Is the Trotterized UCCSD Ansatz Chemically Well-Defined?
Abstract
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.more »
- Authors:
-
[1];
[1]
- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
- Publication Date:
- Research Org.:
- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
- OSTI Identifier:
- 1633019
- Grant/Contract Number:
- SC0019199; SC0019318
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Theory and Computation
- Additional Journal Information:
- Journal Volume: 16; Journal Issue: 1; Journal ID: ISSN 1549-9618
- Publisher:
- American Chemical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Grimsley, Harper R., Claudino, Daniel, Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J. Is the Trotterized UCCSD Ansatz Chemically Well-Defined?. United States: N. p., 2019.
Web. doi:10.1021/acs.jctc.9b01083.
Grimsley, Harper R., Claudino, Daniel, Economou, Sophia E., Barnes, Edwin, & Mayhall, Nicholas J. Is the Trotterized UCCSD Ansatz Chemically Well-Defined?. United States. https://doi.org/10.1021/acs.jctc.9b01083
Grimsley, Harper R., Claudino, Daniel, Economou, Sophia E., Barnes, Edwin, and Mayhall, Nicholas J. Mon .
"Is the Trotterized UCCSD Ansatz Chemically Well-Defined?". United States. https://doi.org/10.1021/acs.jctc.9b01083. https://www.osti.gov/servlets/purl/1633019.
@article{osti_1633019,
title = {Is the Trotterized UCCSD Ansatz Chemically Well-Defined?},
author = {Grimsley, Harper R. and Claudino, Daniel and Economou, Sophia E. and Barnes, Edwin and Mayhall, Nicholas J.},
abstractNote = {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.},
doi = {10.1021/acs.jctc.9b01083},
journal = {Journal of Chemical Theory and Computation},
number = 1,
volume = 16,
place = {United States},
year = {Mon Dec 16 00:00:00 EST 2019},
month = {Mon Dec 16 00:00:00 EST 2019}
}
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