Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

Grimsley, Harper R.; Claudino, Daniel; Economou, Sophia E.; Barnes, Edwin; Mayhall, Nicholas J.

doi:10.1021/acs.jctc.9b01083

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

Journal Article · Mon Dec 16 00:00:00 EST 2019 · Journal of Chemical Theory and Computation

DOI:https://doi.org/10.1021/acs.jctc.9b01083· OSTI ID:1633019

Grimsley, Harper R. ^[1]; ^[2]; Economou, Sophia E. ^[2]; Barnes, Edwin ^[2]; ^[2]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Virginia Tech
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

The variational quantum eigensolver (VQE) has emerged as one of the most enticing near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. Yet, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the non-uniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact k-UpCCGSD ansatz recently proposed by Lee et al. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This letter establishes the need to define not only the operators present in the ansatz, but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a ``model chemistry'', in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators.

View Accepted Manuscript (DOE)

Research Organization:: Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0019199; SC0019318

OSTI ID:: 1633019

Journal Information:: Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 1 Vol. 16; ISSN 1549-9618

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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TEQUILA: a platform for rapid development of quantum algorithms Kottmann, Jakob S.; Alperin-Lea, Sumner; Tamayo-Mendoza, Teresa Quantum Science and Technology, Vol. 6, Issue 2 https://doi.org/10.1088/2058-9565/abe567	journal	March 2021
QASMBench: A Low-level QASM Benchmark Suite for NISQ Evaluation and Simulation Li, Ang; Stein, Samuel; Krishnamoorthy, Sriram arXiv https://doi.org/10.48550/arxiv.2005.13018	preprint	January 2020
A Generic Compilation Strategy for the Unitary Coupled Cluster Ansatz Cowtan, Alexander; Simmons, Will; Duncan, Ross arXiv https://doi.org/10.48550/arxiv.2007.10515	preprint	January 2020
Quantum computational chemistry McArdle, Sam; Endo, Suguru; Aspuru-Guzik, Alán Reviews of Modern Physics, Vol. 92, Issue 1 https://doi.org/10.1103/revmodphys.92.015003	journal	March 2020
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