Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

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

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104 Scopus citations

Abstract

The variational quantum eigensolver (VQE) has emerged as one of the most promising 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. However, 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 nonuniqueness 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. [ J. Chem. Theory Comput., 2019, 15, 311. arXiv, 2019, quant-ph:1909.09114. http://arxiv.org/abs/1909.09114[. 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.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalJournal of Chemical Theory and Computation
Volume16
Issue number1
DOIs
StatePublished - Jan 14 2020
Externally publishedYes

Funding

This research was supported by the U.S. Department of Energy (Award No. DE-SC0019199) and the National Science Foundation (Award No. 1839136). S.E.E. also acknowledges support from Award No. DE-SC0019318 from the U.S. Department of Energy.

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