. Introduction
2. Chemistry on a Quantum Computer
2.1. Chemistry and the Electronic Structure Problem
2.2. Quantum Computation
2.3. Qubit Hamiltonian
2.4. Algorithms
2.4.1. Variational Quantum Eigensolver
Figure 1
Figure 1. Outline of the VQE algorithm, indicating which parts occur on the quantum computer and which parts on the classical.
2.4.2. Quantum Phase Estimation
Figure 2
Figure 2. Outline of the circuit used to perform QPE, as discussed in ref (61).
3. Algorithm Choices
3.1. Algorithm Scaling
3.1.1. VQE Resources
3.1.1.1. Number of Qubits
3.1.1.2. Number of Parameters
enable preparation of a state close to the true ground state;
require as few parameters as possible, so as to minimize the time required to perform the classical optimization;
use as few quantum computational resources as possible.
3.1.1.3. Number of Hamiltonian Expectations
3.1.1.4. Number of Ansatz Circuit Applications
3.1.1.5. Circuit Depth
3.1.1.6. Summary
3.1.2. QPE Resources
3.1.2.1. Circuit Depth and Number of Repetitions
3.1.2.2. Number of Qubits
3.1.2.3. Error Correction Overhead
3.1.2.4. Summary
3.1.3. Comparison and Discussion
3.2. QPE in This Work
4. Implementing Error-Corrected Quantum Algorithms
4.1. Quantum Error Correction and the Surface Code
4.2. Magic-State Factories and the QPU Architecture
Figure 3
Figure 3. (a) Layouts for 15-to-1 (top) and 20-to-4 (bottom) magic-state factories. These consist of 11 and 14 logical qubits, respectively (green). The magic states produced are stored in the blue spaces. (b) Factory which distills 225 imperfect magic states to one higher quality magic state. Eleven first-level 15-to-1 factories (green) are used to produce 15 refined magic states, which are in turn used by the second-level 15-to-1 factory (orange) to produce one magic state of even higher quality (red). Blue lines are used to store and transport lower-quality magic states. White spaces are unused logical qubits.
4.3. Error-Corrected Resource Estimation

5. Trotterization vs Qubitization
5.1. Trotterization
Figure 4
Figure 4. Fit of empirical law for our set of molecules. The fit is done in two steps. In the first step (left), for each of the molecules, we generate δE0 for τ/τmax = [1.0, 0.5, 0.1, 0.05, 0.01, 0.005, 0.001] and do a one-parameter fit of . Note that, for larger molecules, ϵ0 for small values of τ appear to deviate from the quadratic behavior. We attribute this to numerical error and exclude these values from the fits. In the second step (right), we plot a1 for each molecule and fit a1 = a(nq)b, obtaining the parameters of the empirical law in eq 38: a = 1.51 ± 0.84; b = −4.66 ± 0.27.
5.2. Qubitization
6. Drug Design Methods and the Model System
6.1. Computational Chemistry in Pharma
6.2. Active Space Selection
6.3. Model System
Figure 5
Figure 5. Cluster containing part of the binding pocket and the Ibrutinib inhibitor. The various fragments in which the active space orbitals were selected are indicated using various colors.
6.4. Computational Methods
7. Results
Figure 6
Figure 6. Runtime to perform QPE using sparse qubitization. Active spaces from (14e,14o) to (100e,100o) are considered. It is assumed that one time step takes 1 μs to perform. Physical error rates, p, of 0.01 and 0.1% are considered. The Hamiltonian is either truncated using an L2-norm criterion or a CCSD(T) criterion. In each case, the runtime scales as approximately no4.6 with the number of active orbitals.
qubitization | Trotterization | ||
---|---|---|---|
no. of spatial orbitals | L2-norm truncation | CCSD(T) truncation | no truncation |
14 | 5.6 × 108 | 3.7 × 108 | 1.6 × 1012 |
20 | 3.2 × 109 | 2.3 × 109 | 2.7 × 1013 |
32 | 2.0 × 1010 | 1.1 × 1010 | 4.0 × 1014 |
42 | 6.9 × 1010 | 4.1 × 1010 | 2.4 × 1015 |
52 | 1.7 × 1011 | 1.1 × 1011 | 5.2 × 1015 |
66 | 4.7 × 1011 | 3.4 × 1011 | - |
100 | 2.7 × 1012 | 2.1 × 1012 | - |
No truncation of the Hamiltonian is performed for QPE with Trotterization. For QPE using qubitization the Hamiltonian is truncated using both CCSD(T) and the L2-norm to assess the error incurred, with a target truncation error of 0.3 mHa or less. The CCSD(T) criterion truncates more terms, resulting in a lower estimate for the required number of T gates.
Figure 7
Figure 7. Comparison of resources (runtime and total number of physical qubits) using two QPE algorithms. The first (orange) used qubitization, and the Hamiltonian was truncated to remove small terms up to an error budget. The second (green) used textbook QPE with Trotterization and no truncation of the Hamiltonian. The latter algorithm has a much steeper scaling in runtime. Even for a (14e,14o) active space the runtime is multiple orders of magnitude more expensive.
Figure 8
Figure 8. QPU layouts used to perform QPE experiments on the (32e,32o) active space example. Left: layout used for QPE with Trotterization. Right: Layout used for QPE with qubitization. Data block qubits are orange, magic-state factory qubits are green, and routing and storage qubits are blue. Qubitization uses many more data qubits such that the data block is much larger. However, the higher T-gate count in QPE with Trotterization necessitates larger magic-state factories (225-to-1) compared to those in qubitization (116-to-12). Axes are included to indicate the total number of logical qubits in both layouts, with each logical qubit having size 1-by-1. However, note that the code distance is higher in QPE with Trotterization (see Table 2) so that these are not to physical scale.
qubitization | Trotterization | |||
---|---|---|---|---|
no. of spatial orbitals | p = 10–4 | p = 10–3 | p = 10–4 | p = 10–3 |
14 | 13 | 29 | 17 | 36 |
20 | 14 | 31 | 19 | 39 |
32 | 15 | 32 | 20 | 41 |
42 | 16 | 34 | 21 | 43 |
52 | 17 | 35 | 21 | 43 |
66 | 18 | 37 | ||
100 | 19 | 39 |
We consider QPE performed using Trotterization and the full Hamiltonian, and QPE using qubitization and truncating small Hamiltonian elements. Physical error rates (p) of 10–4 and 10–3 are considered.
8. Conclusions
Acknowledgments
This work was performed as part of Astex’s Sustaining Innovation Postdoctoral Program. We acknowledge funding from Innovate UKs Sustainable Innovation Fund via SBRI. O.C.’s contribution to the work was in part supported by an Innovate UK grant (Quantum Enhanced Design for Materials and Chemistry, Project No. 105622). We thank David Plant and James R. Cruise for useful discussions and their valuable input to this work.
Appendix A
A.1. Number of Repetitions of QPE
A.2. QPE Probabilities
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- 12Peruzzo, A.; McClean, J.; Shadbolt, P.; Yung, M.-H.; Zhou, X.-Q.; Love, P. J.; Aspuru-Guzik, A.; O’Brien, J. L. A variational eigenvalue solver on a quantum processor. Nat. Commun. 2014, 5, 4213, DOI: 10.1038/ncomms5213Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitVShsbvM&md5=24adc3eeee68110a19e2f43020062e90A variational eigenvalue solver on a photonic quantum processorPeruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter; Yung, Man-Hong; Zhou, Xiao-Qi; Love, Peter J.; Aspuru-Guzik, Alan; O'Brien, Jeremy L.Nature Communications (2014), 5 (), 4213CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the phys. dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estn. algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state prepn. based on ansatze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We exptl. demonstrate the feasibility of this approach with an example from quantum chem.-calcg. the ground-state mol. energy for He-H+. The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future.
- 13Hempel, C.; Maier, C.; Romero, J.; McClean, J.; Monz, T.; Shen, H.; Jurcevic, P.; Lanyon, B. P.; Love, P.; Babbush, R.; Aspuru-Guzik, A.; Blatt, R.; Roos, C. F. Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator. Phys. Rev. X 2018, 8, 031022, DOI: 10.1103/PhysRevX.8.031022Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltFShu7Y%253D&md5=c5b702bf294cf6e51b4145f0183235d8Quantum Chemistry Calculations on a Trapped-Ion Quantum SimulatorHempel, Cornelius; Maier, Christine; Romero, Jonathan; McClean, Jarrod; Monz, Thomas; Shen, Heng; Jurcevic, Petar; Lanyon, Ben P.; Love, Peter; Babbush, Ryan; Aspuru-Guzik, Alan; Blatt, Rainer; Roos, Christian F.Physical Review X (2018), 8 (3), 031022CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chem. to physics and materials science. We report on the exptl. implementation of such an algorithm to solve a quantum chem. problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calc. the mol. ground-state energies of two simple mols. and exptl. demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chem. accuracy, which may serve as a cross-platform benchmark for multiqubit quantum simulators.
- 14Chen, M.-C.; Gong, M.; Xu, X.-S.; Yuan, X.; Wang, J.-W.; Wang, C.; Ying, C.; Lin, J.; Xu, Y.; Wu, Y.; Wang, S.; Deng, H.; Liang, F.; Peng, C.-Z.; Benjamin, S. C.; Zhu, X.; Lu, C.-Y.; Pan, J.-W. Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor. Phys. Rev. Lett. 2020, 125, 180501, DOI: 10.1103/PhysRevLett.125.180501Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitlens7jK&md5=16ad29873c90606a95eb71b769344838Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum CoprocessorChen, Ming-Cheng; Gong, Ming; Xu, Xiaosi; Yuan, Xiao; Wang, Jian-Wen; Wang, Can; Ying, Chong; Lin, Jin; Xu, Yu; Wu, Yulin; Wang, Shiyu; Deng, Hui; Liang, Futian; Peng, Cheng-Zhi; Benjamin, Simon C.; Zhu, Xiaobo; Lu, Chao-Yang; Pan, Jian-WeiPhysical Review Letters (2020), 125 (18), 180501CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)Adiabatic quantum computing enables the prepn. of many-body ground states. Realization poses major exptl. challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitized version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which employs short quantum circuits and provides a systematic quantum adiabatic optimization of the circuit parameters. The quantum adiabatic theorem promises not only the ground state but also that the excited eigenstates can be found. We report the first exptl. demonstration that many-body eigenstates can be efficiently prepd. by an adiabatic variational algorithm assisted with a multiqubit superconducting coprocessor. We track the real-time evolution of the ground and excited states of transverse-field Ising spins with a fidelity that can reach about 99%.
- 15Google AI Quantum and Collaborators; Arute, F.; Arute, F.; Aryae, K.; Babbush, R.; Bacon, D.; Bardin, J. C.; Barends, R.; Boixo, S.; Broughton, M. Hartree-Fock on a superconducting qubit quantum computer. Science 2020, 369, 1084– 1089, DOI: 10.1126/science.abb9811Google ScholarThere is no corresponding record for this reference.
- 16Roffe, J. Quantum error correction: an introductory guide. Contemp. Phys. 2019, 60, 226– 245, DOI: 10.1080/00107514.2019.1667078Google ScholarThere is no corresponding record for this reference.
- 17Chen, Z.; Satzinger, K. J.; Atalaya, J.; Korotkov, A. N.; Dunsworth, A.; Sank, D.; Quintana, C.; McEwen, M.; Barends, R.; Klimov, P. V. Exponential suppression of bit or phase errors with cyclic error correction. Nature 2021, 595, 383– 387, DOI: 10.1038/s41586-021-03588-yGoogle ScholarThere is no corresponding record for this reference.
- 18Nguyen, N. H.; Li, M.; Green, A. M.; Huerta Alderete, C.; Zhu, Y.; Zhu, D.; Brown, K. R.; Linke, N. M. Demonstration of Shor Encoding on a Trapped-Ion Quantum Computer. Phys. Rev. Appl. 2021, 16, 024057, DOI: 10.1103/PhysRevApplied.16.024057Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitVeku7rK&md5=4386fe584a0803c200ea7c41c6dae8abDemonstration of Shor Encoding on a Trapped-Ion Quantum ComputerNguyen, Nhung H.; Li, Muyuan; Green, Alaina M.; Huerta Alderete, C.; Zhu, Yingyue; Zhu, Daiwei; Brown, Kenneth R.; Linke, Norbert M.Physical Review Applied (2021), 16 (2), 024057CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple phys. qubits to encode a logical qubit, which is protected against errors at the phys. qubit level. Here, we use a trapped-ion system to exptl. prep. m-qubit Greenberger-Horne-Zeilinger states and sample the measurement results to construct mxm logical states of the [[m2, 1, m]] Shor code, up to m=7. The synthetic logical fidelity shows how deeper encoding can compensate for addnl. gate errors in state prepn. for larger logical states. However, the optimal code size depends on the phys. error rate and we find that m=5 has the best performance in our system. We further realize the direct logical encoding of the [[9,1,3]] Shor code on nine qubits in a 13-ion chain for comparison, with 98.8(1)% and 98.5(1)% fidelity for state |±〉L, resp.
- 19Egan, L.; Debroy, D. M.; Noel, C.; Risinger, A.; Zhu, D.; Biswas, D.; Newman, M.; Li, M.; Brown, K. R.; Cetina, M.; Monroe, C. Fault-Tolerant Operation of a Quantum Error-Correction Code. arXiv Preprint (Quantum Physics) , 2020. arXiv:2009.11482. https://doi.org/10.48550/arXiv.2009.11482.Google ScholarThere is no corresponding record for this reference.
- 20Pino, J. M.; Dreiling, J. M.; Figgatt, C.; Gaebler, J. P.; Moses, S. A.; Allman, M. S.; Baldwin, C. H.; Foss-Feig, M.; Hayes, D.; Mayer, K.; Ryan-Anderson, C.; Neyenhuis, B. Demonstration of the trapped-ion quantum CCD computer architecture. Nature 2021, 592, 209– 213, DOI: 10.1038/s41586-021-03318-4Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXosVClsLg%253D&md5=b3ce16dde190ddf4c35478f5840dda48Demonstration of the trapped-ion quantum CCD computer architecturePino, J. M.; Dreiling, J. M.; Figgatt, C.; Gaebler, J. P.; Moses, S. A.; Allman, M. S.; Baldwin, C. H.; Foss-Feig, M.; Hayes, D.; Mayer, K.; Ryan-Anderson, C.; Neyenhuis, B.Nature (London, United Kingdom) (2021), 592 (7853), 209-213CODEN: NATUAS; ISSN:0028-0836. (Nature Research)The trapped-ion quantum charge-coupled device (QCCD) proposal1,2 lays out a blueprint for a universal quantum computer that uses mobile ions as qubits. Analogous to a charge-coupled device (CCD) camera, which stores and processes imaging information as movable elec. charges in coupled pixels, a QCCD computer stores quantum information in the internal state of elec. charged ions that are transported between different processing zones using dynamic elec. fields. The promise of the QCCD architecture is to maintain the low error rates demonstrated in small trapped-ion expts.3-5 by limiting the quantum interactions to multiple small ion crystals, then phys. splitting and rearranging the constituent ions of these crystals into new crystals, where further interactions occur. This approach leverages transport timescales that are fast relative to the coherence times of the qubits, the insensitivity of the qubit states of the ion to the elec. fields used for transport, and the low crosstalk afforded by spatially sepd. crystals. However, engineering a machine capable of executing these operations across multiple interaction zones with low error introduces many difficulties, which have slowed progress in scaling this architecture to larger qubit nos. Here we use a cryogenic surface trap to integrate all necessary elements of the QCCD architecture-a scalable trap design, parallel interaction zones and fast ion transport-into a programmable trapped-ion quantum computer that has a system performance consistent with the low error rates achieved in the individual ion crystals. We apply this approach to realize a teleported CNOT gate using mid-circuit measurement6, negligible crosstalk error and a quantum vol.7 of 26 = 64. These results demonstrate that the QCCD architecture provides a viable path towards high-performance quantum computers.
- 21Postler, L.; Heußen, S.; Pogorelov, I.; Rispler, M.; Feldker, T.; Meth, M.; Marciniak, C. D.; Stricker, R.; Ringbauer, M.; Blatt, R.; Schindler, P.; Müller, M.; Monz, T. Demonstration of fault-tolerant universal quantum gate operations. Nature 2022, 605, 675– 680, DOI: 10.1038/s41586-022-04721-1Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xhtlyju7nO&md5=6f33b605a873e9bb77cd94bb7a7631ecDemonstration of fault-tolerant universal quantum gate operationsPostler, Lukas; Heuβen, Sascha; Pogorelov, Ivan; Rispler, Manuel; Feldker, Thomas; Meth, Michael; Marciniak, Christian D.; Stricker, Roman; Ringbauer, Martin; Blatt, Rainer; Schindler, Philipp; Mueller, Markus; Monz, ThomasNature (London, United Kingdom) (2022), 605 (7911), 675-680CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Abstr.: Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error-correcting codes1,2. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design3-5, which, in general, increases the complexity of the implementation. Here we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In particular, we make use of the recently introduced paradigm of flag fault tolerance, where the absence or presence of dangerous errors is heralded by the use of auxiliary flag qubits6-10. We perform a logical two-qubit controlled-NOT gate between two instances of the seven-qubit color code11,12, and fault-tolerantly prep. a logical magic state8,13. We then realize a fault-tolerant logical T gate by injecting the magic state by teleportation from one logical qubit onto the other14. We observe the hallmark feature of fault tolerance-a superior performance compared with a non-fault-tolerant implementation. In combination with recently demonstrated repeated quantum error-correction cycles15,16, these results provide a route towards error-cor. universal quantum computation.
- 22Abobeih, M. H.; Wang, Y.; Randall, J.; Loenen, S. J. H.; Bradley, C. E.; Markham, M.; Twitchen, D. J.; Terhal, B. M.; Taminiau, T. H. Fault-tolerant operation of a logical qubit in a diamond quantum processor. arXiv Preprint (Quantum Physics) , 2021. arXiv:2108.01646. https://doi.org/10.48550/arXiv.2108.01646.Google ScholarThere is no corresponding record for this reference.
- 23Partington, J. R. A short history of chemistry; Courier: London, 1989.Google ScholarThere is no corresponding record for this reference.
- 24Lewis, G. N. the Atom and the Molecule. J. Am. Chem. Soc. 1916, 38, 762– 785, DOI: 10.1021/ja02261a002Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaC28XlvFSl&md5=9f8b4fdf6c255a1c60dafaad766c9d3aThe atom and the moleculeLewis, G. N.Journal of the American Chemical Society (1916), 38 (), 762-85CODEN: JACSAT; ISSN:0002-7863.cf. C. A. 71 3865 and Bray and Branch, C. A. 7, 3865. Compds. should be classed as polar and nonpolar rather than inorg. and org. These classes are roughly the same. A nonpolar mol. is one in which the electrons belonging to the individual atom are held by such restraints that they do not move far from their normal positions, while in the polar mols. the electrons, being more mobile, so move as to sep. the mol. into positive and negative parts. In an extremely polar mol. such as NaCl it is probable that in the great majority of the mols. the Cl atom has acquired a unit negative charge and therefore the Na atom a unit positive charge, and the process of ionization probably consists only in a further sepn. of these charged parts. If a weakly polar mol. comes into the neighborhood of a more polar one it becomes itself more polar. In this process the weaker bipole stretches and its moment increases. A "cubical atom" is proposed as a basis of a new theory of atomic structure. Thus Li is a cube with a single electron on one corner, Be has 2 electrons, B 3, C 4, N 5, O 6, and F 7. This view is in harmony with the theory developed by Parson, C. A. 10, 406. An atom is considered as having an unalterable kernel which possesses an excess of positive charges corresponding in number to the ordinal number of the group in the periodic table to which the element belongs (cf. Thomson, C. A. 8, 824). There is a shell of electrons around the kernel which, in the case of a neutral atom, contains negative electrons equal in number to the excess of positive charges of the kernel, but the number of electrons in the shell may vary during chem. changes between zero and 8. The atom tends to hold an even number of electrons in the shell (especially 8 at the corners of the cube) but the electrons may ordinarily pass from one position to another in this shell. Two atomic shells are mutually interpenetrable. The paper is a discussion of these ideas applied to the structure of atoms and compds.
- 25Lewis, G. N. Valence and the Structure of Atoms and Molecules; Chemical Catalog, 1923.Google ScholarThere is no corresponding record for this reference.
- 26Burrau, Ø. Berechnung des Energiewertes des Wasserstoffmolekel-Ions (H2.) im Normalzustand. Naturwissenschaften 1927, 15, 16– 17, DOI: 10.1007/BF01504875Google ScholarThere is no corresponding record for this reference.
- 27Heitler, W.; London, F. Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik. Z. Phys. 1927, 44, 455– 472, DOI: 10.1007/BF01397394Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaB2sXivFCksA%253D%253D&md5=0fffa03ec3b765ec813b5f84e9108e7fInteraction of neutral atoms and homopolar binding according to the quantum mechanicsHeitler, W.; London, F.Zeitschrift fuer Physik (1927), 44 (), 455-72CODEN: ZEPYAA; ISSN:0044-3328.The action of forces between neutral atoms has a characteristic ambiguity in the quantum mechanics. The ambiguity seems capable of including the different modes of behavior actually found, i. e., for H either homopolar binding or elastic reflection, but for the rare gases only reflection. It also permits an evaluation of the elastic reflection effects in He, giving results of the right order of magnitude. For the selection and discussion of the various possible interactions the Pauli principle is here applied to a system of several atoms.
- 28Pauling, L. The Nature of the Chemical Bond. Application of Results Obtained from the Quantum Mechanics and from a Theory of Paramagnetic Susceptibility to the Structure of Molecules. J. Am. Chem. Soc. 1931, 53, 1367– 1400, DOI: 10.1021/ja01355a027Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaA3MXis1Cjsw%253D%253D&md5=ab16c2b91de30696fc9ea589520777d8The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of moleculesPauling, LinusJournal of the American Chemical Society (1931), 53 (), 1367-1400CODEN: JACSAT; ISSN:0002-7863.The electron-pair bond is discussed and from quantum mechanics a set of rules is presented which describes the properties of the bond with special ref. to the strength of the bond and the nature of the single-electron proper functions. These rules give information about the relative strengths of bonds formed by different atoms, the angles between bonds, properties of tetrahedral atoms with single and double bonds, cis and trans forms, the no. and spatial configuration of bonds and other properties. Transitions from electron-pair to ionic bonds are also discussed. A theory of the magnetic moments of mol. and complex ions is also developed. For the transition elements the proper functions involved in bond formation show that compds. with CN have electron-pair bonds, those with F have ionic bonds, and those with H2O, ion-dipole bonds. Electron structure, bond angles and other properties of mol. and complex ions can also be detd.from the magnetic data.
- 29Hund, F. Zur Deutung der Molekelspektren. I. Z. Phys. 1927, 40, 742– 764, DOI: 10.1007/BF01400234Google Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaB2sXhtVWltA%253D%253D&md5=5fd6f918920a6e8577c4d6f52b0b5e16Interpretation of the spectra of moleculesHund, I. F.Zeitschrift fuer Physik (1927), 40 (), 742-64CODEN: ZEPYAA; ISSN:0044-3328.The aim of this work is to indicate ways whereby a qual. understanding may be attained of those features of band spectra which depend on electron motions. The wave mechanics of schr.ovrddot.odinger (cf. Phys. Rev. 2S, 1049-70(1926)) are applied first to systems with one degree of freedom, and then to systems of several degrees of freedom, to det. their stationary states. The results of this analysis are in turn used to find the spectral terms of: (1) mols. with 2 unequal nuclei and 1 electron; (2) mols. with 2 equal nuclei and 1 electron; (3) mols. with 2 equal nuclei and 2 electrons. An illustration is afforded by the NaCl mol. The low spectral terms of NaCl, on sepn. of the nuclei, go over into the low terms of Na + Cl and Na+ + Cl-, the former corresponding to large. sepns. of the nuclei, the latter to small sepns. In harmony with the conception of NaCl as a polar mol.-i. e., one which on sepn. of the nuclei goes over into 2 oppositely charged ions-the lowest term of its spectrum must be ascribed to Na+ + Cl-.
- 30Mulliken, R. S. The Assignment of Quantum Numbers for Electrons in Molecules. I. Phys. Rev. 1928, 32, 186– 222, DOI: 10.1103/PhysRev.32.186Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaB1MXitlQ%253D&md5=2724aa2f0808a15490c7330c768c61bbThe assignment of quantum numbers for electrons in molecules. IMulliken, Robert S.Physical Review (1928), 32 (), 186-222CODEN: PHRVAO; ISSN:0031-899X.The problem of making a complete assignment of quantum nos. for the electrons in a (non-rotating) diatomic mol. is considered. A tentative assignment of such quantum nos. is made in this paper for most of the known electronic states of diatomic mols. composed of atoms of the first short period of the periodic system. The assignments are based mainly on band-spectrum and to a lesser extent on ionization-potential and positive-ray data. The methods used involve the application and extension of Hund's theoretical work on the electronic states of mols. Although the actual state of the electrons in a mol., as contrasted with an atom, cannot ordinarily be expected to be described accurately by quantum nos. corresponding to simple mech. quantities, such quantum nos. can nevertheless be assigned formally, with the understanding that their mech. interpretation in the real mol. (obtained by adiabatic correlation) may differ markedly from that corresponding to a literal interpretation. With this understanding, a suitable choice of quantum nos. for a diatomic mol. appears to be one corresponding to an atom in a strong elec. field, namely, quantum nos. nr, lr, σr and Sr (Sr = 1/2 always) for the rth electron and quantum nos. s σl and σs for the mol. as a whole (σlr and σs represent quantized components of lr, and s, resp., with reference to the line joining the nuclei). These quantum nos. may be thought of as those assocd. with the imagined "united atom" formed by bringing the nuclei of the mol. together. A notation is proposed whereby the state of each electron and of the mol. as a whole can be designated, e. g., (1 sε)2 (2 sρ)2 (2sε)2 (2pρ), 2P for a seven-electron mol. with σ = 1, s = 1/2, in a symbol such as 2 sρ the superscript denotes lr, the main letter, σlr, thus 2 sP means that the electron in question has nr = 2, lr = 1, σlr = 0. Electrons with σlr = 0, 1, 2,-are referred to as s, p, d-electrons. It is shown that in a mol. it is usually natural to define a group of equiv. electrons giving a resultant σl = 0, s = 0 as a closed shell; in this sense, two s electrons, or four p, or d, f-, electrons form a closed shell. The possible mol. states corresponding to various electron configurations are deduced by means of the Pauli principle. Electrons which undergo an increase in their n values (principal quantum nos.) when atoms unite to form a mol. (Hund) are here called promoted electrons. The electrons in a mol. may be classified according to their bonding power, positive, zero, or negative. Electrons whose presence tends to hold the mol. together, as judged by the fact that their removal from a stable mol. causes a decrease in the energy of dissociation D or an increase in the equil. internuclear sepn. r0 may be said to have positive bonding power, and are identified with, or defined as, bonding electrons. Bonding power in terms of changes of D and of changes of r0 are distinguished as "energy-bonding-power" and "distance-bonding-power." On the whole, promoted electrons should tend to show negative energy-bonding-power, unpromoted electrons positive energy-bonding-power, but much should depend on "orbit dimensions." Certain rules governing the relations of the electronic states of a mol. to those of its dissociation products are discussed; in addn. to theoretical rules established by Hund in regard to σl and s values, another rule is here proposed, namely, that the σlr values of all the at. electrons before union should be preserved in the mol. (σlr conservation rule). Selection rules for electronic transitions are also discussed; in addn. to rules given by Hund, the following are proposed: Δlr = ±1 for intense transitions: Δσlr = 0, ±1. Results. The key to the assignment of quantum nos. made here is found in the fact that the mols. BO, CO+ and CN show an inverted 2P state instead of the normal 2P which should occur if this state were analogous to the ordinary 2P states of the Na atom. The existence of such a low-lying inverted 2P indicates that in these mols. there exists a closed shell of p electrons from which one is easily excited. It is concluded that this is a (2 pp)4 shell. The identification of 2 other closed shells, of s electrons, very likely (3 sρ)2 and (3 sε)2, follows; the electrons in these and the (2 pρ)4 shell are roughly equal in energy of binding. According to this interpretation, the electron jumps involved in the band spectra of BO, CN, CO+ and N+ are more analogous to x-ray than to optical electron transitions. From this beginning, proceeding to CO, N2, O2, O2+, F2, C2, etc., a self-consistent assignment of quantum nos. is built up for most of the known states of the various mols. treated in this paper. The spectroscopic analogies of CN, N2, NO, etc., to Na, Mg, Al are justified and the partial failure of these analogies such as the chem. resemblance of CN to a halogen, are explained. Nearly all the hitherto observed ionization potentials of the mols. discussed can be accounted for by the removal of a single electron from one or another of the various closed shells supposed to be present. The N2+ band fluorescence produced by short wave-length ultra-violet light (Oldenberg) is accounted for as the expected result of photo-ionization of a 3 SP electron. The steadily decreasing heat of dissocn. in the series, N2-NO-O2-F2, is accounted for by the successive addn. of promoted 3pP electrons with strong neg. bonding power. Starting from N2, whose normal state corresponds to a 1S configuration of closed shells, we add one 3 pP electron to give the 2p normal state of NO, and O2+, two to give the 3S normal state of O2, four to give a closed shell, (3 pP)4, which accounts for the 1S normal state of F2. In N2 (probably also in O2 and the other homopolar mols.) band systems for which Δlr ≠ 1 are notably lacking, thus giving support to Hund's predicted selection rule for homopolar mols., in the analogous heteropolar mol. CO2, many systems occur with Δlr = 0 than those for which Δlr = ±1. On account of this strict selection rule in N2 certain levels should be metastable, in particular the final level of the α afterglow bands of active nitrogen. There is evidence for the existence of a strict selection rule Δs = 1 in homopolar mols.
- 31Lennard-Jones, J. E. The electronic structure of some diatomic molecules. Trans. Faraday Soc. 1929, 25, 668– 686, DOI: 10.1039/tf9292500668Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaA3cXjvFSmsQ%253D%253D&md5=72cce6f87afa58a3f7699e158b557f3aThe electronic structure of some diatomic moleculesLennard-Jones, J. E.Transactions of the Faraday Society (1929), 25 (), 668-86CODEN: TFSOA4; ISSN:0014-7672.A review of the ideas of Franck and Herzberg, Heisenberg, Heitler and London, Hund and Mulliken on the formation of mols. and their dissocn. energy. J. criticizes Hund's application of the Pauli exclusion principle for the definition of mol. states. A notation is given which will make it possible to distinguish between mol, and at. levels in the same mol. The transitions encountered in mol. formation are given.
- 32Dirac, P. A. M.; Fowler, R. H. Quantum mechanics of many-electron systems. Proc. R. Soc. London. Ser. A 1929, 123, 714– 733, DOI: 10.1098/rspa.1929.0094Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaB1MXivVymtw%253D%253D&md5=cdbf897d93676ba39bba591ad7334bf5Quantum mechanics of many-electron systemsDirac, P. A. M.Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences (1929), 123 (), 714-33CODEN: PRLAAZ; ISSN:1364-5021.The Bohr atom model, according to which the stationary states correspond to electron orbits, is now replaced by a structure in accordance with quantum mechanics in which the orbits are replaced by quantum-mech. states represented by a wave function in 3 dimensions. According to the old theory the spins were either parallel or anti-parallel, necessitating large form coupling the spin vectors, an assumption not justified by theory. The new theory shows that there is a definite magnitude of the spin vector connected with each stationary state, but in general it is not possible to give a meaning to the direction of spin. An explanation of multiplet structure requires some means of accounting for the large coupling energy between spin vectors. The soln. is provided by the exchange interaction of the electrons, which arises because of the electrons being indistinguishable from one another. A proof is given for the existence of exclusive sets of states and a formula is derived for the energy levels of these states.
- 33Born, M.; Oppenheimer, R. Zur Quantentheorie der Molekeln. Ann. Phys. 1927, 389, 457– 484, DOI: 10.1002/andp.19273892002Google ScholarThere is no corresponding record for this reference.
- 34Slater, J. C. The Theory of Complex Spectra. Phys. Rev. 1929, 34, 1293– 1322, DOI: 10.1103/PhysRev.34.1293Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaA3cXptlKi&md5=cd267a5cabf0d095ce8b6ea0e1af9314The theory of complex spectraSlater, J. C.Physical Review (1929), 34 (), 1293-1323CODEN: PHRVAO; ISSN:0031-899X.At. multiplets are treated by wave mechanics. The first part deals with the derivation of Hund's scheme for multiplet classification directly from theory. The second part deals with the computation of energy distances between multiplets and their comparison with exptl. values for some examples.
- 35Hartree, D. R. The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods. Math. Proc. Cambridge Philos. Soc. 1928, 24, 89– 110, DOI: 10.1017/S0305004100011919Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaB1cXhtVKksQ%253D%253D&md5=b571ada868a91f5404eeab1cadec029bThe wave mechanics of an atom with a non-coulomb central field. I. Theory and methodsHartree, D. R.Proceedings of the Cambridge Philosophical Society (1928), 24 (), 89-110CODEN: PCPSA4; ISSN:0068-6735.Upon the assumption that the effects of the different electrons of an atom upon each other can be represented by supposing each to move in a central non-coulomb field of force, characteristic values and functions of the wave equation of Schroedinger are detd. The wave mechanics of Schroedinger is chosen as the most suitable form of the new quantum theory to use for the application of this assumption. The method used is to integrate a modification of the wave equation outward from initial conditions corresponding to a soln. finite at r = 0 (r = distance from nucleus) and inward from initial conditions corresponding to a soln. zero at r = ∞, with a trial value of the parameter (the energy) whose characteristic values are to be detd.; the values of this parameter for which the 2 solns. fit at some convenient intermediate radius are the characteristic values required and the solns. which so fit are the characteristic functions.
- 36Slater, J. C. Note on Hartree’s Method. Phys. Rev. 1930, 35, 210– 211, DOI: 10.1103/PhysRev.35.210.2Google ScholarThere is no corresponding record for this reference.
- 37Fock, V. Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Z. Phys. 1930, 61, 126– 148, DOI: 10.1007/BF01340294Google ScholarThere is no corresponding record for this reference.
- 38Roothaan, C. C. J. New Developments in Molecular Orbital Theory. Rev. Mod. Phys. 1951, 23, 69– 89, DOI: 10.1103/RevModPhys.23.69Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaG38XksVakuw%253D%253D&md5=200a0ce85fea3870e3322cdafd1cd1bcNew developments in molecular orbital theoryRoothaan, C. C. J.Reviews of Modern Physics (1951), 23 (), 69-89CODEN: RMPHAT; ISSN:0034-6861.The mathematics of the "mol. orbital" method are reviewed.
- 39Knowles, P. J.; Schütz, M.; Werner, H.-J. Ab Initio Methods for Electron Correlation in Molecules. In Modern Methods and Algorithms Quantum Chemitry; Grotendorst, J., Ed.; John von Neumann Institute for Computing (NIC): Jülich, Germany, 2000; Vol. 1, pp 69– 151.Google ScholarThere is no corresponding record for this reference.
- 40Roos, B. O.; Taylor, P. R.; Sigbahn, P. E. A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach. Chem. Phys. 1980, 48, 157– 173, DOI: 10.1016/0301-0104(80)80045-0Google Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL3cXksFOjt7s%253D&md5=099ec82832160f6fe76bd7754027384cA complete active space SCF method (CASSCF) using a density matrix formulated super-CI approachRoos, Bjoern O.; Taylor, Peter R.; Siegbahn, E. M.Chemical Physics (1980), 48 (2), 157-73CODEN: CMPHC2; ISSN:0301-0104.A d. matrix formulation of the super-CI MCSCF method is presented. The MC expansion is assumed to be complete in an active subset of the orbital space, and the corresponding CI secular problem is solved by a direct scheme using the unitary group approach. With a d. matrix formulation the orbital optimization step becomes independent of the size of the CI expansion. It is possible to formulate the super-CI in terms of d. matrices defined only in the small active subspace; the doubly occupied orbitals (the inactive subspace) do not enter. Further, in the unitary group formalism it is straightforward and simple to obtain the necessary d. matrices from the symbolic formula list. It then becomes possible to treat very long MC expansions, the largest so far comprising 726 configurations. The method is demonstrated in a calcn. of the potential curves for the 3 lowest states (1.sum.g+, 3.sum.u+ and 3πg) of the N2 mol., using a medium-sized gaussian basis set. 7 Active orbitals were used yielding the following results: Dc:8.76(9.90), 2.43(3.68) and 3.39 (4.90) eV; rc:1.108 (1.098), 1.309(1.287) and 1.230 (1.213) Å; ωe: 2333 (2359), 1385 (1461) and 1680 (1733) cm-1, for the 3 states (exptl. values within parentheses). The results of these calcns. indicate that it is important to consider not only the dissocn. limit but also the united atom limit in partitioning the occupied orbital space into an active and an inactive part.
- 41Reiher, M.; Wiebe, N.; Svore, K. M.; Wecker, D.; Troyer, M. Elucidating reaction mechanisms on quantum computers. Proc. Natl. Acad. Sci. U. S. A. 2017, 114, 7555– 7560, DOI: 10.1073/pnas.1619152114Google Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhtFSmt7%252FN&md5=3b7148a5d436d3c1f5c0da80391a28f3Elucidating reaction mechanisms on quantum computersReiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, MatthiasProceedings of the National Academy of Sciences of the United States of America (2017), 114 (29), 7555-7560CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)With rapid recent advances in quantum technol., we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chem. systems, using the open problem of biol. nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource ests. show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chem. without requiring exorbitant resources.
- 42Genin, S. N.; Ryabinkin, I. G.; Paisley, N. R.; Whelan, S. O.; Helander, M. G.; Hudson, Z. M. Estimating Phosphorescent Emission Energies in IrIII Complexes Using Large-Scale Quantum Computing Simulations. Angew. Chem., Int. Ed. 2022, 134, e202116175, DOI: 10.1002/ange.202116175Google ScholarThere is no corresponding record for this reference.
- 43Lee, S.; Lee, J.; Zhai, H.; Tong, Y.; Dalzell, A. M.; Kumar, A.; Helms, P.; Gray, J.; Cui, Z.-H.; Liu, W.; Is there evidence for exponential quantum advantage in quantum chemistry?. arXiv Preprint (Chemical Physics) , 2022. arXiv:2208.02199. https://doi.org/10.48550/arXiv.2208.02199.Google ScholarThere is no corresponding record for this reference.
- 44Anighoro, A. Underappreciated Chemical Interactions in Protein–Ligand Complexes. In Quantum Mechanics in Drug Discovery; Heifetz, A., Ed.; Springer: New York, NY, USA, 2020; pp 75– 86. DOI: 10.1007/978-1-0716-0282-9_5 .Google ScholarThere is no corresponding record for this reference.
- 45Shor, P. W. The Early Days of Quantum Computation. arXiv Preprint (Quantum Physics) , 2022. arXiv:2208.09964v1. https://doi.org/10.48550/arXiv.2208.09964.Google ScholarThere is no corresponding record for this reference.
- 46Shor, P. Algorithms for quantum computation: discrete logarithms and factoring. Proceedings 35th Annual Symposium on Foundations of Computer Science; IEEE, 1994; pp 124– 134. DOI: 10.1109/SFCS.1994.365700 .Google ScholarThere is no corresponding record for this reference.
- 47Grover, L. K. A Fast Quantum Mechanical Algorithm for Database Search. Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing . New York, NY, USA, 1996; pp 212– 219. DOI: 10.1145/237814.237866Google ScholarThere is no corresponding record for this reference.
- 48Kitaev, A. Y. Quantum measurements and the Abelian Stabilizer problem. arXiv Preprint (Quantum Physics) , 1995. arXiv:quant-ph/9511026. https://doi.org/10.48550/arXiv.quant-ph/9511026.Google ScholarThere is no corresponding record for this reference.
- 49Cleve, R.; Ekert, A.; Macchiavello, C.; Mosca, M. Quantum algorithms revisited. Proc. R. Soc. London, A 1998, 454, 339– 354, DOI: 10.1098/rspa.1998.0164Google ScholarThere is no corresponding record for this reference.
- 50Nielsen, M. A.; Chuang, I. L. Quantum computation and quantum information, 10th ed.; Cambridge University Press, 2011. DOI: 10.1017/CBO9780511976667 .Google ScholarThere is no corresponding record for this reference.
- 51Dyall, K. G. The choice of a zeroth-order Hamiltonian for second-order perturbation theory with a complete active space self-consistent-field reference function. J. Chem. Phys. 1995, 102, 4909– 4918, DOI: 10.1063/1.469539Google Scholar51https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXksFWgsrY%253D&md5=a1e229d4d47de9a8196c8a9e0c6fdb32The choice of a zeroth-order Hamiltonian for second-order perturbation theory with a complete active space self-consistent-field reference functionDyall, Kenneth G.Journal of Chemical Physics (1995), 102 (12), 4909-18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The choice of a zeroth-order Hamiltonian, H0, for second-order perturbation theory with a complete active space self-consistent-field (CASSCF) ref. function is discussed in detail, in the context of the inclusion of the denominator shifts found to be important in recent single-ref. high-spin open-shell theories and the formulation of a computationally efficient method. Using projection operators and second quantization algebra, an operator is constructed which consists of the complete active space Hamiltonian in the active space and the Moeller-Plesset zeroth-order Hamiltonian in the inactive and secondary spaces. This operator, designated CAS/A, has the ref. as an eigenfunction without the necessity of projection, it naturally incorporates denominator shifts which appear in terms of active space Fock operators, it does not give rise to intruder states, and it costs little more than CASSCF perturbation theories. The incorporation of the complete active space Hamiltonian introduces addnl. active space two-particle terms into the zeroth-order energies over the Fock operators, which may be regarded as an inconsistency. To achieve an approx. consistency, they may be removed or supplemented with other particle-particle and hole-hole terms. The results of test calcns. indicate that supplementation is not advisable and that removal has only a modest effect. The test calcns. are compared with other results and expt., and support the effectiveness of the proposed CAS/A H0.
- 52Jordan, P.; Wigner, E. Über das Paulische Äquivalenzverbot. Z. Phys. 1928, 47, 631– 651, DOI: 10.1007/BF01331938Google Scholar52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaB1cXjs1KnsA%253D%253D&md5=b7be327253da5e8b6911507f29f387a4The Pauli exclusion principleJordan, P.; Wigner, E.Zeitschrift fuer Physik (1928), 47 (), 631-51CODEN: ZEPYAA; ISSN:0044-3328.If a body of gas is considered to be a 3-dimensional wave field with non-commutative multiplication of amplitude, and if the Pauli principle of restricted equivalence is applied, it is possible to develop the theory of the gas without use of the concept of abstract phase space, using only the ordinary three dimensional co.ovrddot.ordinates.
- 53Bravyi, S. B.; Kitaev, A. Y. Fermionic Quantum Computation. Ann. Phys. 2002, 298, 210– 226, DOI: 10.1006/aphy.2002.6254Google Scholar53https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD38Xktlals7k%253D&md5=bf5f820b3807c536755f65324b1853e7Fermionic Quantum ComputationBravyi, Sergey B.; Kitaev, Alexei Yu.Annals of Physics (San Diego, CA, United States) (2002), 298 (1), 210-226CODEN: APNYA6; ISSN:0003-4916. (Elsevier Science)We define a model of quantum computation with local fermionic modes (LFMs)-sites which can be either empty or occupied by a fermion. With the std. correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a const., resp. Nearest neighbors fermionic gates on a graph of bounded degree can be simulated at a const. cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.
- 54Seeley, J. T.; Richard, M. J.; Love, P. J. The Bravyi-Kitaev transformation for quantum computation of electronic structure. J. Chem. Phys. 2012, 137, 224109, DOI: 10.1063/1.4768229Google Scholar54https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhvVaht7bP&md5=cbdf40b94f0d98c6aef9c9fb8d2af259The Bravyi-Kitaev transformation for quantum computation of electronic structureSeeley, Jacob T.; Richard, Martin J.; Love, Peter J.Journal of Chemical Physics (2012), 137 (22), 224109/1-224109/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Quantum simulation is an important application of future quantum computers with applications in quantum chem., condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here, we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev (2002) that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chem. Hamiltonians, and give a detailed example for the simplest possible case of mol. hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equiv. circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for mol. hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure. (c) 2012 American Institute of Physics.
- 55Tranter, A.; Love, P. J.; Mintert, F.; Coveney, P. V. A Comparison of the Bravyi–Kitaev and Jordan–Wigner Transformations for the Quantum Simulation of Quantum Chemistry. J. Chem. Theory Comput. 2018, 14, 5617– 5630, DOI: 10.1021/acs.jctc.8b00450Google Scholar55https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhs1KhtbzL&md5=128cb8044dab8d0af53426569b8ca0a9A Comparison of the Bravyi-Kitaev and Jordan-Wigner Transformations for the Quantum Simulation of Quantum ChemistryTranter, Andrew; Love, Peter J.; Mintert, Florian; Coveney, Peter V.Journal of Chemical Theory and Computation (2018), 14 (11), 5617-5630CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)The ability to perform classically intractable electronic structure calcns. is often cited as one of the principal applications of quantum computing. A great deal of theor. algorithmic development has been performed in support of this goal. Most techniques require a scheme for mapping electronic states and operations to states of and operations upon qubits. The two most commonly used techniques for this are the Jordan-Wigner transformation and the Bravyi-Kitaev transformation. However, comparisons of these schemes have previously been limited to individual small mols. In this paper, we discuss resource implications for the use of the Bravyi-Kitaev mapping scheme, specifically with regard to the no. of quantum gates required for simulation. We consider both small systems, which may be simulatable on near-future quantum devices, and systems sufficiently large for classical simulation to be intractable. We use 86 mol. systems to demonstrate that the use of the Bravyi-Kitaev transformation is typically at least approx. as efficient as the canonical Jordan-Wigner transformation and results in substantially reduced gate count ests. when performing limited circuit optimizations.
- 56Higgott, O.; Wang, D.; Brierley, S. Variational Quantum Computation of Excited States. Quantum 2019, 3, 156, DOI: 10.22331/q-2019-07-01-156Google ScholarThere is no corresponding record for this reference.
- 57McClean, J. R.; Kimchi-Schwartz, M. E.; Carter, J.; de Jong, W. A. Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states. Phys. Rev. A 2017, 95, 042308, DOI: 10.1103/PhysRevA.95.042308Google Scholar57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXntFGmu7c%253D&md5=625fe962827ac0b79402267b86fee6feHybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited statesMcClean, Jarrod R.; Kimchi-Schwartz, Mollie E.; Carter, Jonathan; de Jong, Wibe A.Physical Review A (2017), 95 (4), 042308/1-042308/10CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)Using quantum devices supported by classical computational resources is a promising approach to quantumenabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the soln. of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state prepn. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solns. by leveraging addnl. measurements and classical resources.We demonstrate numerically on a sample electronic system that this method both allows for the accurate detn. of excited electronic states as well as reduces the impact of decoherence, without using any addnl. quantum coherence time or formal error-correction codes.
- 58Motta, M.; Sun, C.; Tan, A. T.; O’Rourke, M. J.; Ye, E.; Minnich, A. J.; Brandao, F. G.; Chan, G. K. Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution. Nat. Phys. 2020, 16, 205– 210, DOI: 10.1038/s41567-019-0704-4Google Scholar58https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitFelsrjM&md5=47c741d9798c63ba74f3414d9fb10e1cDetermining eigenstates and thermal states on a quantum computer using quantum imaginary time evolutionMotta, Mario; Sun, Chong; Tan, Adrian T. K.; O'Rourke, Matthew J.; Ye, Erika; Minnich, Austin J.; Brandao, Fernando G. S. L.; Chan, Garnet Kin-LicNature Physics (2020), 16 (2), 205-210CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the phys. and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estn. or variational algorithms display potential disadvantages; phase estn. requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail addnl. high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogs of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs avs. through an analog of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit.
- 59Zhang, D.-B.; Yuan, Z.-H.; Yin, T. Variational quantum eigensolvers by variance minimization. arXiv Preprint (Quantum Physics) , 2020. arXiv:2006.15781. https://doi.org/10.48550/arXiv.2006.15781.Google ScholarThere is no corresponding record for this reference.
- 60Ryabinkin, I. G.; Genin, S. N.; Izmaylov, A. F. Constrained variational quantum eigensolver: Quantum computer search engine in the Fock space. J. Chem. Theory Comput. 2019, 15, 249– 255, DOI: 10.1021/acs.jctc.8b00943Google Scholar60https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitlylt7fO&md5=e465101c986c4e766e9340c88d2f7687Constrained Variational Quantum Eigensolver: Quantum Computer Search Engine in the Fock SpaceRyabinkin, Ilya G.; Genin, Scott N.; Izmaylov, Artur F.Journal of Chemical Theory and Computation (2019), 15 (1), 249-255CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Variational quantum eigensolver (VQE) is an efficient computational method promising chem. accuracy in electronic structure calcns. on a universal-gate quantum computer. However, such a simple task as computing the electronic energy of a hydrogen mol. cation, H2+, is not possible for a general VQE protocol because the calcn. will invariably collapse to a lower energy of the corresponding neutral form, H2. The origin of the problem is that VQE effectively performs an unconstrained energy optimization in the Fock space of the original electronic problem. We show how this can be avoided by introducing necessary constraints directing VQE toward the electronic state of interest. The proposed constrained VQE can find an electronic state with a certain no. of electrons, a certain spin, or any other property. Moreover, the new algorithm naturally removes unphys. kinks in potential energy surfaces (PESs), which frequently appeared in the regular VQE and required significant addnl. quantum resources for their removal. We demonstrate the performance of the constrained VQE by simulating PESs of various states of H2 and H2O on Rigetti Computing Inc.'s 19Q-Acorn quantum processor.
- 61Nielsen, M. A.; Chuang, I. Quantum computation and quantum information; Cambridge University Press, 2002.Google ScholarThere is no corresponding record for this reference.
- 62Kitaev, A. Y.; Shen, A.; Vyalyi, M. N.; Vyalyi, M. N. Classical and quantum computation; American Mathematical Society, 2002.Google ScholarThere is no corresponding record for this reference.
- 63Tilly, J.; Chen, H.; Cao, S.; Picozzi, D.; Setia, K.; Li, Y.; Grant, E.; Wossnig, L.; Rungger, I.; Booth, G. H.; The Variational Quantum Eigensolver: a review of methods and best practices. arXiv Preprint (Quantum Physics) , 2021. arXiv:2111.05176. https://doi.org/10.48550/arXiv.2111.05176.Google ScholarThere is no corresponding record for this reference.
- 64Bravyi, S.; Gambetta, J. M.; Mezzacapo, A.; Temme, K. Tapering off qubits to simulate fermionic Hamiltonians. arXiv Preprint (Quantum Physics) , 2017. arXiv:1701.08213. https://doi.org/10.48550/arXiv.1701.08213.Google ScholarThere is no corresponding record for this reference.
- 65Romero, J.; Babbush, R.; McClean, J. R.; Hempel, C.; Love, P. J.; Aspuru-Guzik, A. Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz. Quantum Sci. Technol. 2019, 4, 014008, DOI: 10.1088/2058-9565/aad3e4Google ScholarThere is no corresponding record for this reference.
- 66Lee, J.; Huggins, W. J.; Head-Gordon, M.; Whaley, K. B. Generalized unitary coupled cluster wave functions for quantum computation. J. Chem. Theory Comput. 2019, 15, 311– 324, DOI: 10.1021/acs.jctc.8b01004Google Scholar66https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitlKms7%252FK&md5=4caa687a3358571bbf9d1916fa7a09c9Generalized Unitary Coupled Cluster Wave functions for Quantum ComputationLee, Joonho; Huggins, William J.; Head-Gordon, Martin; Whaley, K. BirgittaJournal of Chemical Theory and Computation (2019), 15 (1), 311-324CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We introduce a unitary coupled-cluster (UCC) ansatz termed k-UpCCGSD that is based on a family of sparse generalized doubles operators, which provides an affordable and systematically improvable unitary coupled-cluster wave function suitable for implementation on a near-term quantum computer. K-UpCCGSD employs k products of the exponential of pair coupled-cluster double excitation operators (pCCD), together with generalized single excitation operators. We compare its performance in both efficiency of implementation and accuracy with that of the generalized UCC ansatz employing the full generalized single and double excitation operators (UCCGSD), as well as with the std. ansatz employing only single and double excitations (UCCSD). K-UpCCGSD is found to show the best scaling for quantum computing applications, requiring a circuit depth of O(kN), compared with O(N3) for UCCGSD, and O((N-η)2η) for UCCSD, where N is the no. of spin orbitals and η is the no. of electrons. We analyzed the accuracy of these three ansatze by making classical benchmark calcns. on the ground state and the first excited state of H4 (STO-3G, 6-31G), H2O (STO-3G), and N2 (STO-3G), making addnl. comparisons to conventional coupled cluster methods. The results for ground states show that k-UpCCGSD offers a good trade-off between accuracy and cost, achieving chem. accuracy for lower cost of implementation on quantum computers than both UCCGSD and UCCSD. UCCGSD is also found to be more accurate than UCCSD but at a greater cost for implementation. Excited states are calcd. with an orthogonally constrained variational quantum eigensolver approach. This is seen to generally yield less accurate energies than for the corresponding ground states. We demonstrate that using a specialized multideterminantal ref. state constructed from classical linear response calcns. allows these excited state energetics to be improved.
- 67Grimsley, H. R.; Economou, S. E.; Barnes, E.; Mayhall, N. J. An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nat. Commun. 2019, 10, 3007, DOI: 10.1038/s41467-019-10988-2Google Scholar67https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3MzltlCrtA%253D%253D&md5=d0290eacb02a0e579953630222914a6aAn adaptive variational algorithm for exact molecular simulations on a quantum computerGrimsley Harper R; Mayhall Nicholas J; Economou Sophia E; Barnes EdwinNature communications (2019), 10 (1), 3007 ISSN:.Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that, instead of fixing an ansatz upfront, grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.
- 68Wecker, D.; Hastings, M. B.; Troyer, M. Progress towards practical quantum variational algorithms. Phys. Rev. A 2015, 92, 042303, DOI: 10.1103/PhysRevA.92.042303Google Scholar68https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XkvFeisw%253D%253D&md5=c89f00b47e6180a66ef6433be62d03dbProgress towards practical quantum variational algorithmsWecker, Dave; Hastings, Matthew B.; Troyer, MatthiasPhysical Review A: Atomic, Molecular, and Optical Physics (2015), 92 (4-A), 042303/1-042303/10CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)The prepn. of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, esp. if the circuit is short enough and the fidelity of gates high enough that it can be executed without quantum error correction. Such quantum state prepn. can be used in variational approaches, optimizing parameters in the circuit to minimize the energy of the constructed quantum state for a given problem Hamiltonian. For this purpose we propose a simple-to-implement class of quantum states motivated by adiabatic state prepn. We test its accuracy and det. the required circuit depth for a Hubbard model on ladders with up to 12 sites (24 spin orbitals), and for small mols. We find that this ansatz converges faster than previously proposed schemes based on unitary coupled clusters. While the required no. of measurements is astronomically large for quantum chem. applications to mols., applying the variational approach to the Hubbard model (and related models) is found to be far less demanding and potentially practical on small quantum computers. We also discuss another application of quantum state prepn. using short quantum circuits, to prep. trial ground states of models faster than using adiabatic state prepn.
- 69McClean, J. R.; Romero, J.; Babbush, R.; Aspuru-Guzik, A. The theory of variational hybrid quantum-classical algorithms. New J. Phys. 2016, 18, 023023, DOI: 10.1088/1367-2630/18/2/023023Google Scholar69https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsFWks7zO&md5=5e2e073c37c8c0f88655498120d86506The theory of variational hybrid quantum-classical algorithmsMcClean, Jarrod R.; Romero, Jonathan; Babbush, Ryan; Aspuru-Guzik, AlanNew Journal of Physics (2016), 18 (Feb.), 023023/1-023023/22CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)A review. Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as 'the quantum variational eigensolver' was developed with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Addnl., we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern deriv. free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.
- 70Yen, T.-C.; Verteletskyi, V.; Izmaylov, A. F. Measuring all compatible operators in one series of single-qubit measurements using unitary transformations. J. Chem. Theory Comput. 2020, 16, 2400– 2409, DOI: 10.1021/acs.jctc.0c00008Google Scholar70https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXksFaitb0%253D&md5=4e6415247b5869ecd3f714749f0d6dd9Measuring All Compatible Operators in One Series of Single-Qubit Measurements Using Unitary TransformationsYen, Tzu-Ching; Verteletskyi, Vladyslav; Izmaylov, Artur F.Journal of Chemical Theory and Computation (2020), 16 (4), 2400-2409CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or compatible operators simultaneously. Unfortunately, the current hardware permits measuring only a much more limited subset of operators that share a common tensor product eigen-basis. We introduce unitary transformations that transform any fully commuting group of operators to a group that can be measured on current hardware. These unitary operations can be encoded as a sequence of Clifford gates and let us not only measure much larger groups of terms but also to obtain these groups efficiently on a classical computer. The problem of finding the min. no. of fully commuting groups of terms covering the whole Hamiltonian is found to be equiv. to the min. clique cover problem for a graph representing Hamiltonian terms as vertices and commutativity between them as edges. Tested on a set of mol. electronic Hamiltonians with up to 50 thousand terms, the introduced technique allows for the redn. of the no. of sep. measurable operator groups down to few hundreds, thus achieving up to 2 orders of magnitude redn. Based on the test set results, the obtained gain scales at least linearly with the no. of qubits.
- 71Gokhale, P.; Angiuli, O.; Ding, Y.; Gui, K.; Tomesh, T.; Suchara, M.; Martonosi, M.; Chong, F. T. Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families. arXiv Preprint (Quantum Physics) , 2019. arXiv:1907.13623. https://doi.org/10.48550/arXiv.1907.13623.Google ScholarThere is no corresponding record for this reference.
- 72Crawford, O.; van Straaten, B.; Wang, D.; Parks, T.; Campbell, E.; Brierley, S. Efficient quantum measurement of Pauli operators in the presence of finite sampling error. Quantum 2021, 5, 385, DOI: 10.22331/q-2021-01-20-385Google ScholarThere is no corresponding record for this reference.
- 73Huggins, W. J.; McClean, J.; Rubin, N.; Jiang, Z.; Wiebe, N.; Whaley, K. B.; Babbush, R. Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers. arXiv Preprint (Quantum Physics) , 2019. arXiv:1907.13117. https://doi.org/10.48550/arXiv.1907.13117.Google ScholarThere is no corresponding record for this reference.
- 74Wang, D.; Higgott, O.; Brierley, S. Accelerated variational quantum eigensolver. Phys. Rev. Lett. 2019, 122, 140504, DOI: 10.1103/PhysRevLett.122.140504Google Scholar74https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXpsF2iur8%253D&md5=6da25a8663176bae29c7a4113dddc91eAccelerated Variational Quantum EigensolverWang, Daochen; Higgott, Oscar; Brierley, StephenPhysical Review Letters (2019), 122 (14), 140504CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)A review. The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estn. (QPE) or variational quantum eigensolver (VQE) algorithms. For precision ε, QPE requires O(1) repetitions of circuits with depth O(1/ε), whereas each expectation estn. subroutine within VQE requires O(1/ε2) samples from circuits with depth O(1). We propose a generalized VQE algorithm that interpolates between these two regimes via a free parameter α∈[0,1], which can exploit quantum coherence over a circuit depth of O(1/εα) to reduce the no. of samples to O(1/ε2(1-α)). Along the way, we give a new routine for expectation estn. under limited quantum resources that is of independent interest.
- 75Wang, G.; Koh, D. E.; Johnson, P. D.; Cao, Y. Minimizing Estimation Runtime on Noisy Quantum Computers. PRX Quantum 2021, 2, 010346, DOI: 10.1103/PRXQuantum.2.010346Google ScholarThere is no corresponding record for this reference.
- 76Lin, L.; Tong, Y. Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers. arXiv Preprint (Quantum Physics) , 2021. arXiv:2102.11340. https://doi.org/10.48550/arXiv.2102.11340.Google ScholarThere is no corresponding record for this reference.
- 77Lee, J.; Berry, D. W.; Gidney, C.; Huggins, W. J.; McClean, J. R.; Wiebe, N.; Babbush, R. Even more efficient quantum computations of chemistry through tensor hypercontraction. arXiv Preprint (Quantum Physics) , 2020. arXiv:2011.03494. https://doi.org/10.48550/arXiv.2011.03494.Google ScholarThere is no corresponding record for this reference.
- 78Kitaev, A. Y. Quantum measurements and the Abelian stabilizer problem. Electronic Colloquium on Computational Complexity, Paper TR96-003; Computational Complexity Foundation, 1996.Google ScholarThere is no corresponding record for this reference.
- 79Tubman, N. M.; Mejuto-Zaera, C.; Epstein, J. M.; Hait, D.; Levine, D. S.; Huggins, W.; Jiang, Z.; McClean, J. R.; Babbush, R.; Head-Gordon, M.; Postponing the orthogonality catastrophe: efficient state preparation for electronic structure simulations on quantum devices. arXiv Preprint (Quantum Physics) , 2018. arXiv:1809.05523. https://doi.org/10.48550/arXiv.1809.05523.Google ScholarThere is no corresponding record for this reference.
- 80Elfving, V. E.; Broer, B. W.; Webber, M.; Gavartin, J.; Halls, M. D.; Lorton, K. P.; Bochevarov, A. How will quantum computers provide an industrially relevant computational advantage in quantum chemistry?. arXiv Preprint (Quantum Physics) , 2020. arXiv:2009.12472. https://doi.org/10.48550/arXiv.2009.12472Google ScholarThere is no corresponding record for this reference.
- 81Gonthier, J. F.; Radin, M. D.; Buda, C.; Doskocil, E. J.; Abuan, C. M.; Romero, J. Identifying challenges towards practical quantum advantage through resource estimation: the measurement roadblock in the variational quantum eigensolver. arXiv Preprint (Quantum Physics) , 2020. arXiv:2012.04001. https://doi.org/10.48550/arXiv.2012.04001.Google ScholarThere is no corresponding record for this reference.
- 82Johnson, P. D.; Kunitsa, A. A.; Gonthier, J. F.; Radin, M. D.; Buda, C.; Doskocil, E. J.; Abuan, C. M.; Romero, J. Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation. arXiv Peprint (Quantum Physics) , 2022. arXiv:2203.07275. https://doi.org/10.48550/arXiv.2203.07275.Google ScholarThere is no corresponding record for this reference.
- 83Campbell, E. A random compiler for fast Hamiltonian simulation. arXiv Preprint (Quantum Physics) , 2018. arXiv:1811.08017. https://doi.org/10.48550/arXiv.1811.08017.Google ScholarThere is no corresponding record for this reference.
- 84Shor, P. Fault-tolerant quantum computation. Proceedings of 37th Conference on Foundations of Computer Science; IEEE, 1996. DOI: 10.1109/SFCS.1996.548464Google ScholarThere is no corresponding record for this reference.
- 85Aharonov, D.; Ben-Or, M. Fault-Tolerant Quantum Computation with Constant Error Rate. SIAM J. Comput. 2008, 38, 1207– 1282, DOI: 10.1137/S0097539799359385Google ScholarThere is no corresponding record for this reference.
- 86Knill, E.; Laflamme, R.; Zurek, W. H. Resilient Quantum Computation. Science 1998, 279, 342– 345, DOI: 10.1126/science.279.5349.342Google Scholar86https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXmtlKmsg%253D%253D&md5=e00c5d866f409731f5b8a8011f281664Resilient quantum computationKnill, Emanuel; Laflamme, Raymond; Zurek, Wojciech H.Science (Washington, D. C.) (1998), 279 (5349), 342-345CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)Practical realization of quantum computers will require overcoming decoherence and operational errors, which lead to problems that are more severe than in classical computation. It is shown that arbitrarily accurate quantum computation is possible provided that the error per operation is below a threshold value.
- 87Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 2003, 303, 2– 30, DOI: 10.1016/S0003-4916(02)00018-0Google Scholar87https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3sXisl2hsg%253D%253D&md5=3f372b0bc398fd477681a79820d90f6bFault-tolerant quantum computation by anyonsKitaev, A. Yu.Annals of Physics (San Diego, CA, United States) (2003), 303 (1), 2-30CODEN: APNYA6; ISSN:0003-4916. (Elsevier Science)A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its phys. nature.
- 88Fowler, A. G.; Mariantoni, M.; Martinis, J. M.; Cleland, A. N. Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A 2012, 86, 032324, DOI: 10.1103/PhysRevA.86.032324Google Scholar88https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsF2ju7jJ&md5=6083440c22691ad91a6939288975bbd7Surface codes: towards practical large-scale quantum computationFowler, Austin G.; Mariantoni, Matteo; Martinis, John M.; Cleland, Andrew N.Physical Review A: Atomic, Molecular, and Optical Physics (2012), 86 (3-A), 032324/1-032324/48CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)This article provides an introduction to surface code quantum computing. We first est. the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of phys. qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical ests. of their fault tolerance. We outline how logical qubits are phys. moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equiv. to a controlled-NOT. We then describe the single-qubit Hadamard, S and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing phys. implementations of the surface code. We include a no. of Appendices in which we provide supplementary information to the main text.
- 89Litinski, D. A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery. Quantum 2019, 3, 128, DOI: 10.22331/q-2019-03-05-128Google ScholarThere is no corresponding record for this reference.
- 90Eastin, B.; Knill, E. Restrictions on Transversal Encoded Quantum Gate Sets. Phys. Rev. Lett. 2009, 102, 110502, DOI: 10.1103/PhysRevLett.102.110502Google Scholar90https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXjsFSgtrs%253D&md5=1e2ff02062ce4d6e44a4d5caf3c93978Restrictions on Transversal Encoded Quantum Gate SetsEastin, Bryan; Knill, EmanuelPhysical Review Letters (2009), 102 (11), 110502/1-110502/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple phys. subsystems within the same code block. Consequently, such operators do not spread errors within code blocks and are, therefore, fault tolerant. Nonetheless, other methods of ensuring fault tolerance are required, as it is invariably the case that some encoded gates cannot be implemented transversally. This observation has led to a long-standing conjecture that transversal encoded gate sets cannot be universal. Here we show that the ability of a quantum code to detect an arbitrary error on any single phys. subsystem is incompatible with the existence of a universal, transversal encoded gate set for the code.
- 91Litinski, D. Magic State Distillation: Not as Costly as You Think. arXiv Preprint (Quantum Physics) , 2019. arXiv:1905.06903. https://doi.org/10.48550/arXiv.1905.06903.Google ScholarThere is no corresponding record for this reference.
- 92Haah, J.; Hastings, M. B. Codes and Protocols for Distilling T, controlled-S, and Toffoli Gates. Quantum 2018, 2, 71, DOI: 10.22331/q-2018-06-07-71Google ScholarThere is no corresponding record for this reference.
- 93Haah, J.; Hastings, M. B. Codes and Protocols for Distilling T, controlled-S, and Toffoli Gates. Quantum 2018, 2, 71, DOI: 10.22331/q-2018-06-07-71Google ScholarThere is no corresponding record for this reference.
- 94Lodi, A.; Martello, S.; Monaci, M. Two-dimensional packing problems: A survey. Eur. J. Oper. Res. 2002, 141, 241– 252, DOI: 10.1016/S0377-2217(02)00123-6Google ScholarThere is no corresponding record for this reference.
- 95Childs, A. M.; Maslov, D.; Nam, Y.; Ross, N. J.; Su, Y. Toward the first quantum simulation with quantum speedup. Proc. Natl. Acad. Sci. U. S. A. 2018, 115, 9456– 9461, DOI: 10.1073/pnas.1801723115Google Scholar95https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXitVKhu7rP&md5=b83e31a68f4d388c4b2f817b018fcbabToward the first quantum simulation with quantum speedupChilds, Andrew M.; Maslov, Dmitri; Nam, Yunseong; Ross, Neil J.; Su, YuanProceedings of the National Academy of Sciences of the United States of America (2018), 115 (38), 9456-9461CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error ests. suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chem., bringing practical quantum computation closer to reality.
- 96Childs, A. M.; Su, Y.; Tran, M. C.; Wiebe, N.; Zhu, S. Theory of trotter error with commutator scaling. Phys. Rev. X 2021, 11, 011020, DOI: 10.1103/PhysRevX.11.011020Google Scholar96https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXovVCntLk%253D&md5=ceb538c2607c68116a8a9911d59230bcTheory of Trotter Error with Commutator ScalingChilds, Andrew M.; Su, Yuan; Tran, Minh C.; Wiebe, Nathan; Zhu, ShuchenPhysical Review X (2021), 11 (1), 011020CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decompg. the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our anal. directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds, in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, k-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a byproduct. Our anal. reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of 5, and it is close to tight for power-law interactions and other orderings of terms. This result suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and const. prefactor.
- 97Reiher, M.; Wiebe, N.; Svore, K. M.; Wecker, D.; Troyer, M. Elucidating reaction mechanisms on quantum computers. Proc. Natl. Acad. Sci. U. S. A. 2017, 114, 7555– 7560, DOI: 10.1073/pnas.1619152114Google Scholar97https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhtFSmt7%252FN&md5=3b7148a5d436d3c1f5c0da80391a28f3Elucidating reaction mechanisms on quantum computersReiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, MatthiasProceedings of the National Academy of Sciences of the United States of America (2017), 114 (29), 7555-7560CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)With rapid recent advances in quantum technol., we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chem. systems, using the open problem of biol. nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource ests. show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chem. without requiring exorbitant resources.
- 98Bocharov, A.; Roetteler, M.; Svore, K. M. Efficient synthesis of universal repeat-until-success quantum circuits. Phys. Rev. Lett. 2015, 114, 080502, DOI: 10.1103/PhysRevLett.114.080502Google Scholar98https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXmsVGltrw%253D&md5=fcc770f8e5371bf0ce914dece7f90c59Efficient synthesis of universal repeat-until-success quantum circuitsBocharov, Alex; Roetteler, Martin; Svore, Krysta M.Physical Review Letters (2015), 114 (8), 080502/1-080502/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Recently it was shown that the resources required to implement unitary operations on a quantum computer can be reduced by using probabilistic quantum circuits called repeat-until-success (RUS) circuits. However, the previously best-known algorithm to synthesize a RUS circuit for a given target unitary requires exponential classical runtime. We present a probabilistically polynomial-time algorithm to synthesize a RUS circuit to approx. any given single-qubit unitary to precision ε over the Clifford + T basis. Surprisingly, the T count of the synthesized RUS circuit surpasses the theor. lower bound of 3 log2(1/ε) that holds for purely unitary single-qubit circuit decompn. By taking advantage of measurement and an ancilla qubit, RUS circuits achieve an expected T count of 1.15 log2(1/ε) for single-qubit z rotations. Our method leverages the fact that the set of unitaries implementable by RUS protocols has a higher d. in the space of all unitaries compared to the d. of purely unitary implementations.
- 99Wecker, D.; Hastings, M. B.; Wiebe, N.; Clark, B. K.; Nayak, C.; Troyer, M. Solving strongly correlated electron models on a quantum computer. Phys. Rev. A 2015, 92, 062318, DOI: 10.1103/PhysRevA.92.062318Google Scholar99https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XnvVOgsLo%253D&md5=66858204e2c586dfba31d99ee206a5f4Solving strongly correlated electron models on a quantum computerWecker, Dave; Hastings, Matthew B.; Wiebe, Nathan; Clark, Bryan K.; Nayak, Chetan; Troyer, MatthiasPhysical Review A: Atomic, Molecular, and Optical Physics (2015), 92 (6-A), 062318/1-062318/24CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to det. the ground-state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to det. its phase diagram and ground-state properties on a quantum computer. In particular, we discuss strategies for efficiently detg. and prepg. the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prep. arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms, each time step in the evolution can be performed with just O(N) gates and O(log N) circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, in both the time and the frequency domains. We further present efficient nondestructive approaches to measurement that avoid the need to reprepare the ground state after each measurement and that quadratically reduce the measurement error.
- 100Low, G. H.; Chuang, I. L. Hamiltonian Simulation by Qubitization. Quantum 2019, 3, 163, DOI: 10.22331/q-2019-07-12-163Google ScholarThere is no corresponding record for this reference.
- 101Babbush R. Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity. Phys. Rev. X 2018, 8, 041015, DOI: 10.1103/PhysRevX.8.041015Google Scholar101https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltFSiur8%253D&md5=d187b0b6d04c754062bb30fa3e75e07cEncoding Electronic Spectra in Quantum Circuits with Linear T ComplexityBabbush, Ryan; Gidney, Craig; Berry, Dominic W.; Wiebe, Nathan; McClean, Jarrod; Paler, Alexandru; Fowler, Austin; Neven, HartmutPhysical Review X (2018), 8 (4), 041015CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)We construct quantum circuits that exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use quantum phase estn. to sample states in the Hamiltonian eigenbasis with optimal query complexity O(λ/ε), where λ is an abs. sum of Hamiltonian coeffs. and ε is the target precision. For both the Hubbard model and electronic structure Hamiltonian in a second quantized basis diagonalizing the Coulomb operator, our circuits have T-gate complexity O(N+log(1/ε)), where N is the no. of orbitals in the basis. This scenario enables sampling in the eigenbasis of electronic structure Hamiltonians with T complexity O(N3/ε+N2log(1/ε)/ε). Compared to prior approaches, our algorithms are asymptotically more efficient in gate complexity and require fewer T gates near the classically intractable regime. Compiling to surface code fault-tolerant gates and assuming per-gate error rates of one part in a thousand reveals that one can error correct phase estn. on interesting instances of these problems beyond the current capabilities of classical methods using only about a million superconducting qubits in a matter of hours.
- 102Berry, D. W.; Gidney, C.; Motta, M.; McClean, J. R.; Babbush, R. Qubitization of Arbitrary Basis Quantum Chemistry by Low Rank Factorization. arXiv Preprint (Quantum Physics) , 2019. arXiv:1902.02134. https://doi.org/10.48550/arXiv.1902.02134.Google ScholarThere is no corresponding record for this reference.
- 103von Burg, V.; Low, G. H.; Häner, T.; Steiger, D. S.; Reiher, M.; Roetteler, M.; Troyer, M. Quantum computing enhanced computational catalysis. arXiv Preprint (Quantum Physics) , 2020. arXiv:2007.14460. https://doi.org/10.48550/arXiv.2007.14460.Google ScholarThere is no corresponding record for this reference.
- 104Luis, A.; Perina, J. Optimum phase-shift estimation and the quantum description of the phase difference. Phys. Rev. A 1996, 54, 4564– 4570, DOI: 10.1103/PhysRevA.54.4564Google Scholar104https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XmvVyitbg%253D&md5=90b7e7c1854031c9c774687c4be7b8c4Optimum phase-shift estimation and the quantum description of the phase differenceLuis, A.; Perina, J.Physical Review A: Atomic, Molecular, and Optical Physics (1996), 54 (5), 4564-4570CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)The problem of a correct quantum description of the phase difference is examd. from the perspective of parameter estn. theory. It is shown that an optimum phase-shift measurement defines a phase difference operator which coincides with other approaches to the same problem. We also study the fundamental limit to the accuracy of a phase difference shift detection. We show that this limit can be reached by a measurement having countable outcomes despite the fact that a phase shift can take any value. We show that this is the case of the phase difference operator defined by an optimum phase-shift measurement.
- 105Visscher, K. M.; Geerke, D. P. Deriving Force-Field Parameters from First Principles Using a Polarizable and Higher Order Dispersion Model. J. Chem. Theory Comput. 2019, 15, 1875– 1883, DOI: 10.1021/acs.jctc.8b01105Google Scholar105https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXivFWhsL4%253D&md5=02c0da0ade9d662b4a036194bf9eceb7Deriving Force-Field Parameters from First Principles Using a Polarizable and Higher Order Dispersion ModelVisscher, Koen M.; Geerke, Daan P.Journal of Chemical Theory and Computation (2019), 15 (3), 1875-1883CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)In this work we propose a strategy based on quantum mech. (QM) calcns. to parametrize a polarizable force field for use in mol. dynamics (MD) simulations. We investigate the use of multiple atoms-in-mols. (AIM) strategies to partition QM detd. mol. electron densities into at. subregions. The partitioned at. densities are subsequently used to compute at. dispersion coeffs. from effective exchange-hole-dipole moment (XDM) calcns. In order to derive values for the repulsive van der Waals parameters from first principles, we use a simple vol. relation to scale effective at. radii. Explicit inclusion of higher order dispersion coeffs. was tested for a series of alkanes, and we show that combining C6 and C8 attractive terms together with a C11 repulsive potential yields satisfying models when used in combination with our van der Waals parameters and electrostatic and bonded parameters as directly obtained from quantum calcns. as well. This result highlights that explicit inclusion of higher order dispersion terms could be viable in simulation, and it suggests that currently available QM anal. methods allow for first-principles parametrization of mol. mechanics models.
- 106Jing, Z.; Liu, C.; Cheng, S. Y.; Qi, R.; Walker, B. D.; Piquemal, J.-P.; Ren, P. Polarizable force fields for biomolecular simulations: Recent advances and applications. Annu. Rev. Biophys. 2019, 48, 371– 394, DOI: 10.1146/annurev-biophys-070317-033349Google Scholar106https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXmtVGnu7s%253D&md5=87b2bbf40c3e1977cd0e55e90b314d45Polarizable Force Fields for Biomolecular Simulations: Recent Advances and ApplicationsJing, Zhifeng; Liu, Chengwen; Cheng, Sara Y.; Qi, Rui; Walker, Brandon D.; Piquemal, Jean-Philip; Ren, PengyuAnnual Review of Biophysics (2019), 48 (), 371-394CODEN: ARBNCV; ISSN:1936-122X. (Annual Reviews)A review. Realistic modeling of biomol. systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in phys. models, simulation algorithms, and computing hardware, biomol. simulations with advanced force fields at biol. relevant timescales are becoming increasingly promising. These advancements have not only led to new biophys. insights but also afforded opportunities to advance our understanding of fundamental intermol. forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomol. simulations.
- 107Nerenberg, P. S.; Head-Gordon, T. New developments in force fields for biomolecular simulations. Curr. Opin. Struct. Biol. 2018, 49, 129– 138, DOI: 10.1016/j.sbi.2018.02.002Google Scholar107https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXislSmtrw%253D&md5=c1ef88efb2c82318160775348f769030New developments in force fields for biomolecular simulationsNerenberg, Paul S.; Head-Gordon, TeresaCurrent Opinion in Structural Biology (2018), 49 (), 129-138CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)A review. Biomol. force field development has been instrumental in improving the predictive power of mol. simulations over the past four decades. More recently, the era of large quant. exptl. datasets and ubiquitous high performance computing power has enabled rapid progress in the field. In this review we summarize recent developments in all-atom protein, nucleic acid, and small mol. force fields, paying specific attention to developments in parameterization methods and improvements in the representations of nonbonded interactions that are crit. for solving the challenging biophys. problems of the present. We also sketch out new avenues for force field development and grand challenge applications for the near future.
- 108Xu, P.; Guidez, E. B.; Bertoni, C.; Gordon, M. S. Perspective: Ab initio force field methods derived from quantum mechanics. J. Chem. Phys. 2018, 148, 090901, DOI: 10.1063/1.5009551Google Scholar108https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXjvVCktbw%253D&md5=4222345e3799a0713daa18e3ade9e33cPerspective: Ab initio force field methods derived from quantum mechanicsXu, Peng; Guidez, Emilie B.; Bertoni, Colleen; Gordon, Mark S.Journal of Chemical Physics (2018), 148 (9), 090901/1-090901/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A review. It is often desirable to accurately and efficiently model the behavior of large mol. systems in the condensed phase (thousands to tens of thousands of atoms) over long time scales (from nanoseconds to milliseconds). In these cases, ab initio methods are difficult due to the increasing computational cost with the no. of electrons. A more computationally attractive alternative is to perform the simulations at the at. level using a parameterized function to model the electronic energy. Many empirical force fields have been developed for this purpose. However, the functions that are used to model interat. and intermol. interactions contain many fitted parameters obtained from selected model systems, and such classical force fields cannot properly simulate important electronic effects. Furthermore, while such force fields are computationally affordable, they are not reliable when applied to systems that differ significantly from those used in their parameterization. They also cannot provide the information necessary to analyze the interactions that occur in the system, making the systematic improvement of the functional forms that are used difficult. Ab initio force field methods aim to combine the merits of both types of methods. The ideal ab initio force fields are built on first principles and require no fitted parameters. Ab initio force field methods surveyed in this perspective are based on fragmentation approaches and intermol. perturbation theory. This perspective summarizes their theor. foundation, key components in their formulation, and discusses key aspects of these methods such as accuracy and formal computational cost. The ab initio force fields considered here were developed for different targets, and this perspective also aims to provide a balanced presentation of their strengths and shortcomings. Finally, this perspective suggests some future directions for this actively developing area. (c) 2018 American Institute of Physics.
- 109Sakharov, D. V.; Lim, C. Force fields including charge transfer and local polarization effects: Application to proteins containing multi/heavy metal ions. J. Comput. Chem. 2009, 30, 191– 202, DOI: 10.1002/jcc.21048Google Scholar109https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXns1Wgtw%253D%253D&md5=81acba75980eafb9219452cc7c1aeaf2Force fields including charge transfer and local polarization effects: application to proteins containing multi/heavy metal ionsSakharov, Dmitri V.; Lim, CarmayJournal of Computational Chemistry (2009), 30 (2), 191-202CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)The question whether mol. dynamics (MD) simulations can yield reliable structural and dynamical properties of metalloproteins depend on the accuracy of the force field, i.e., the potential energy function (PEF) and assocd. parameters modeling the interactions of the metal ion of interest with water and protein ligands. Previously, we had developed a CTPOL PEF for protein simulations of Zn2+ bound to Cys- and/or His0 that includes charge transfer and local polarization effects as well as metal van der Waals parameters that reproduce the structural and thermodynamical properties of 22 dications. Here, we evaluate if the CTPOL PEF and the new metal parameters (referred to as the CTPOLa force field) can be applied to proteins contg. polynuclear metal-binding sites and heavy toxic metal ions, using the CdZn2-Cys9 β-domain of rat liver metallothionein-2 and the Hg2+-bound 18-residue peptide from MerP as test systems. Using the CTPOLa force field, simulations of the β-domain of rat liver metallothionein-2 totaling 19 ns could preserve the exptl. obsd. CdZn2-Cys9 complex geometry and overall protein structure, whereas simulations neglecting charge transfer and local polarization effects could not. However, the CTPOLa force field cannot reproduce the exptl. obsd. linear bicoordination of Hg2+ in the MerP peptide without adding an angular restraint to the CTPOL PEF to correct the angle distribution about Hg2+. Thus, the force fields presented herein for the group IIB metal ions can be applied to simulation studies of proteins contg. polynuclear metal-binding sites and heavy metal ions in aq. soln. PEF neglecting charge transfer and local polarization effects in conjunction with vdW parameters adjusted to reproduce the structural and thermodynamical properties of only the metal ion in question could not yield an accurate representation of the metal-binding site and overall protein structure.
- 110Cieplak, P.; Dupradeau, F.-Y.; Duan, Y.; Wang, J. Polarization effects in molecular mechanical force fields. J. Phys.: Condens. Matter 2009, 21, 333102, DOI: 10.1088/0953-8984/21/33/333102Google Scholar110https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtFWgsLfL&md5=00110340ba462d1e8466c78f907aa9e3Polarization effects in molecular mechanical force fieldsCieplak, Piotr; Dupradeau, Francois-Yves; Duan, Yong; Wang, JunmeiJournal of Physics: Condensed Matter (2009), 21 (33), 333102/1-333102/21CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)A review. The focus here is on incorporating electronic polarization into classical mol. mech. force fields used for macromol. simulations. First, we briefly examine currently used mol. mech. force fields and the current status of intermol. forces as viewed by quantum mech. approaches. Next, we demonstrate how some components of quantum mech. energy are effectively incorporated into classical mol. mech. force fields. Finally, we assess the modeling methods of one such energy component-polarization energy-and present an overview of polarizable force fields and their current applications. Incorporating polarization effects into current force fields paves the way to developing potentially more accurate, though more complex, parameterizations that can be used for more realistic mol. simulations.
- 111Li, P.; Merz, K. M., Jr Metal ion modeling using classical mechanics. Chem. Rev. 2017, 117, 1564– 1686, DOI: 10.1021/acs.chemrev.6b00440Google Scholar111https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXjvVSg&md5=1cd2a84bd580b3b4e3493bfdd4bc4da1Metal Ion Modeling Using Classical MechanicsLi, Pengfei; Merz, Kenneth M., Jr.Chemical Reviews (Washington, DC, United States) (2017), 117 (3), 1564-1686CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review. Metal ions play significant roles in numerous fields including chem., geochem., biochem. and materials science. With computational tools increasingly becoming important in chem. research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aq. and solid phases. Herein we review both quantum and classical modeling strategies for metal ion contg. systems that have been developed over the past few decades. This review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond based models. Quantum mech. studies of metal ion contg. systems at the semiempirical, ab initio and d. functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion contg. systems.
- 112Seifert, G.; Joswig, J.-O. Density-functional tight binding–an approximate density-functional theory method. WIREs Comput. Mol. Sci. 2012, 2, 456– 465, DOI: 10.1002/wcms.1094Google Scholar112https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XovVyrs7g%253D&md5=ebfe512e5516aaf1e6ccc1d6c6139b45Density-functional tight binding-an approximate density-functional theory methodSeifert, Gotthard; Joswig, Jan-OleWiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (3), 456-465CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)In this paper, we review the foundations of the d.-functional tight-binding (DFTB) method. The method is based on the d.-functional theory as formulated by Hohenberg and Kohn. It introduces several approxns.: First, densities and potentials are written as superpositions of at. densities and potentials. Second, many-center terms are summarized together with nuclear repulsion energy terms in a way that they can be written as a sum of pairwise repulsive terms. For small distances, the nuclear repulsion dominates, whereas for large distances, these terms vanish. The Kohn-Sham orbitals are expanded in a set of localized atom-centered functions. They are represented in a minimal basis of optimized AOs, which are obtained for spherical sym. spinunpolarized neutral atoms self-consistently. The whole Hamilton and overlap matrixes contain one- and two-center contributions only. Therefore, they can be calcd. and tabulated in advance as functions of the distance between at. pairs. In addn., we discuss a self-consistent charge extension, the treatment of weak interactions, and a linear response scheme in connection with the DFTB method. Finally, some practical aspects are presented.
- 113Sure, R.; Grimme, S. Corrected small basis set Hartree-Fock method for large systems. J. Comput. Chem. 2013, 34, 1672– 1685, DOI: 10.1002/jcc.23317Google Scholar113https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXnsFGqsbk%253D&md5=f9faef018cfcf94387c1d9382b7d639dCorrected small basis set Hartree-Fock method for large systemsSure, Rebecca; Grimme, StefanJournal of Computational Chemistry (2013), 34 (19), 1672-1685CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)A quantum chem. method based on a Hartree-Fock calcn. with a small Gaussian AO basis set is presented. Its main area of application is the computation of structures, vibrational frequencies, and noncovalent interaction energies in huge mol. systems. The method is suggested as a partial replacement of semiempirical approaches or d. functional theory (DFT) in particular when self-interaction errors are acute. In order to get accurate results three phys. plausible atom pair-wise correction terms are applied for London dispersion interactions (D3 scheme), basis set superposition error (gCP scheme), and short-ranged basis set incompleteness effects. In total nine global empirical parameters are used. This so-called Hartee-Fock-3c (HF-3c) method is tested for geometries of small org. mols., interaction energies and geometries of noncovalently bound complexes, for supramol. systems, and protein structures. In the majority of realistic test cases good results approaching large basis set DFT quality are obtained at a tiny fraction of computational cost. © 2013 Wiley Periodicals, Inc.
- 114Goez, A.; Neugebauer, J. Embedding Methods in Quantum Chemistry. Frontiers of Quantum Chemistry; Springer, 2018; pp 139– 179. DOI: 10.1007/978-981-10-5651-2_7 .Google ScholarThere is no corresponding record for this reference.
- 115Sun, Q.; Chan, G. K.-L. Quantum embedding theories. Acc. Chem. Res. 2016, 49, 2705– 2712, DOI: 10.1021/acs.accounts.6b00356Google Scholar115https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslyntrbM&md5=5908130580b088e4ea49c788bda516d8Quantum Embedding TheoriesSun, Qiming; Chan, Garnet Kin-LicAccounts of Chemical Research (2016), 49 (12), 2705-2712CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)A review. In complex systems, it is often the case that the region of interest forms only one part of a much larger system. The idea of joining two different quantum simulations - a high level calcn. on the active region of interest, and a low level calcn. on its environment - formally defines a quantum embedding. While any combination of techniques constitutes an embedding, several rigorous formalisms have emerged that provide for exact feedback between the embedded system and its environment. These three formulations: d. functional embedding, Green's function embedding, and d. matrix embedding, resp., use the single-particle d., single-particle Green's function, and single-particle d. matrix as the quantum variables of interest. Many excellent reviews exist covering these methods individually. However, a unified presentation of the different formalisms is so far lacking. Indeed, the various languages commonly used, functional equations for d. functional embedding, diagrammatics for Green's function embedding, and entanglement arguments for d. matrix embedding, make the three formulations appear vastly different. In this Account, we introduce the basic equations of all three formulations in such a way as to highlight their many common intellectual strands. While we focus primarily on a straightforward theor. perspective, we also give a brief overview of recent applications and possible future developments. The first section starts with d. functional embedding, where we introduce the key embedding potential via the Euler equation. We then discuss recent work concerning the treatment of the nonadditive kinetic potential, before describing mean-field d. functional embedding and wave function in d. functional embedding. We finish the section with extensions to time-dependence and excited states. The second section is devoted to Green's function embedding. Here, we use the Dyson equation to obtain equations that parallel as closely as possible the d. functional embedding equations, with the hybridization playing the role of the embedding potential. Embedding a high-level self-energy within a low-level self-energy is treated analogously to wave function in d. functional embedding. The numerical computation of the high-level self-energy allows us to briefly introduce the bath representation in the quantum impurity problem. We then consider translationally invariant systems to bring in the important dynamical mean-field theory. Recent developments to incorporate screening and long-range interactions are discussed.The third section concerns d. matrix embedding. Here, we first highlight some math. complications assocd. with a simple Euler equation derivation, arising from the open nature of fragments. This motivates the d. matrix embedding theory, where we use the Schmidt decompn. to represent the entanglement through bath orbitals. The resulting impurity plus bath formulation resembles that of dynamical mean-field theory. We discuss the numerical self-consistency assocd. with using a high-level correlated wave function with a mean-field low-level treatment, and connect the resulting numerical inversion to that used in d. functional embedding. We finish with perspectives on the future of all three methods.
- 116Ikegami, T.; Ishida, T.; Fedorov, D. G.; Kitaura, K.; Inadomi, Y.; Umeda, H.; Yokokawa, M.; Sekiguchi, S. Full electron calculation beyond 20,000 atoms: ground electronic state of photosynthetic proteins. SC’05 Proceedings of the 2005 ACM/IEEE Conference on Supercomputing; IEEE, 2005; p 10. DOI: 10.1109/SC.2005.28 .Google ScholarThere is no corresponding record for this reference.
- 117Senn, H. M.; Thiel, W. QM/MM Methods for Biomolecular Systems. Angew. Chem., Int. Ed. 2009, 48, 1198– 1229, DOI: 10.1002/anie.200802019Google Scholar117https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXitFOqs7g%253D&md5=c51da58b0525651c71f9c393a79023beQM/MM methods for biomolecular systemsSenn, Hans Martin; Thiel, WalterAngewandte Chemie, International Edition (2009), 48 (7), 1198-1229CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)A review. Combined quantum-mechanics/mol.-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomol. systems. Quantum-mech. (QM) methods are required for describing chem. reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based mol. mechanics (MM) methods. Thus to model large biomols. the logical approach is to combine the two techniques and, to use a QM method for the chem. active region (e.g., substrates and co-factors in an enzymic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomol. systems at a reasonable computational effort while providing the necessary accuracy.
- 118Wu, L.; Qin, L.; Nie, Y.; Xu, Y.; Zhao, Y.-L. Computer-aided understanding and engineering of enzymatic selectivity. Biotechnol. Adv. 2022, 54, 107793, DOI: 10.1016/j.biotechadv.2021.107793Google Scholar118https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit1alsrvO&md5=74d5a040b6db8b1a0ecbaa1a0fb6fb47Computer-aided understanding and engineering of enzymatic selectivityWu, Lunjie; Qin, Lei; Nie, Yao; Xu, Yan; Zhao, Yi-LeiBiotechnology Advances (2022), 54 (), 107793CODEN: BIADDD; ISSN:0734-9750. (Elsevier Inc.)A review. Enzymes offering chemo-, regio-, and stereoselectivity enable the asym. synthesis of high-value chiral mols. Unfortunately, the drawback that naturally occurring enzymes are often inefficient or have undesired selectivity toward non-native substrates hinders the broadening of biocatalytic applications. To match the demands of specific selectivity in asym. synthesis, biochemists have implemented various computer-aided strategies in understanding and engineering enzymic selectivity, diversifying the available repository of artificial enzymes. Here, given that the entire asym. catalytic cycle, involving precise interactions within the active pocket and substrate transport in the enzyme channel, could affect the enzymic efficiency and selectivity, we presented a comprehensive overview of the computer-aided workflow for enzymic selectivity. This review includes a mechanistic understanding of enzymic selectivity based on quantum mech. calcns., rational design of enzymic selectivity guided by enzyme-substrate interactions, and enzymic selectivity regulation via enzyme channel engineering. Finally, we discussed the computational paradigm for designing enzyme selectivity in silico to facilitate the advancement of asym. biosynthesis.
- 119Warshel, A.; Levitt, M. Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. J. Mol. Biol. 1976, 103, 227– 249, DOI: 10.1016/0022-2836(76)90311-9Google Scholar119https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE28XktFKhtr0%253D&md5=f34df33b5971b6b02bd03be95dcd7ba5Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozymeWarshel, A.; Levitt, M.Journal of Molecular Biology (1976), 103 (2), 227-49CODEN: JMOBAK; ISSN:0022-2836.A general method for detailed study of enzymic reactions is presented. The method considers the complete enzyme-substrate complex together with the surrounding solvent and evaluates all the different quantum mech. and classical energy factors that can affect the reaction pathway. These factors include the quantum mech. energies assocd. with bond cleavage and charge redistribution of the substrate and the classical energies of steric and electrostatic interactions between the substrate and the enzyme. The electrostatic polarization of the enzyme atoms and the orientation of the dipoles of the surrounding H2O mols. is simulated by a microscopic dielec. model. The solvation energy resulting from this polarization is considerable and must be included in any realistic calcn. of chem. reactions involving anything more than an isolated mol. in vacuo. Without it, acidic groups can never become ionized and the charge distribution on the substrate will not be reasonable. The same dielec. model can also be used to study the reaction of the substrate in soln. In this way the reaction in soln. can be compared with the enzymic reaction. The stability of the carbonium ion intermediate formed in the cleavage of a glycosidic bond by lysozyme was studied. Electrostatic stabilization is an important factor in increasing the rate of the reaction step that leads to the formation of the carbonium ion intermediate. Steric factors, such as the strain of the substrate on binding to lysozyme, do not seem to contribute significantly.
- 120Cui, Q.; Pal, T.; Xie, L. Biomolecular QM/MM Simulations: What Are Some of the “Burning Issues”?. J. Phys. Chem. B 2021, 125, 689– 702, DOI: 10.1021/acs.jpcb.0c09898Google Scholar120https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXislWksw%253D%253D&md5=903b4525cb8437a1da1d167deb718486Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?Cui, Qiang; Pal, Tanmoy; Xie, LukeJournal of Physical Chemistry B (2021), 125 (3), 689-702CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)A review. QM/MM simulations have become an indispensable tool in many chem. and biochem. investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chem., are there still "burning challenges" in QM/MM methods, esp. for biomol. systems. In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quant. applicability of QM/MM simulations to many, if not all, biomols. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate addnl. developments that help push the field forward in meaningful directions.
- 121Lu, X.; Fang, D.; Ito, S.; Okamoto, Y.; Ovchinnikov, V.; Cui, Q. QM/MM free energy simulations: recent progress and challenges. Mol. Simul. 2016, 42, 1056– 1078, DOI: 10.1080/08927022.2015.1132317Google Scholar121https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhtFertrrK&md5=12fda847cd54f527407725cd53d64575QM/MM free energy simulations: recent progress and challengesLu, Xiya; Fang, Dong; Ito, Shingo; Okamoto, Yuko; Ovchinnikov, Victor; Cui, QiangMolecular Simulation (2016), 42 (13), 1056-1078CODEN: MOSIEA; ISSN:0892-7022. (Taylor & Francis Ltd.)Due to the higher computational cost relative to pure mol. mech. (MM) simulations, hybrid quantum mech./mol. mech. (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here, we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chem. reactions, we highlight the value of invoking enhanced sampling technique (e.g. replica-exchange) in umbrella sampling calcns. and the value of including collective environmental variables (e.g. hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calcns., esp. free energy along the path, to various parameters in the computation. Alchem. free energy simulations with a specific thermodn. cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyze two different approaches: the QM/MM-MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analyzed here, both approaches seem productive although care needs to be exercised when analyzing the perturbative corrections.
- 122Cao, L.; Ryde, U. On the Difference Between Additive and Subtractive QM/MM Calculations. Front. Chem. 2018, 6, 89, DOI: 10.3389/fchem.2018.00089Google Scholar122https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisVCgtr3J&md5=512f3841895f2ea13cba1e5c462be77bOn the difference between additive and subtractive QM/MM calculationsCao, Lili; Ryde, UlfFrontiers in Chemistry (Lausanne, Switzerland) (2018), 6 (), 89/1-89/15CODEN: FCLSAA; ISSN:2296-2646. (Frontiers Media S.A.)The combined quantum mech. (QM) and mol. mech. (MM) approach (QM/MM) is a popular method to study reactions in biochem. macromols. Even if the general procedure of using QM for a small, but interesting part of the system and MM for the rest is common to all approaches, the details of the implementations vary extensively, esp. the treatment of the interface between the two systems. For example, QM/MM can use either additive or subtractive schemes, of which the former is often said to be preferable, although the two schemes are often mixed up with mech. and electrostatic embedding. In this article, we clarify the similarities and differences of the two approaches. We show that inherently, the two approaches should be identical and in practice require the same sets of parameters. However, the subtractive scheme provides an opportunity to correct errors introduced by the truncation of the QM system, i.e., the link atoms, but such corrections require addnl. MM parameters for the QM system. We describe and test three types of link-atom correction, viz. for van der Waals, electrostatic, and bonded interactions. The calcns. show that electrostatic and bonded link-atom corrections often give rise to problems in the geometries and energies. The van der Waals link-atom corrections are quite small and give results similar to a pure additive QM/MM scheme. Therefore, both approaches can be recommended.
- 123Himo, F. Recent Trends in Quantum Chemical Modeling of Enzymatic Reactions. J. Am. Chem. Soc. 2017, 139, 6780– 6786, DOI: 10.1021/jacs.7b02671Google Scholar123https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXns1WmsL4%253D&md5=e0e4daa1dcd14233c37a57f22057235fRecent Trends in Quantum Chemical Modeling of Enzymatic ReactionsHimo, FahmiJournal of the American Chemical Society (2017), 139 (20), 6780-6786CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)A review. The quantum chem. cluster approach is a powerful method for investigating enzymic reactions. Over the past two decades, a large no. of highly diverse systems have been studied and a great wealth of mechanistic insight has been developed using this technique. This Perspective reviews the current status of the methodol. The latest tech. developments are highlighted, and challenges are discussed. Some recent applications are presented to illustrate the capabilities and progress of this approach, and likely future directions are outlined.
- 124Cerqueira, N. M. F. S. A.; Fernandes, P. A.; Ramos, M. Protocol for Computational Enzymatic Reactivity Based on Geometry Optimisation. ChemPhysChem 2018, 19, 669– 689, DOI: 10.1002/cphc.201700339Google Scholar124https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhvVWmtrk%253D&md5=b9d857fe39452d4cabe3d7768ee04c6cProtocol for Computational Enzymatic Reactivity Based on Geometry OptimizationCerqueira, N. M. F. S. A.; Fernandes, P. A.; Ramos, M. J.ChemPhysChem (2018), 19 (6), 669-689CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)A review. Enzymes play a biol. essential role in performing and controlling an important share of the chem. processes occurring in life. However, despite their crit. role in nature, attaining a clear understanding of the way an enzyme acts is still cumbersome. Computational enzymol. is playing an increasingly important role in this field of research. It allows the elucidation of a complete and detailed mechanism of an enzymic reaction, including the characterization of reaction intermediates and transition states from both structural and energetic points of view, which is something that no other single expt. can produce alone. In this review, the authors present a general computational strategy to study enzymic mechanisms based on adiabatic mapping and free geometry optimization. These methods allow chem. reactions to be studied with high theor. levels, and allow a more exhaustive exploration of the chem. reactional space than other available methods, albeit being limited to the extent that they explore the enzyme conformational space. Special attention is given to the choice of the theor. levels, as well as describing the model systems that are currently used to study enzymic reactions. With this, the authors aim to provide a good introduction for non-specialized users in this field of research. The authors also provide a selection of hand-picked examples from the authors' own work that illustrate the power of computational enzymol. to study catalytic mechanisms. Some of these studies constitute pioneering work in the field that were later validated by exptl. means.
- 125Boulanger, E.; Harvey, J. N. QM/MM methods for free energies and photochemistry. Curr. Opin. Struct. Biol. 2018, 49, 72– 76, DOI: 10.1016/j.sbi.2018.01.003Google Scholar125https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhsVensbk%253D&md5=4923ff97afaa3c338776f259ee7a6866QM/MM methods for free energies and photochemistryBoulanger, Eliot; Harvey, Jeremy N.Current Opinion in Structural Biology (2018), 49 (), 72-76CODEN: COSBEF; ISSN:0959-440X. (Elsevier Ltd.)A review. Hybrid computational methods describing a small region of a biomol. system with quantum mechanics and the bulk with mol. mechanics, referred to as QM/MM methods, are now a central part of computational biochem. This review considers developments in the QM/MM approach that make it easier to calc. free energies using accurate QM-based potential energy expressions. We also describe techniques to treat electronic coupling between the core region and the MM environment. Polarizability of the protein matrix is important but so is electronic coupling. Applications of these new methods, esp. to photochem., are discussed.
- 126Hu, L.; Söderhjelm, P.; Ryde, U. Accurate Reaction Energies in Proteins Obtained by Combining QM/MM and Large QM Calculations. J. Chem. Theory Comput. 2013, 9, 640– 649, DOI: 10.1021/ct3005003Google Scholar126https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsFygt7nM&md5=649e8cecc92aa6dabcdddc8b6b86bf90Accurate Reaction Energies in Proteins Obtained by Combining QM/MM and Large QM CalculationsHu, LiHong; Soederhjelm, Paer; Ryde, UlfJournal of Chemical Theory and Computation (2013), 9 (1), 640-649CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)We here suggest and test a new method to obtain stable energies in proteins for charge-neutral reactions by running large quantum mech. (QM) calcns. on structures obtained by combined QM and mol. mechanics (QM/MM) geometry optimization on several snapshots from mol. dynamics simulations. As a test case, we use a proton transfer between a metal-bound cysteine residue and a second-sphere histidine residue in the active site of [Ni,Fe] hydrogenase, which has been shown to be very sensitive to the surroundings. We include in the QM calcns. all residues within 4.5 Å of the active site, two capped residues on each side of the active-site residues, and all charged groups that are buried inside the protein, which for this enzyme includes three iron-sulfur clusters, in total, 930 atoms. These calcns. are performed at the BP86/def2-SV(P) level, but the energies are then extrapolated to the B3LYP/def2-TZVP level with a smaller QM system, and zero-point energy, entropy, and thermal effects are added. We test three approaches to model the remaining atoms of the protein solvent, viz., by std. QM/MM approaches using either mech. or electrostatic embedding or by using a continuum solvation model for the large QM systems. Quite encouragingly, the three approaches give the same results within 14 kJ/mol, and variations in the size of the QM system do not change the energies by more than 8 kJ/mol, provided that the QM/MM junctions are not moved closer to the QM system. The statistical precision for the av. over 10 snapshots is 1-3 kJ/mol.
- 127Pandharkar, R.; Hermes, M. R.; Cramer, C. J.; Gagliardi, L. Localized Active Space State Interaction: A Multireference Method For Chemical Insight. ChemRxiv Preprint (Theoretical and Computational Chemistry) , 2022. DOI: 10.26434/chemrxiv-2022-jdzlrGoogle ScholarThere is no corresponding record for this reference.
- 128Otten, M.; Hermes, M. R.; Pandharkar, R.; Alexeev, Y.; Gray, S. K.; Gagliardi, L. Localized Quantum Chemistry on Quantum Computers. arXiv Preprint (Quantum Physics) , 2022. arXiv:2203.02012. https://doi.org/10.48550/arXiv.2203.02012Google ScholarThere is no corresponding record for this reference.
- 129Bauer, B.; Wecker, D.; Millis, A. J.; Hastings, M. B.; Troyer, M. Hybrid Quantum-Classical Approach to Correlated Materials. Phys. Rev. X 2016, 6, 031045, DOI: 10.1103/PhysRevX.6.031045Google Scholar129https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslyrtbnP&md5=8be7455f5a66158b814a6c7e27ff3ea2Hybrid quantum-classical approach to correlated materialsBauer, Bela; Wecker, Dave; Millis, Andrew J.; Hastings, Matthew B.; Troyer, MatthiasPhysical Review X (2016), 6 (3), 031045/1-031045/11CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)Recent improvements in the control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amt. of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently detd. via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around 100 logical qubits becomes available.
- 130Rubin, N. C. A hybrid classical/quantum approach for large-scale studies of quantum systems with density matrix embedding theory. arXiv Preprint (Quantum Physics) , 2016. arXiv:1610.06910. https://doi.org/10.48550/arXiv.1610.06910.Google ScholarThere is no corresponding record for this reference.
- 131Yamazaki, T.; Matsuura, S.; Narimani, A.; Saidmuradov, A.; Zaribafiyan, A. Towards the practical application of near-term quantum computers in quantum chemistry simulations: A problem decomposition approach. arXiv Preprint (Quantum Physics) , 2018. arXiv:1806.01305. https://doi.org/10.48550/arXiv.1806.01305.Google ScholarThere is no corresponding record for this reference.
- 132Tilly, J.; Sriluckshmy, P. V.; Patel, A.; Fontana, E.; Rungger, I.; Grant, E.; Anderson, R.; Tennyson, J.; Booth, G. H. Reduced density matrix sampling: Self-consistent embedding and multiscale electronic structure on current generation quantum computers. Phys. Rev. Res. 2021, 3, 033230, DOI: 10.1103/PhysRevResearch.3.033230Google Scholar132https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit1Oqs7zF&md5=8c6183801d47ec92b591621f059b2ec5Reduced density matrix sampling: Self-consistent embedding and multiscale electronic structure on current generation quantum computersTilly, Jules; Sriluckshmy, P. V.; Patel, Akashkumar; Fontana, Enrico; Rungger, Ivan; Grant, Edward; Anderson, Robert; Tennyson, Jonathan; Booth, George H.Physical Review Research (2021), 3 (3), 033230CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum chem. and condensed matter physics. In both of these contexts, a strongly correlated quantum region of the extended system is isolated and self-consistently coupled to its environment via the sampling of reduced d. matrixes. We analyze the viability of current generation quantum devices to provide the required fidelity of these objects for a robust and efficient optimization of this subspace. We show that with a simple error mitigation strategy these self-consistent algorithms are indeed highly robust, even in the presence of significant noises on quantum hardware. Furthermore, we demonstrate the use of these d. matrixes for the sampling of nonenergetic properties, including dipole moments and Fermi liq. parameters in condensed phase systems, achieving a reliable accuracy with sparse sampling. It appears that uncertainties derived from the iterative optimization of these subspaces is smaller than variances in the energy for a single subspace optimization with current quantum hardware. This boosts the prospect for routine self-consistency to improve the choice of correlated subspaces in hybrid quantum-classical approaches to electronic structure for large systems in this multiscale fashion.
- 133Yao, Y.; Zhang, F.; Wang, C.-Z.; Ho, K.-M.; Orth, P. P. Gutzwiller hybrid quantum-classical computing approach for correlated materials. Phys. Rev. Res. 2021, 3, 013184, DOI: 10.1103/PhysRevResearch.3.013184Google Scholar133https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXovVajsL0%253D&md5=c94c34de5202b79c7602786d0a7cfe56Gutzwiller hybrid quantum-classical computing approach for correlated materialsYao, Yongxin; Zhang, Feng; Wang, Cai-Zhuang; Ho, Kai-Ming; Orth, Peter P.Physical Review Research (2021), 3 (1), 013184CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)Rapid progress in noisy intermediate-scale quantum (NISQ) computing technol. has led to the development of novel resource-efficient hybrid quantum-classical algorithms, such as the variational quantum eigensolver (VQE), that can address open challenges in quantum chem., physics, and material science. Proof-of-principle quantum chem. simulations for small mols. have been demonstrated on NISQ devices. While several approaches have been theor. proposed for correlated materials, NISQ simulations of interacting periodic models on current quantum devices have not yet been demonstrated. Here, we develop a hybrid quantum-classical simulation framework for correlated electron systems based on the Gutzwiller variational embedding approach. We implement this framework on Rigetti quantum processing units (QPUs) and apply it to the periodic Anderson model, which describes a correlated heavy electron band hybridizing with noninteracting conduction electrons. Our simulation results quant. reproduce the known ground state quantum phase diagram including metallic, Kondo and Mott insulating phases. This is the first fully self-consistent hybrid quantum-classical simulation of an infinite correlated lattice model executed on QPUs, demonstrating that the Gutzwiller hybrid quantum-classical embedding framework is a powerful approach to simulate correlated materials on NISQ hardware. This benchmark study also puts forth a concrete pathway towards practical quantum advantage on NISQ devices.
- 134Kirsopp, J. J. M.; Paola, C. D.; Manrique, D. Z.; Krompiec, M.; Greene-Diniz, G.; Guba, W.; Meyder, A.; Wolf, D.; Strahm, M.; Ramo, D. M. Quantum Computational Quantification of Protein-Ligand Interactions. Int. J. Quantum Chem. 2021, e26975, DOI: 10.1002/qua.26975Google ScholarThere is no corresponding record for this reference.
- 135Izsak, R.; Riplinger, C.; Blunt, N. S.; de Souza, B.; Holzmann, N.; Crawford, O.; Camps, J.; Neese, F.; Schopf, P. Quantum Computing in Pharma: A Multilayer Embedding Approach for Near Future Applications. arXiv Preprint (Chemical Physics) , 2022. arXiv:2202.04460. https://arxiv.org/pdf/2202.04460.pdf.Google ScholarThere is no corresponding record for this reference.
- 136Fock, V.; Veselov, M.; Petrashen’, M. Incomplete separation of variables for divalence atoms. Zh. Eksp. Teor. Fiz. 1940, 10, 723– 739Google ScholarThere is no corresponding record for this reference.
- 137Huzinaga, S.; Cantu, A. A. Theory of separability of many-electron systems. J. Chem. Phys. 1971, 55, 5543– 5549, DOI: 10.1063/1.1675720Google Scholar137https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE38Xhsl2ruw%253D%253D&md5=57073e274c58fc9dd1649b90d089272cTheory of separability of many-electron systemsHuzinaga, S.; Cantu, A. A.Journal of Chemical Physics (1971), 55 (12), 5543-9CODEN: JCPSA6; ISSN:0021-9606.At. and mol. systems are often intuitively sepd. into almost independent subsystems as, for example, the core and valence parts of an atom. Consequently, if this sepn. provides a good approxn., one can obtain the states of the system from the states of the subsystems which best represent the entire system. In the light of the work of McWeeny, in which one assumes strong orthogonality among subsystem wavefunctions, an effective Hamiltonian is detd. for a given subsystem which should properly describe the states of that subsystem. Previous work has dealt with an improper effective Hamiltonian.
- 138FDA expands approved use of Imbruvica for rare form of non-Hodgkin lymphoma. FDA News Release, U.S. Department of Health and Human Services, 2015;https://wayback.archive-it.org/7993/20170112222810/http://www.fda.gov/NewsEvents/Newsroom/PressAnnouncements/ucm432123.htm (accessed 2022-03-02).Google ScholarThere is no corresponding record for this reference.
- 139Honigberg, L. A.; Smith, A. M.; Sirisawad, M.; Verner, E.; Loury, D.; Chang, B.; Li, S.; Pan, Z.; Thamm, D. H.; Miller, R. A.; Buggy, J. J. The Bruton tyrosine kinase inhibitor PCI-32765 blocks B-cell activation and is efficacious in models of autoimmune disease and B-cell malignancy. Proc. Natl. Acad. Sci. 2010, 107, 13075– 13080, DOI: 10.1073/pnas.1004594107Google Scholar139https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXpsVCrsbk%253D&md5=196ce4a05bb9c622c49cb7e908682e63The Bruton tyrosine kinase inhibitor PCI-32765 blocks B-cell activation and is efficacious in models of autoimmune disease and B-cell malignancyHonigberg, Lee A.; Smith, Ashley M.; Sirisawad, Mint; Verner, Erik; Loury, David; Chang, Betty; Li, Shyr; Pan, Zhengying; Thamm, Douglas H.; Miller, Richard A.; Buggy, Joseph J.Proceedings of the National Academy of Sciences of the United States of America (2010), 107 (29), 13075-13080, S13075/1-S13075/3CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Activation of the B-cell antigen receptor (BCR) signaling pathway contributes to the initiation and maintenance of B-cell malignancies and autoimmune diseases. The Bruton tyrosine kinase (Btk) is specifically required for BCR signaling as demonstrated by human and mouse mutations that disrupt Btk function and prevent B-cell maturation at steps that require a functional BCR pathway. Herein we describe a selective and irreversible Btk inhibitor, PCI-32765, that is currently under clin. development in patients with B-cell non-Hodgkin lymphoma. We have used this inhibitor to investigate the biol. effects of Btk inhibition on mature B-cell function and the progression of B cell-assocd. diseases in vivo. PCI-32765 blocked BCR signaling in human peripheral B cells at concns. that did not affect T cell receptor signaling. In mice with collagen-induced arthritis, orally administered PCI-32765 reduced the level of circulating autoantibodies and completely suppressed disease. PCI-32765 also inhibited autoantibody prodn. and the development of kidney disease in the MRL-Fas(lpr) lupus model. Occupancy of the Btk active site by PCI-32765 was monitored in vitro and in vivo using a fluorescent affinity probe for Btk. Active site occupancy of Btk was tightly correlated with the blockade of BCR signaling and in vivo efficacy. Finally, PCI-32765 induced objective clin. responses in dogs with spontaneous B-cell non-Hodgkin lymphoma. These findings support Btk inhibition as a therapeutic approach for the treatment of human diseases assocd. with activation of the BCR pathway.
- 140Voice, A. T.; Tresadern, G.; Twidale, R. M.; van Vlijmen, H.; Mulholland, A. J. Mechanism of covalent binding of ibrutinib to Bruton’s tyrosine kinase revealed by QM/MM calculations. Chem. Sci. 2021, 12, 5511– 5516, DOI: 10.1039/D0SC06122KGoogle Scholar140https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit12gsLw%253D&md5=336c200963268af5fa8dd38e6494937dMechanism of covalent binding of ibrutinib to Bruton's tyrosine kinase revealed by QM/MM calculationsVoice, Angus T.; Tresadern, Gary; Twidale, Rebecca M.; van Vlijmen, Herman; Mulholland, Adrian J.Chemical Science (2021), 12 (15), 5511-5516CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)Ibrutinib is the first covalent inhibitor of Bruton's tyrosine kinase (BTK) to be used in the treatment of B-cell cancers. Understanding the mechanism of covalent inhibition will aid in the design of safer and more selective covalent inhibitors that target BTK. The mechanism of covalent inhibition in BTK has been uncertain because there is no appropriate residue nearby that can act as a base to deprotonate the cysteine thiol prior to covalent bond formation. We investigate several mechanisms of covalent modification of C481 in BTK by ibrutinib using combined quantum mechanics/mol. mechanics (QM/MM) mol. dynamics reaction simulations. The lowest energy pathway involves direct proton transfer from C481 to the acrylamide warhead in ibrutinib, followed by covalent bond formation to form an enol intermediate. There is a subsequent rate-limiting keto-enol tautomerisation step (ΔG‡ = 10.5 kcal mol-1) to reach the inactivated BTK/ibrutinib complex. Our results represent the first mechanistic study of BTK inactivation by ibrutinib to consider multiple mechanistic pathways. These findings should aid in the design of covalent drugs that target BTK and other similar targets.
- 141Lodola, A.; Callegari, D.; Scalvini, L.; Rivara, S.; Mor, M. Design and SAR Analysis of Covalent Inhibitors Driven by Hybrid QM/MM Simulations. In Quantum Mechanics in Drug Discovery; Heifetz, A., Ed.; Methods in Molecular Biology, Vol. 2114; Springer, 2020; pp 307– 337. DOI: 10.1007/978-1-0716-0282-9_19 .Google ScholarThere is no corresponding record for this reference.
- 142Ahmadi, S.; Barrios Herrera, L.; Chehelamirani, M.; Hostaš, J.; Jalife, S.; Salahub, D. R. Multiscale modeling of enzymes: QM-cluster, QM/MM, and QM/MM/MD: A tutorial review. Int. J. Quantum Chem. 2018, 118, e25558, DOI: 10.1002/qua.25558Google ScholarThere is no corresponding record for this reference.
- 143Cerqueira, N. M. F. S. A.; Moorthy, H.; Fernandes, P. A.; Ramos, M. J. The mechanism of the Ser-(cis)Ser-Lys catalytic triad of peptide amidases. Phys. Chem. Chem. Phys. 2017, 19, 12343– 12354, DOI: 10.1039/C7CP00277GGoogle Scholar143https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXltl2msbc%253D&md5=c03a3c1e78efa7a8e7f4907159ea5afcThe mechanism of the Ser-(cis)Ser-Lys catalytic triad of peptide amidasesCerqueira, N. M. F. S. A.; Moorthy, H.; Fernandes, P. A.; Ramos, M. J.Physical Chemistry Chemical Physics (2017), 19 (19), 12343-12354CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)In this paper, we report a theor. investigation of the catalytic mechanism of peptide amidases that involve a Ser-(cis)Ser-Lys catalytic triad. Previous suggestions proposed that these enzymes should follow a distinct catalytic mechanism from the one that is present in the classic Ser-His-Asp catalytic triad. The theor. and computational results obtained in this work indicated the opposite idea, showing that both mechanisms are very similar and only few differences were obsd. between both reactions. In this study, we used malonamidase E2 as a template to study the catalytic mechanism involved in amidases and the role that the unusual catalytic triad formed by Ser-(cis)Ser-Lys plays in catalysis. The results revealed that the different alignment of the Ser-(cis)Ser-Lys catalytic triad in relation to the classical Ser-His-Asp triad may provide a better stabilization of the reaction intermediates, and therefore make these enzymes catalytically more efficient. The catalytic mechanism was detd. at the M06-2X/6-311++G**//B3LYP/6-31G* level of theory and required 5 sequential steps instead of the 2 that are generally proposed: (1) nucleophilic attack of serine on the carbonyl group of the substrate, forming the 1st tetrahedral intermediate; (2) formation of an acyl-enzyme complex; (3) release of an ammonia product; (4) nucleophilic attack of a water mol. forming the 2nd tetrahedral intermediate; and (5) the release of the product of the reaction, the carboxylic acid. The computational results suggested that the rate-limiting step is the 1st one that requires an activation free energy of 15.93 kcal/mol. This result agreed very well with the available exptl. data that predict a reaction rate of 2200 s-1, which corresponds to a free energy barrier of 14 kcal/mol.
- 144Prejanó, M.; Marino, T.; Russo, N. QM Cluster or QM/MM in Computational Enzymology: The Test Case of LigW-Decarboxylase. Front. Chem. 2018, 6, 249, DOI: 10.3389/fchem.2018.00249Google Scholar144https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisFaisbjE&md5=4245e072bdd1cd651ec5a2b12c7801d4QM cluster or QM/MM in computational enzymology: the test case of LigW-decarboxylasePrejano, Mario; Marino, Tiziana; Russo, NinoFrontiers in Chemistry (Lausanne, Switzerland) (2018), 6 (), 249/1-249/9CODEN: FCLSAA; ISSN:2296-2646. (Frontiers Media S.A.)The catalytic mechanism of the decarboxylation of 5-carboxyvanillate by LigWproducing vanillic acid has been studied by using QM cluster and hybrid QM/MM methodologies. In the QM cluster model, the environment of a small QM model is treated with a bulky potential while two QM/MM models studies include partial and full protein with and without explicitly treated water solvent. The studied reaction involves two sequential steps: the protonation of the carbon of the 5-carboxy-vanillate substrate and the decarboxylation of the intermediate from which results deprotonated vanillic acid as product. The structures and energetics obtained by using three structural models and two d. functionals are quite consistent to each other. This indicates that the small QM cluster model of the presently considered enzymic reaction is appropriate enough and the reaction is mainly influenced by the active site.
- 145Blomberg, M. R. A. The structure of the oxidized state of cytochrome c oxidase - experiments and theory compared. J. Inorg. Biochem. 2020, 206, 111020, DOI: 10.1016/j.jinorgbio.2020.111020Google Scholar145https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXjsVOlsL0%253D&md5=a8d9af3fac3922ee4507ad42a5b5d043The structure of the oxidized state of cytochrome c oxidase - experiments and theory comparedBlomberg, Margareta R. A.Journal of Inorganic Biochemistry (2020), 206 (), 111020CODEN: JIBIDJ; ISSN:0162-0134. (Elsevier)Cytochrome c oxidase (CcO), the terminal enzyme in the respiratory chain, reduces mol. oxygen to water. Exptl. data on the midpoint potentials of the heme iron/copper active site cofactors do not match the overall reaction energetics, and are also in conflict with the obsd. efficiency of energy conservation in CcO. Therefore it has been postulated that the ferric/cupric intermediate (the oxidized state) exists in two forms. One form, labeled OH, is presumably involved during catalytic turnover, and should have a high CuB midpoint potential due to a metastable high energy structure. When no more electrons are supplied, the OH state supposedly relaxes to the resting form, labeled O, with a lower energy and a lower midpoint potential. It has been suggested that there is a pure geometrical difference between the OH and O states, obtained by moving a water mol. inside the active site. It is shown here that the difference between the two forms of the oxidized state must be of a more chem. nature. The reason is that all types of geometrically relaxed structures of the oxidized intermediate have similar energies, all with a high proton coupled redn. potential in accordance with the postulated OH state. One hypothesized chem. modification of the OH state is the transfer of an extra proton, possibly internal, into the active site. Such a protonated state has several properties that agree with exptl. data on the relaxed oxidized state, including a decreased midpoint potential.
- 146Bender, A. T.; Gardberg, A.; Pereira, A.; Johnson, T.; Wu, Y.; Grenningloh, R.; Head, J.; Morandi, F.; Haselmayer, P.; Liu-Bujalski, L. Ability of Bruton’s Tyrosine Kinase Inhibitors to Sequester Y551 and Prevent Phosphorylation Determines Potency for Inhibition of Fc Receptor but not B-Cell Receptor Signaling. Mol. Pharmacol. 2017, 91, 208– 219, DOI: 10.1124/mol.116.107037Google Scholar146https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXpsFajtr8%253D&md5=f869d52d6bc1aabf352988787ff1cbcfAbility of Bruton's tyrosine kinase inhibitors to sequester Y551 and prevent phosphorylation determines potency for inhibition of Fc receptor but not B-cell receptor signalingBender, Andrew T.; Gardberg, Anna; Pereira, Albertina; Johnson, Theresa; Wu, Yin; Grenningloh, Roland; Head, Jared; Morandi, Federica; Haselmayer, Philipp; Liu-Bujalski, LesleyMolecular Pharmacology (2017), 91 (3), 208-219CODEN: MOPMA3; ISSN:1521-0111. (American Society for Pharmacology and Experimental Therapeutics)Bruton's tyrosine kinase (Btk) is expressed in a variety of hematopoietic cells. Btk has been demonstrated to regulate signaling downstream of the B-cell receptor (BCR), Fc receptors (FcRs), and toll-like receptors. It has become an attractive drug target because its inhibition may provide significant efficacy by simultaneously blocking multiple disease mechanisms. Consequently, a large no. of Btk inhibitors have been developed. These compds. have diverse binding modes, and both reversible and irreversible inhibitors have been developed. Reported herein, we have tested nine Btk inhibitors and characterized on a mol. level how their interactions with Btk define their ability to block different signaling pathways. By solving the crystal structures of Btk inhibitors bound to the enzyme, we discovered that the compds. can be classified by their ability to trigger sequestration of Btk residue Y551. In cells, we found that sequestration of Y551 renders it inaccessible for phosphorylation. The ability to sequester Y551 was an important determinant of potency against FcγR signaling as Y551 sequestering compds. were more potent for inhibiting basophils and mast cells. This result was true for the inhibition of FcγR signaling as well. In contrast, Y551 sequestration was less a factor in detg. potency against BCR signaling. We also found that Btk activity is regulated differentially in basophils and B cells. These results elucidate important determinants for Btk inhibitor potency against different signaling pathways and provide insight for designing new compds. with a broader inhibitory profile that will likely result in greater efficacy.
- 147Maestro, Release 2021-3; Schrödinger: New York, NY, 2021.Google ScholarThere is no corresponding record for this reference.
- 148Madhavi Sastry, G.; Adzhigirey, M.; Day, T.; Annabhimoju, R.; Sherman, W. Protein and ligand preparation: parameters, protocols, and influence on virtual screening enrichments. J. Comput.-Aided Mol. Des. 2013, 27, 221– 234, DOI: 10.1007/s10822-013-9644-8Google Scholar148https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXmslalu7c%253D&md5=259a6d547ef3e1310e091fb50fe8de16Protein and ligand preparation: parameters, protocols, and influence on virtual screening enrichmentsMadhavi Sastry, G.; Adzhigirey, Matvey; Day, Tyler; Annabhimoju, Ramakrishna; Sherman, WoodyJournal of Computer-Aided Molecular Design (2013), 27 (3), 221-234CODEN: JCADEQ; ISSN:0920-654X. (Springer)Structure-based virtual screening plays an important role in drug discovery and complements other screening approaches. In general, protein crystal structures are prepd. prior to docking in order to add hydrogen atoms, optimize hydrogen bonds, remove at. clashes, and perform other operations that are not part of the x-ray crystal structure refinement process. In addn., ligands must be prepd. to create 3-dimensional geometries, assign proper bond orders, and generate accessible tautomer and ionization states prior to virtual screening. While the prerequisite for proper system prepn. is generally accepted in the field, an extensive study of the prepn. steps and their effect on virtual screening enrichments has not been performed. In this work, we systematically explore each of the steps involved in prepg. a system for virtual screening. We first explore a large no. of parameters using the Glide validation set of 36 crystal structures and 1,000 decoys. We then apply a subset of protocols to the DUD database. We show that database enrichment is improved with proper prepn. and that neglecting certain steps of the prepn. process produces a systematic degrdn. in enrichments, which can be large for some targets. We provide examples illustrating the structural changes introduced by the prepn. that impact database enrichment. While the work presented here was performed with the Protein Prepn. Wizard and Glide, the insights and guidance are expected to be generalizable to structure-based virtual screening with other docking methods.
- 149Jacobson, M. P.; Pincus, D. L.; Rapp, C. S.; Day, T. J. F.; Honig, B.; Shaw, D. E.; Friesner, R. A. A hierarchical approach to all-atom protein loop prediction. Proteins: Struct., Funct., Bioinf. 2004, 55, 351– 367, DOI: 10.1002/prot.10613Google Scholar149https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXjtFKhsrc%253D&md5=e0eff655eeefb30ea00ae041ea9099c8A hierarchical approach to all-atom protein loop predictionJacobson, Matthew P.; Pincus, David L.; Rapp, Chaya S.; Day, Tyler J. F.; Honig, Barry; Shaw, David E.; Friesner, Richard A.Proteins: Structure, Function, and Bioinformatics (2004), 55 (2), 351-367CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)The application of all-atom force fields (and explicit or implicit solvent models) to protein homol.-modeling tasks such as side-chain and loop prediction remains challenging both because of the expense of the individual energy calcns. and because of the difficulty of sampling the rugged all-atom energy surface. Here the authors address this challenge for the problem of loop prediction through the development of numerous new algorithms, with an emphasis on multiscale and hierarchical techniques. As a first step in evaluating the performance of the authors' loop prediction algorithm, the authors have applied it to the problem of reconstructing loops in native structures; the authors also explicitly include crystal packing to provide a fair comparison with crystal structures. In brief, large nos. of loops are generated by using a dihedral angle-based buildup procedure followed by iterative cycles of clustering, side-chain optimization, and complete energy minimization of selected loop structures. The authors evaluate this method by the largest test set yet used for validation of a loop prediction method, with a total of 833 loops ranging from 4 to 12 residues in length. Av./median backbone root-mean-square deviations (RMSDs) to the native structures (superimposing the body of the protein, not the loop itself) are 0.42/0.24 Å for 5 residue loops, 1.00/0.44 Å for 8 residue loops, and 2.47/1.83 Å for 11 residue loops. Median RMSDs are substantially lower than the avs. because of a small no. of outliers; the causes of these failures are examd. in some detail, and many can be attributed to errors in assignment of protonation states of titratable residues, omission of ligands from the simulation, and, in a few cases, probable errors in the exptl. detd. structures. When these obvious problems in the data sets are filtered out, av. RMSDs to the native structures improve to 0.43 Å for 5 residue loops, 0.84 Å for 8 residue loops, and 1.63 Å for 11 residue loops. In the vast majority of cases, the method locates energy min. that are lower than or equal to that of the minimized native loop, thus indicating that sampling rarely limits prediction accuracy. The overall results are, to the authors' knowledge, the best reported to date, and the authors attribute this success to the combination of an accurate all-atom energy function, efficient methods for loop buildup and side-chain optimization, and, esp. for the longer loops, the hierarchical refinement protocol.
- 150Jacobson, M. P.; Friesner, R. A.; Xiang, Z.; Honig, B. On the Role of the Crystal Environment in Determining Protein Side-chain Conformations. J. Mol. Biol. 2002, 320, 597– 608, DOI: 10.1016/S0022-2836(02)00470-9Google Scholar150https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD38XltVKmu70%253D&md5=006de6bd2d0f233ab32d6798dc1a3fbcOn the Role of the Crystal Environment in Determining Protein Side-chain ConformationsJacobson, Matthew P.; Friesner, Richard A.; Xiang, Zhexin; Honig, BarryJournal of Molecular Biology (2002), 320 (3), 597-608CODEN: JMOBAK; ISSN:0022-2836. (Elsevier Science Ltd.)The role of crystal packing in detg. the obsd. conformations of amino acid side-chains in protein crystals is investigated by (1) anal. of a database of proteins that have been crystd. in different unit cells (space group or unit cell dimensions) and (2) theor. predictions of side-chain conformations with the crystal environment explicitly represented. Both of these approaches indicate that the crystal environment plays an important role in detg. the conformations of polar side-chains on the surfaces of proteins. Inclusion of the crystal environment permits a more sensitive measurement of the achievable accuracy of side-chain prediction programs, when validating against structures obtained by x-ray crystallog. Our side-chain prediction program uses an all-atom force field and a Generalized Born model of solvation and is thus capable of modeling simple packing effects (i.e. van der Waals interactions), electrostatic effects, and desolvation, which are all important mechanisms by which the crystal environment impacts obsd. side-chain conformations. Our results are also relevant to the understanding of changes in side-chain conformation that may result from ligand docking and protein-protein assocn., insofar as the results reveal how side-chain conformations change in response to their local environment.
- 151Søndergaard, C. R.; Olsson, M. H. M.; Rostkowski, M.; Jensen, J. H. Improved Treatment of Ligands and Coupling Effects in Empirical Calculation and Rationalization of pKa Values. J. Chem. Theory Comput. 2011, 7, 2284– 2295, DOI: 10.1021/ct200133yGoogle Scholar151https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXnt1Gnsrs%253D&md5=cf4d4e20d6daa70de6ac623915e78160Improved Treatment of Ligands and Coupling Effects in Empirical Calculation and Rationalization of pKa ValuesSondergaard, Chresten R.; Olsson, Mats H. M.; Rostkowski, Michal; Jensen, Jan H.Journal of Chemical Theory and Computation (2011), 7 (7), 2284-2295CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)The new empirical rules for protein pKa predictions implemented in the PROPKA3.0 software package have been extended to the prediction of pKa shifts of active site residues and ionizable ligand groups in protein-ligand complexes. The authors present new algorithms that allow pKa shifts due to inductive (i.e., covalently coupled) intraligand interactions, as well as noncovalently coupled interligand interactions in multiligand complexes, to be included in the prediction. The no. of different ligand chem. groups that are automatically recognized has been increased to 18, and the general implementation has been changed so that new functional groups can be added easily by the user, aided by a new and more general protonation scheme. Except for a few cases, the new algorithms in PROPKA3.1 are found to yield results similar to or better than those obtained with PROPKA2.0. Finally, the authors present a novel algorithm that identifies noncovalently coupled ionizable groups, where pKa prediction may be esp. difficult. This is a general improvement to PROPKA and is applied to proteins with and without ligands.
- 152Olsson, M. H. M.; Søndergaard, C. R.; Rostkowski, M.; Jensen, J. H. PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa Predictions. J. Chem. Theory Comput. 2011, 7, 525– 537, DOI: 10.1021/ct100578zGoogle Scholar152https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXit1aqsA%253D%253D&md5=9b1666b1c56e1129789e62948eb4d001PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa PredictionsOlsson, Mats H. M.; Sondergaard, Chresten R.; Rostkowski, Michal; Jensen, Jan H.Journal of Chemical Theory and Computation (2011), 7 (2), 525-537CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)The authors have revised the rules and parameters for one of the most commonly used empirical pKa predictors, PROPKA, based on better phys. description of the desolvation and dielec. response for the protein. The authors have introduced a new and consistent approach to interpolate the description between the previously distinct classifications into internal and surface residues, which otherwise is found to give rise to an erratic and discontinuous behavior. Since the goal of this study is to lay out the framework and validate the concept, it focuses on Asp and Glu residues where the protein pKa values and structures are assumed to be more reliable. The new and improved implementation is evaluated and discussed; it is found to agree better with expt. than the previous implementation (in parentheses): rmsd = 0.79 (0.91) for Asp and Glu, 0.75 (0.97) for Tyr, 0.65 (0.72) for Lys, and 1.00 (1.37) for His residues. The most significant advance, however, is in reducing the no. of outliers and removing unreasonable sensitivity to small structural changes that arise from classifying residues as either internal or surface.
- 153Bochevarov, A. D.; Harder, E.; Hughes, T. F.; Greenwood, J. R.; Braden, D. A.; Philipp, D. M.; Rinaldo, D.; Halls, M. D.; Zhang, J.; Friesner, R. A. Jaguar: A high-performance quantum chemistry software program with strengths in life and materials sciences. Int. J. Quantum Chem. 2013, 113, 2110– 2142, DOI: 10.1002/qua.24481Google Scholar153https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhtVCqs7%252FP&md5=2fc119bb9e0501e55d7292f7735c24eaJaguar: A high-performance quantum chemistry software program with strengths in life and materials sciencesBochevarov, Art D.; Harder, Edward; Hughes, Thomas F.; Greenwood, Jeremy R.; Braden, Dale A.; Philipp, Dean M.; Rinaldo, David; Halls, Mathew D.; Zhang, Jing; Friesner, Richard A.International Journal of Quantum Chemistry (2013), 113 (18), 2110-2142CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)A review. Jaguar is an ab initio quantum chem. program that specializes in fast electronic structure predictions for mol. systems of medium and large size. Jaguar focuses on computational methods with reasonable computational scaling with the size of the system, such as d. functional theory (DFT) and local second-order Moller-Plesset perturbation theory. The favorable scaling of the methods and the high efficiency of the program make it possible to conduct routine computations involving several thousand MOs. This performance is achieved through a utilization of the pseudospectral approxn. and several levels of parallelization. The speed advantages are beneficial for applying Jaguar in biomol. computational modeling. Addnl., owing to its superior wave function guess for transition-metal-contg. systems, Jaguar finds applications in inorg. and bioinorg. chem. The emphasis on larger systems and transition metal elements paves the way toward developing Jaguar for its use in materials science modeling. The article describes the historical and new features of Jaguar, such as improved parallelization of many modules, innovations in ab initio pKa prediction, and new semiempirical corrections for nondynamic correlation errors in DFT. Jaguar applications in drug discovery, materials science, force field parameterization, and other areas of computational research are reviewed. Timing benchmarks and other results obtained from the most recent Jaguar code are provided. The article concludes with a discussion of challenges and directions for future development of the program. © 2013 Wiley Periodicals, Inc.
- 154Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648– 5652, DOI: 10.1063/1.464913Google Scholar154https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3sXisVWgtrw%253D&md5=291bbfc119095338bb1624f0c21c7ca8Density-functional thermochemistry. III. The role of exact exchangeBecke, Axel D.Journal of Chemical Physics (1993), 98 (7), 5648-52CODEN: JCPSA6; ISSN:0021-9606.Despite the remarkable thermochem. accuracy of Kohn-Sham d.-functional theories with gradient corrections for exchange-correlation, the author believes that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional (contg. local-spin-d., gradient, and exact-exchange terms) is tested for 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total at. energies of first- and second-row systems. This functional performs better than previous functionals with gradient corrections only, and fits expt. atomization energies with an impressively small av. abs. deviation of 2.4 kcal/mol.
- 155Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785– 789, DOI: 10.1103/PhysRevB.37.785Google Scholar155https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL1cXktFWrtbw%253D&md5=ee7b59267a2ff72e15171a481819ccf8Development of the Colle-Salvetti correlation-energy formula into a functional of the electron densityLee, Chengteh; Yang, Weitao; Parr, Robert G.Physical Review B: Condensed Matter and Materials Physics (1988), 37 (2), 785-9CODEN: PRBMDO; ISSN:0163-1829.A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
- 156Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104, DOI: 10.1063/1.3382344Google Scholar156https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXkvVyks7o%253D&md5=2bca89d904579d5565537a0820dc2ae8A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-PuGrimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, HelgeJournal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
- 157Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 2011, 32, 1456– 1465, DOI: 10.1002/jcc.21759Google Scholar157https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXjsF2isL0%253D&md5=370c4fe3164f548718b4bfcf22d1c753Effect of the damping function in dispersion corrected density functional theoryGrimme, Stefan; Ehrlich, Stephan; Goerigk, LarsJournal of Computational Chemistry (2011), 32 (7), 1456-1465CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)It is shown by an extensive benchmark on mol. energy data that the math. form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a std. "zero-damping" formula and rational damping to finite values for small interat. distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coeffs. is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interat. forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramol. dispersion in four representative mol. structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermol. distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of cor. GGAs for non-covalent interactions. According to the thermodn. benchmarks BJ-damping is more accurate esp. for medium-range electron correlation problems and only small and practically insignificant double-counting effects are obsd. It seems to provide a phys. correct short-range behavior of correlation/dispersion even with unmodified std. functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying d. functional. © 2011 Wiley Periodicals, Inc.; J. Comput. Chem., 2011.
- 158Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model. J. Comput. Chem. 2003, 24, 669– 681, DOI: 10.1002/jcc.10189Google Scholar158https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3sXivFWqsbc%253D&md5=570ef9f44e925c9f78de6c7d97123229Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation modelCossi, Maurizio; Rega, Nadia; Scalmani, Giovanni; Barone, VincenzoJournal of Computational Chemistry (2003), 24 (6), 669-681CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)The conductor-like solvation model, as developed in the framework of the polarizable continuum model (PCM), has been reformulated and newly implemented in order to compute energies, geometric structures, harmonic frequencies, and electronic properties in soln. for any chem. system that can be studied in vacuo. Particular attention is devoted to large systems requiring suitable iterative algorithms to compute the solvation charges: the fast multipole method (FMM) has been extensively used to ensure a linear scaling of the computational times with the size of the solute. A no. of test applications are presented to evaluate the performances of the method.
- 159Siegbahn, P. E. M.; Blomberg, M. R. A. Transition-Metal Systems in Biochemistry Studied by High-Accuracy Quantum Chemical Methods. Chem. Rev. 2000, 100, 421– 438, DOI: 10.1021/cr980390wGoogle Scholar159https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXjsFWisg%253D%253D&md5=ee55482e699d746842043c3fdd6db243Transition-Metal Systems in Biochemistry Studied by High-Accuracy Quantum Chemical MethodsSiegbahn, Per E. M.; Blomberg, Margareta R. A.Chemical Reviews (Washington, D. C.) (2000), 100 (2), 421-437CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review with 112 refs. Topics discussed include: quantum mech. methods; dielec. methods; reaction mechanisms; O2 activation in cytochrome c oxidase; water oxidn. in photosystem II; nitrogenases; hydrogenases; cytochrome P 450; heme peroxidases; non-heme oxygenases; molybdenum oxotransferases; iron-sulfur proteins; superoxide dismutases; spectroscopic applications; electronic spectra; spin-spin spectra.
- 160Siegbahn, P. E. M.; Himo, F. The quantum chemical cluster approach for modeling enzyme reactions. WIREs Comput. Mol. Sci. 2011, 1, 323– 336, DOI: 10.1002/wcms.13Google Scholar160https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmt1KgsLY%253D&md5=584f66ef32b8337de3933aace50ae0c7The quantum chemical cluster approach for modeling enzyme reactionsSiegbahn, Per E. M.; Himo, FahmiWiley Interdisciplinary Reviews: Computational Molecular Science (2011), 1 (3), 323-356CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)A review. The authors describe the general concepts behind the quantum chem. cluster approach for modeling enzyme active sites and reaction mechanisms. First, the underlying DFT electronic structure method is briefly recapitulated. The cluster methodol. is then discussed, including the important observation on the convergence of the solvation effects. The concepts are illustrated using examples from recent applications, such as the discrimination between different reaction mechanisms in phosphotriesterase, the elucidation of origins of regioselectivity in the epoxide-opening reaction of haloalc. dehalogenase, and finally the use of the cluster methodol. to establish the detailed structure of the O2-evolving complex in photosystem II.
- 161Neese, F. Software update: the ORCA program system, version 4.0. WIREs Comput. Mol. Sci. 2017, 8, e1327, DOI: 10.1002/wcms.1327Google ScholarThere is no corresponding record for this reference.
- 162Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297– 305, DOI: 10.1039/b508541aGoogle Scholar162https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXpsFWgu7o%253D&md5=a820fb6055c993b50c405ba0fc62b194Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracyWeigend, Florian; Ahlrichs, ReinhartPhysical Chemistry Chemical Physics (2005), 7 (18), 3297-3305CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 mols. representing (nearly) all elements-except lanthanides-in their common oxidn. states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, d. functional theory and correlated methods, for which we had chosen Moller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.
- 163Pipek, J.; Mezey, P. G. A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions. J. Chem. Phys. 1989, 90, 4916– 4926, DOI: 10.1063/1.456588Google Scholar163https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL1MXks1Cht7w%253D&md5=c983656b61c0ec520ce20cd8773f87c6A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functionsPipek, Janos; Mezey, Paul G.Journal of Chemical Physics (1989), 90 (9), 4916-26CODEN: JCPSA6; ISSN:0021-9606.A new intrinsic localization algorithm is suggested based on a recently developed math. measure of localization. No external criteria are used to define a priori bonds, lone pairs, and core orbitals. The method similarly to Edmiston-Ruedenberg's localization prefers the well established chem. concept of σ-π sepn., while on the other hand, works as economically as Boys' procedure. For the applications of the new localization algorithm, no addnl. quantities are to be calcd., the knowledge of at. overlap integrals is sufficient. This feature allows a unique formulation of the theory, adaptable for both ab initio and semiempirical methods, even in those cases where the exact form of the at. basis functions is not defined (line in the EHT and PPP calcns). The implementation of the procedure in already existing program systems is particularly easy. The Emiston-Ruedenberg and Boys localized orbitals are compared with those calcd. by the method suggested here, within both the CNDO/2 and ab initio frameworks (using STO-3G and 6-31G** basis sets) for several mols. (CO, H2CO, B2H6, and N2O4).
- 164Knizia, G. Intrinsic atomic orbitals: An unbiased bridge between quantum theory and chemical concepts. J. Chem. Theory Comput. 2013, 9, 4834– 4843, DOI: 10.1021/ct400687bGoogle Scholar164https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhtlKktbzO&md5=4a225fb6e6e8ccfef6f71d8848ced2e3Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical ConceptsKnizia, GeraldJournal of Chemical Theory and Computation (2013), 9 (11), 4834-4843CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Modern quantum chem. can make quant. predictions on an immense array of chem. systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an exceptionally simple algebraic construction allows for defining at. core and valence orbitals, polarized by the mol. environment, which can exactly represent SCF wave functions. This construction provides an unbiased and direct connection between quantum chem. and empirical chem. concepts, and can be used, for example, to calc. the nature of bonding in mols., in chem. terms, from first principles. In particular, we find consistency with electronegativities (χ), C 1s core-level shifts, resonance substituent parameters (σR), Lewis structures, and oxidn. states of transition-metal complexes.
- 165IBM Quantum breaks the 100-qubit processor barrier. IBM, 2021; https://research.ibm.com/blog/127-qubit-quantum-processor-eagle (accessed 2022-03-02).Google ScholarThere is no corresponding record for this reference.
- 166Google Quantum AI. Suppressing quantum errors by scaling a surface code logical qubit. arXiv Preprint (Quantum Physics) , 2022. arXiv:2207.06431. https://doi.org/10.48550/arXiv.2207.06431.Google ScholarThere is no corresponding record for this reference.
- 167Wright, K.; Beck, K. M.; Debnath, S.; Amini, J. M.; Nam, Y.; Grzesiak, N.; Chen, J.-S.; Pisenti, N. C.; Chmielewski, M.; Collins, C.; Hudek, K. M.; Mizrahi, J.; Wong-Campos, J. D.; Allen, S.; Apisdorf, J.; Solomon, P.; Williams, M.; Ducore, A. M.; Blinov, A.; Kreikemeier, S. M.; Chaplin, V.; Keesan, M.; Monroe, C.; Kim, J. Benchmarking an 11-qubit quantum computer. Nat. Commun. 2019, 10, 5464, DOI: 10.1038/s41467-019-13534-2Google Scholar167https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3MfkvVylug%253D%253D&md5=410d9e4b9da02a978a97453755841fc2Benchmarking an 11-qubit quantum computerWright K; Beck K M; Debnath S; Amini J M; Nam Y; Grzesiak N; Chen J-S; Pisenti N C; Chmielewski M; Collins C; Hudek K M; Mizrahi J; Wong-Campos J D; Allen S; Apisdorf J; Solomon P; Williams M; Ducore A M; Blinov A; Kreikemeier S M; Chaplin V; Keesan M; Monroe C; Kim J; Chmielewski M; Monroe C; Kim JNature communications (2019), 10 (1), 5464 ISSN:.The field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum physics, and optimizing complex cost functions. Here, we present an 11-qubit fully-connected, programmable quantum computer in a trapped ion system composed of 13 (171)Yb(+) ions. We demonstrate average single-qubit gate fidelities of 99.5[Formula: see text], average two-qubit-gate fidelities of 97.5[Formula: see text], and SPAM errors of 0.7[Formula: see text]. To illustrate the capabilities of this universal platform and provide a basis for comparison with similarly-sized devices, we compile the Bernstein-Vazirani and Hidden Shift algorithms into our native gates and execute them on the hardware with average success rates of 78[Formula: see text] and 35[Formula: see text], respectively. These algorithms serve as excellent benchmarks for any type of quantum hardware, and show that our system outperforms all other currently available hardware.
- 168Erhard, A.; Poulsen Nautrup, H.; Meth, M.; Postler, L.; Stricker, R.; Stadler, M.; Negnevitsky, V.; Ringbauer, M.; Schindler, P.; Briegel, H. J.; Blatt, R.; Friis, N.; Monz, T. Entangling logical qubits with lattice surgery. Nature 2021, 589, 220– 224, DOI: 10.1038/s41586-020-03079-6Google Scholar168https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXht1Okt78%253D&md5=94be452bd20b03f3ddbac2d1de3b88faEntangling logical qubits with lattice surgeryErhard, Alexander; Poulsen Nautrup, Hendrik; Meth, Michael; Postler, Lukas; Stricker, Roman; Stadler, Martin; Negnevitsky, Vlad; Ringbauer, Martin; Schindler, Philipp; Briegel, Hans J.; Blatt, Rainer; Friis, Nicolai; Monz, ThomasNature (London, United Kingdom) (2021), 589 (7841), 220-224CODEN: NATUAS; ISSN:0028-0836. (Nature Research)Abstr.: The development of quantum computing architectures from early designs and current noisy devices to fully fledged quantum computers hinges on achieving fault tolerance using quantum error correction1-4. However, these correction capabilities come with an overhead for performing the necessary fault-tolerant logical operations on logical qubits (qubits that are encoded in ensembles of phys. qubits and protected by error-correction codes)5-8. One of the most resource-efficient ways to implement logical operations is lattice surgery9-11, where groups of phys. qubits, arranged on lattices, can be merged and split to realize entangling gates and teleport logical information. Here we report the exptl. realization of lattice surgery between two qubits protected via a topol. error-correction code in a ten-qubit ion-trap quantum information processor. In this system, we can carry out the necessary quantum non-demolition measurements through a series of local and entangling gates, as well as measurements on auxiliary qubits. In particular, we demonstrate entanglement between two logical qubits and we implement logical state teleportation between them. The demonstration of these operations-fundamental building blocks for quantum computation-through lattice surgery represents a step towards the efficient realization of fault-tolerant quantum computation.
- 169Dobšíček, M.; Johansson, G.; Shumeiko, V.; Wendin, G. Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark. Phys. Rev. A 2007, 76, 030306, DOI: 10.1103/PhysRevA.76.030306Google Scholar169https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXhtFCjur%252FP&md5=e770d796c283f36b1c41ead3cd6609d3Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmarkDobsicek, Miroslav; Johansson, Goran; Shumeiko, Vitaly; Wendin, GoranPhysical Review A: Atomic, Molecular, and Optical Physics (2007), 76 (3, Pt. A), 030306/1-030306/4CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)We discuss the implementation of an iterative quantum phase estn. algorithm with a single ancillary qubit. We suggest using this algorithm as a benchmark for multiqubit implementations. Furthermore, we describe in detail the smallest possible realization, using only two qubits, and exemplify with a superconducting circuit. We discuss the robustness of the algorithm in the presence of gate errors, and show that seven bits of precision is obtainable, even with very limited gate accuracies.
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Abstract
Figure 1
Figure 1. Outline of the VQE algorithm, indicating which parts occur on the quantum computer and which parts on the classical.
Figure 2
Figure 2. Outline of the circuit used to perform QPE, as discussed in ref (61).
Figure 3
Figure 3. (a) Layouts for 15-to-1 (top) and 20-to-4 (bottom) magic-state factories. These consist of 11 and 14 logical qubits, respectively (green). The magic states produced are stored in the blue spaces. (b) Factory which distills 225 imperfect magic states to one higher quality magic state. Eleven first-level 15-to-1 factories (green) are used to produce 15 refined magic states, which are in turn used by the second-level 15-to-1 factory (orange) to produce one magic state of even higher quality (red). Blue lines are used to store and transport lower-quality magic states. White spaces are unused logical qubits.
Figure 4
Figure 4. Fit of empirical law for our set of molecules. The fit is done in two steps. In the first step (left), for each of the molecules, we generate δE0 for τ/τmax = [1.0, 0.5, 0.1, 0.05, 0.01, 0.005, 0.001] and do a one-parameter fit of . Note that, for larger molecules, ϵ0 for small values of τ appear to deviate from the quadratic behavior. We attribute this to numerical error and exclude these values from the fits. In the second step (right), we plot a1 for each molecule and fit a1 = a(nq)b, obtaining the parameters of the empirical law in eq 38: a = 1.51 ± 0.84; b = −4.66 ± 0.27.
Figure 5
Figure 5. Cluster containing part of the binding pocket and the Ibrutinib inhibitor. The various fragments in which the active space orbitals were selected are indicated using various colors.
Figure 6
Figure 6. Runtime to perform QPE using sparse qubitization. Active spaces from (14e,14o) to (100e,100o) are considered. It is assumed that one time step takes 1 μs to perform. Physical error rates, p, of 0.01 and 0.1% are considered. The Hamiltonian is either truncated using an L2-norm criterion or a CCSD(T) criterion. In each case, the runtime scales as approximately no4.6 with the number of active orbitals.
Figure 7
Figure 7. Comparison of resources (runtime and total number of physical qubits) using two QPE algorithms. The first (orange) used qubitization, and the Hamiltonian was truncated to remove small terms up to an error budget. The second (green) used textbook QPE with Trotterization and no truncation of the Hamiltonian. The latter algorithm has a much steeper scaling in runtime. Even for a (14e,14o) active space the runtime is multiple orders of magnitude more expensive.
Figure 8
Figure 8. QPU layouts used to perform QPE experiments on the (32e,32o) active space example. Left: layout used for QPE with Trotterization. Right: Layout used for QPE with qubitization. Data block qubits are orange, magic-state factory qubits are green, and routing and storage qubits are blue. Qubitization uses many more data qubits such that the data block is much larger. However, the higher T-gate count in QPE with Trotterization necessitates larger magic-state factories (225-to-1) compared to those in qubitization (116-to-12). Axes are included to indicate the total number of logical qubits in both layouts, with each logical qubit having size 1-by-1. However, note that the code distance is higher in QPE with Trotterization (see Table 2) so that these are not to physical scale.
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- 8Quantinuum Announces Quantum Volume 4096 Achievement. Quantinuum, 2022; https://www.quantinuum.com/pressrelease/quantinuum-announces-quantum-volume-4096-achievement (accessed 2022-03-02).There is no corresponding record for this reference.
- 9Arute, F.; Arya, K.; Babbush, R.; Bacon, D.; Bardin, J. C.; Barends, R.; Biswas, R.; Boixo, S.; Brandao, F. G. S. L.; Buell, D. A.; Burkett, B.; Chen, Y.; Chen, Z.; Chiaro, B.; Collins, R.; Courtney, W.; Dunsworth, A.; Farhi, E.; Foxen, B.; Fowler, A.; Gidney, C.; Giustina, M.; Graff, R.; Guerin, K.; Habegger, S.; Harrigan, M. P.; Hartmann, M. J.; Ho, A.; Hoffmann, M.; Huang, T.; Humble, T. S.; Isakov, S. V.; Jeffrey, E.; Jiang, Z.; Kafri, D.; Kechedzhi, K.; Kelly, J.; Klimov, P. V.; Knysh, S.; Korotkov, A.; Kostritsa, F.; Landhuis, D.; Lindmark, M.; Lucero, E.; Lyakh, D.; Mandrá, S.; McClean, J. R.; McEwen, M.; Megrant, A.; Mi, X.; Michielsen, K.; Mohseni, M.; Mutus, J.; Naaman, O.; Neeley, M.; Neill, C.; Niu, M. Y.; Ostby, E.; Petukhov, A.; Platt, J. C.; Quintana, C.; Rieffel, E. G.; Roushan, P.; Rubin, N. C.; Sank, D.; Satzinger, K. J.; Smelyanskiy, V.; Sung, K. J.; Trevithick, M. D.; Vainsencher, A.; Villalonga, B.; White, T.; Yao, Z. J.; Yeh, P.; Zalcman, A.; Neven, H.; Martinis, J. M. Quantum supremacy using a programmable superconducting processor. Nature 2019, 574, 505– 510, DOI: 10.1038/s41586-019-1666-59https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitVagsb3I&md5=36849d6b5afa880d97c3ef892414e6aeQuantum supremacy using a programmable superconducting processorArute, Frank; Arya, Kunal; Babbush, Ryan; Bacon, Dave; Bardin, Joseph C.; Barends, Rami; Biswas, Rupak; Boixo, Sergio; Brandao, Fernando G. S. L.; Buell, David A.; Burkett, Brian; Chen, Yu; Chen, Zijun; Chiaro, Ben; Collins, Roberto; Courtney, William; Dunsworth, Andrew; Farhi, Edward; Foxen, Brooks; Fowler, Austin; Gidney, Craig; Giustina, Marissa; Graff, Rob; Guerin, Keith; Habegger, Steve; Harrigan, Matthew P.; Hartmann, Michael J.; Ho, Alan; Hoffmann, Markus; Huang, Trent; Humble, Travis S.; Isakov, Sergei V.; Jeffrey, Evan; Jiang, Zhang; Kafri, Dvir; Kechedzhi, Kostyantyn; Kelly, Julian; Klimov, Paul V.; Knysh, Sergey; Korotkov, Alexander; Kostritsa, Fedor; Landhuis, David; Lindmark, Mike; Lucero, Erik; Lyakh, Dmitry; Mandra, Salvatore; McClean, Jarrod R.; McEwen, Matthew; Megrant, Anthony; Mi, Xiao; Michielsen, Kristel; Mohseni, Masoud; Mutus, Josh; Naaman, Ofer; Neeley, Matthew; Neill, Charles; Niu, Murphy Yuezhen; Ostby, Eric; Petukhov, Andre; Platt, John C.; Quintana, Chris; Rieffel, Eleanor G.; Roushan, Pedram; Rubin, Nicholas C.; Sank, Daniel; Satzinger, Kevin J.; Smelyanskiy, Vadim; Sung, Kevin J.; Trevithick, Matthew D.; Vainsencher, Amit; Villalonga, Benjamin; White, Theodore; Yao, Z. Jamie; Yeh, Ping; Zalcman, Adam; Neven, Hartmut; Martinis, John M.Nature (London, United Kingdom) (2019), 574 (7779), 505-510CODEN: NATUAS; ISSN:0028-0836. (Nature Research)The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated expts. sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 s to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equiv. task for a state-of-the-art classical supercomputer would take approx. 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an exptl. realization of quantum supremacy8-14 for this specific computational task, heralding a much-anticipated computing paradigm.
- 10Wu, Y.; Bao, W.-S.; Cao, S.; Chen, F.; Chen, M.-C.; Chen, X.; Chung, T.-H.; Deng, H.; Du, Y.; Fan, D.; Gong, M.; Guo, C.; Guo, C.; Guo, S.; Han, L.; Hong, L.; Huang, H.-L.; Huo, Y.-H.; Li, L.; Li, N.; Li, S.; Li, Y.; Liang, F.; Lin, C.; Lin, J.; Qian, H.; Qiao, D.; Rong, H.; Su, H.; Sun, L.; Wang, L.; Wang, S.; Wu, D.; Xu, Y.; Yan, K.; Yang, W.; Yang, Y.; Ye, Y.; Yin, J.; Ying, C.; Yu, J.; Zha, C.; Zhang, C.; Zhang, H.; Zhang, K.; Zhang, Y.; Zhao, H.; Zhao, Y.; Zhou, L.; Zhu, Q.; Lu, C.-Y.; Peng, C.-Z.; Zhu, X.; Pan, J.-W. Strong Quantum Computational Advantage Using a Superconducting Quantum Processor. Phys. Rev. Lett. 2021, 127, 180501, DOI: 10.1103/PhysRevLett.127.18050110https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXis1SmtrbM&md5=9bdffc6d5b91a821244e5bab3762929aStrong Quantum Computational Advantage Using a Superconducting Quantum ProcessorWu, Yulin; Bao, Wan-Su; Cao, Sirui; Chen, Fusheng; Chen, Ming-Cheng; Chen, Xiawei; Chung, Tung-Hsun; Deng, Hui; Du, Yajie; Fan, Daojin; Gong, Ming; Guo, Cheng; Guo, Chu; Guo, Shaojun; Han, Lianchen; Hong, Linyin; Huang, He-Liang; Huo, Yong-Heng; Li, Liping; Li, Na; Li, Shaowei; Li, Yuan; Liang, Futian; Lin, Chun; Lin, Jin; Qian, Haoran; Qiao, Dan; Rong, Hao; Su, Hong; Sun, Lihua; Wang, Liangyuan; Wang, Shiyu; Wu, Dachao; Xu, Yu; Yan, Kai; Yang, Weifeng; Yang, Yang; Ye, Yangsen; Yin, Jianghan; Ying, Chong; Yu, Jiale; Zha, Chen; Zhang, Cha; Zhang, Haibin; Zhang, Kaili; Zhang, Yiming; Zhao, Han; Zhao, Youwei; Zhou, Liang; Zhu, Qingling; Lu, Chao-Yang; Peng, Cheng-Zhi; Zhu, Xiaobo; Pan, Jian-WeiPhysical Review Letters (2021), 127 (18), 180501CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)Scaling up to a large no. of qubits with high-precision control is essential in the demonstrations of quantum computational advantage to exponentially outpace the classical hardware and algorithmic improvements. Here, we develop a two-dimensional programmable superconducting quantum processor, Zuchongzhi, which is composed of 66 functional qubits in a tunable coupling architecture. To characterize the performance of the whole system, we perform random quantum circuits sampling for benchmarking, up to a system size of 56 qubits and 20 cycles. The computational cost of the classical simulation of this task is estd. to be 2-3 orders of magnitude higher than the previous work on 53-qubit Sycamore processor [Nature574, 505 (2019)NATUAS0028-083610.1038/s41586-019-1666-5. We est. that the sampling task finished by Zuchongzhi in about 1.2 h will take the most powerful supercomputer at least 8 yr. Our work establishes an unambiguous quantum computational advantage that is infeasible for classical computation in a reasonable amt. of time. The high-precision and programmable quantum computing platform opens a new door to explore novel many-body phenomena and implement complex quantum algorithms.
- 11Collins, H.; Easterly, K. IBM Unveils Breakthrough 127-Qubit Quantum Processor. IBM, 2021; https://newsroom.ibm.com/2021-11-16-IBM-Unveils-Breakthrough-127-Qubit-Quantum-Processor [accessed 2022-03-02].There is no corresponding record for this reference.
- 12Peruzzo, A.; McClean, J.; Shadbolt, P.; Yung, M.-H.; Zhou, X.-Q.; Love, P. J.; Aspuru-Guzik, A.; O’Brien, J. L. A variational eigenvalue solver on a quantum processor. Nat. Commun. 2014, 5, 4213, DOI: 10.1038/ncomms521312https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitVShsbvM&md5=24adc3eeee68110a19e2f43020062e90A variational eigenvalue solver on a photonic quantum processorPeruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter; Yung, Man-Hong; Zhou, Xiao-Qi; Love, Peter J.; Aspuru-Guzik, Alan; O'Brien, Jeremy L.Nature Communications (2014), 5 (), 4213CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the phys. dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estn. algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state prepn. based on ansatze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We exptl. demonstrate the feasibility of this approach with an example from quantum chem.-calcg. the ground-state mol. energy for He-H+. The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future.
- 13Hempel, C.; Maier, C.; Romero, J.; McClean, J.; Monz, T.; Shen, H.; Jurcevic, P.; Lanyon, B. P.; Love, P.; Babbush, R.; Aspuru-Guzik, A.; Blatt, R.; Roos, C. F. Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator. Phys. Rev. X 2018, 8, 031022, DOI: 10.1103/PhysRevX.8.03102213https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltFShu7Y%253D&md5=c5b702bf294cf6e51b4145f0183235d8Quantum Chemistry Calculations on a Trapped-Ion Quantum SimulatorHempel, Cornelius; Maier, Christine; Romero, Jonathan; McClean, Jarrod; Monz, Thomas; Shen, Heng; Jurcevic, Petar; Lanyon, Ben P.; Love, Peter; Babbush, Ryan; Aspuru-Guzik, Alan; Blatt, Rainer; Roos, Christian F.Physical Review X (2018), 8 (3), 031022CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chem. to physics and materials science. We report on the exptl. implementation of such an algorithm to solve a quantum chem. problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calc. the mol. ground-state energies of two simple mols. and exptl. demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chem. accuracy, which may serve as a cross-platform benchmark for multiqubit quantum simulators.
- 14Chen, M.-C.; Gong, M.; Xu, X.-S.; Yuan, X.; Wang, J.-W.; Wang, C.; Ying, C.; Lin, J.; Xu, Y.; Wu, Y.; Wang, S.; Deng, H.; Liang, F.; Peng, C.-Z.; Benjamin, S. C.; Zhu, X.; Lu, C.-Y.; Pan, J.-W. Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor. Phys. Rev. Lett. 2020, 125, 180501, DOI: 10.1103/PhysRevLett.125.18050114https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitlens7jK&md5=16ad29873c90606a95eb71b769344838Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum CoprocessorChen, Ming-Cheng; Gong, Ming; Xu, Xiaosi; Yuan, Xiao; Wang, Jian-Wen; Wang, Can; Ying, Chong; Lin, Jin; Xu, Yu; Wu, Yulin; Wang, Shiyu; Deng, Hui; Liang, Futian; Peng, Cheng-Zhi; Benjamin, Simon C.; Zhu, Xiaobo; Lu, Chao-Yang; Pan, Jian-WeiPhysical Review Letters (2020), 125 (18), 180501CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)Adiabatic quantum computing enables the prepn. of many-body ground states. Realization poses major exptl. challenges: Direct analog implementation requires complex Hamiltonian engineering, while the digitized version needs deep quantum gate circuits. To bypass these obstacles, we suggest an adiabatic variational hybrid algorithm, which employs short quantum circuits and provides a systematic quantum adiabatic optimization of the circuit parameters. The quantum adiabatic theorem promises not only the ground state but also that the excited eigenstates can be found. We report the first exptl. demonstration that many-body eigenstates can be efficiently prepd. by an adiabatic variational algorithm assisted with a multiqubit superconducting coprocessor. We track the real-time evolution of the ground and excited states of transverse-field Ising spins with a fidelity that can reach about 99%.
- 15Google AI Quantum and Collaborators; Arute, F.; Arute, F.; Aryae, K.; Babbush, R.; Bacon, D.; Bardin, J. C.; Barends, R.; Boixo, S.; Broughton, M. Hartree-Fock on a superconducting qubit quantum computer. Science 2020, 369, 1084– 1089, DOI: 10.1126/science.abb9811There is no corresponding record for this reference.
- 16Roffe, J. Quantum error correction: an introductory guide. Contemp. Phys. 2019, 60, 226– 245, DOI: 10.1080/00107514.2019.1667078There is no corresponding record for this reference.
- 17Chen, Z.; Satzinger, K. J.; Atalaya, J.; Korotkov, A. N.; Dunsworth, A.; Sank, D.; Quintana, C.; McEwen, M.; Barends, R.; Klimov, P. V. Exponential suppression of bit or phase errors with cyclic error correction. Nature 2021, 595, 383– 387, DOI: 10.1038/s41586-021-03588-yThere is no corresponding record for this reference.
- 18Nguyen, N. H.; Li, M.; Green, A. M.; Huerta Alderete, C.; Zhu, Y.; Zhu, D.; Brown, K. R.; Linke, N. M. Demonstration of Shor Encoding on a Trapped-Ion Quantum Computer. Phys. Rev. Appl. 2021, 16, 024057, DOI: 10.1103/PhysRevApplied.16.02405718https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitVeku7rK&md5=4386fe584a0803c200ea7c41c6dae8abDemonstration of Shor Encoding on a Trapped-Ion Quantum ComputerNguyen, Nhung H.; Li, Muyuan; Green, Alaina M.; Huerta Alderete, C.; Zhu, Yingyue; Zhu, Daiwei; Brown, Kenneth R.; Linke, Norbert M.Physical Review Applied (2021), 16 (2), 024057CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple phys. qubits to encode a logical qubit, which is protected against errors at the phys. qubit level. Here, we use a trapped-ion system to exptl. prep. m-qubit Greenberger-Horne-Zeilinger states and sample the measurement results to construct mxm logical states of the [[m2, 1, m]] Shor code, up to m=7. The synthetic logical fidelity shows how deeper encoding can compensate for addnl. gate errors in state prepn. for larger logical states. However, the optimal code size depends on the phys. error rate and we find that m=5 has the best performance in our system. We further realize the direct logical encoding of the [[9,1,3]] Shor code on nine qubits in a 13-ion chain for comparison, with 98.8(1)% and 98.5(1)% fidelity for state |±〉L, resp.
- 19Egan, L.; Debroy, D. M.; Noel, C.; Risinger, A.; Zhu, D.; Biswas, D.; Newman, M.; Li, M.; Brown, K. R.; Cetina, M.; Monroe, C. Fault-Tolerant Operation of a Quantum Error-Correction Code. arXiv Preprint (Quantum Physics) , 2020. arXiv:2009.11482. https://doi.org/10.48550/arXiv.2009.11482.There is no corresponding record for this reference.
- 20Pino, J. M.; Dreiling, J. M.; Figgatt, C.; Gaebler, J. P.; Moses, S. A.; Allman, M. S.; Baldwin, C. H.; Foss-Feig, M.; Hayes, D.; Mayer, K.; Ryan-Anderson, C.; Neyenhuis, B. Demonstration of the trapped-ion quantum CCD computer architecture. Nature 2021, 592, 209– 213, DOI: 10.1038/s41586-021-03318-420https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXosVClsLg%253D&md5=b3ce16dde190ddf4c35478f5840dda48Demonstration of the trapped-ion quantum CCD computer architecturePino, J. M.; Dreiling, J. M.; Figgatt, C.; Gaebler, J. P.; Moses, S. A.; Allman, M. S.; Baldwin, C. H.; Foss-Feig, M.; Hayes, D.; Mayer, K.; Ryan-Anderson, C.; Neyenhuis, B.Nature (London, United Kingdom) (2021), 592 (7853), 209-213CODEN: NATUAS; ISSN:0028-0836. (Nature Research)The trapped-ion quantum charge-coupled device (QCCD) proposal1,2 lays out a blueprint for a universal quantum computer that uses mobile ions as qubits. Analogous to a charge-coupled device (CCD) camera, which stores and processes imaging information as movable elec. charges in coupled pixels, a QCCD computer stores quantum information in the internal state of elec. charged ions that are transported between different processing zones using dynamic elec. fields. The promise of the QCCD architecture is to maintain the low error rates demonstrated in small trapped-ion expts.3-5 by limiting the quantum interactions to multiple small ion crystals, then phys. splitting and rearranging the constituent ions of these crystals into new crystals, where further interactions occur. This approach leverages transport timescales that are fast relative to the coherence times of the qubits, the insensitivity of the qubit states of the ion to the elec. fields used for transport, and the low crosstalk afforded by spatially sepd. crystals. However, engineering a machine capable of executing these operations across multiple interaction zones with low error introduces many difficulties, which have slowed progress in scaling this architecture to larger qubit nos. Here we use a cryogenic surface trap to integrate all necessary elements of the QCCD architecture-a scalable trap design, parallel interaction zones and fast ion transport-into a programmable trapped-ion quantum computer that has a system performance consistent with the low error rates achieved in the individual ion crystals. We apply this approach to realize a teleported CNOT gate using mid-circuit measurement6, negligible crosstalk error and a quantum vol.7 of 26 = 64. These results demonstrate that the QCCD architecture provides a viable path towards high-performance quantum computers.
- 21Postler, L.; Heußen, S.;