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
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- Srinivasan S. Iyengar*Srinivasan S. Iyengar*Email: [email protected]Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United StatesMore by Srinivasan S. Iyengar
Abstract
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.
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.1c01303.
A few key ideas regarding our graph-theoretic formalism including the generation of nodes, edges, and the definition of higher-order (
-rank) simplexes that capture 
-body interactions in the molecular system as per eqs 4 and 10 (PDF)
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Cited By
This article is cited by 7 publications.
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- 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
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