Graph-|Q⟩⟨C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance
- Juncheng Harry ZhangJuncheng Harry ZhangDepartment of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United StatesMore by Juncheng Harry Zhang
- Srinivasan S. Iyengar*
We present a procedure to reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree–Fock electronic structure energies in large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph-theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of processes, some of which can be treated on quantum hardware and others on classical hardware. Thus, we develop a procedure for an electronic structure that can be asynchronously spawned onto a potentially large ensemble of classical and quantum hardware systems. We demonstrate this method by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies for a set of [H2]n clusters, with n ranging from 4 to 128. We implement our methodology using quantum circuits, and when these quantum circuits are processed on a quantum simulator, we obtain energies in agreement with the UCCSD energies in the milli-hartree energy range. We also show that our circuit decomposition approach yields up to 9 orders of magnitude reduction in the number of CNOT gates and quantum circuit depth for the large-sized clusters when compared to a standard quantum circuit implementation available on IBM’s Quantum Information Science kit, known as Qiskit.
This article is cited by 7 publications.
- Timothy C. Ricard, Xiao Zhu, Srinivasan S. Iyengar. Capturing Weak Interactions in Surface Adsorbate Systems at Coupled Cluster Accuracy: A Graph-Theoretic Molecular Fragmentation Approach Improved through Machine Learning. Journal of Chemical Theory and Computation 2023, Article ASAP.
- Srinivasan S. Iyengar, Juncheng Harry Zhang, Debadrita Saha, Timothy C. Ricard. Graph-|Q⟩⟨C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure. The Journal of Physical Chemistry A 2023, 127
, 9334-9345. https://doi.org/10.1021/acs.jpca.3c04261
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, 7256-7263. https://doi.org/10.1021/acs.jpclett.3c01601
- Srinivasan S. Iyengar, Sabre Kais. Analogy between Boltzmann Machines and Feynman Path Integrals. Journal of Chemical Theory and Computation 2023, 19
, 2446-2454. https://doi.org/10.1021/acs.jctc.3c00187
- Anup Kumar, Nicole DeGregorio, Timothy Ricard, Srinivasan S. Iyengar. Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics. Journal of Chemical Theory and Computation 2022, 18
, 7243-7259. https://doi.org/10.1021/acs.jctc.2c00484
- Xiao Zhu, Srinivasan S. Iyengar. Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol. Journal of Chemical Theory and Computation 2022, 18
, 5125-5144. https://doi.org/10.1021/acs.jctc.1c01241
- Junjie Hu, Zhe-Yong Zhang, Guo-Xiang Zhao, Qiao-Hong Li, Peng Gao, Rong-Jian Sa. Data-driven generation of mixed X-anion perovskite properties. Physical Chemistry Chemical Physics 2022, 24
, 29120-29129. https://doi.org/10.1039/D2CP02484E