The Trotter step size required for accurate quantum simulation of quantum chemistry
Abstract
The simulation of molecules is a widely anticipated application of quantum computers. However, recent studies [1, 2] have cast a shadow on this hope by revealing that the complexity in gate count of such simulations increases with the number of spin orbitals N as N8 , which becomes prohibitive even for molecules of modest size N ∼ 100. This study was partly based on a scaling analysis of the Trotter step required for an ensemble of random artificial molecules. Here, we revisit this analysis and find instead that the scaling is closer to N6 in worst case for real model molecules we have studied, indicating that the random ensemble fails to accurately capture the statistical properties of real world molecules. Actual scaling may be significantly better than this due to averaging effects. We then present an alternative simulation scheme and show that it can sometimes outperform existing schemes, but that this possibility depends crucially on the details of the simulated molecule. We obtain further improvements using a version of the coalescing scheme of [1]; this scheme is based on using different Trotter steps for different terms. The method we use to bound the complexity of simulating a given molecule is efficient, in contrast to the approach of [1, 2] which relied on exponentially costly classical exact simulation.
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Classical techniques for molecular simulation are currently limited to molecules with 50-70 spin orbitals.
“Classical techniques for molecular simulation are currently limited to molecules with 50 -70 spin orbitals. 72”
From Quantum algorithms: an overview (2016) · cites this paper as [72]
The simulation time for quantum chemistry is polynomial in the number of orbitals; it initially seemed prohibitively long but was rapidly improved via detailed analysis.
“The challenge in this context is optimising the simulation time; although polynomial in the number of orbitals, this initially seemed prohibitively long, 73 but was rapidly improved via detailed analysis. 72”
From Quantum algorithms: an overview (2016) · cites this paper as [72]
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Self-citation
- Authors
- Poulin, D., Hastings, M. B., Wecker, D., Wiebe, N., Doberty, A. C., & Troyer, M.
- Affiliations
- Université de Sherbrooke (CA)
- Microsoft (United States) (US)
- ETH Zurich (CH)
- ORCID
- Venue
- Quantum Information and Computation
- Publisher
- Rinton Press
- Published
- 2015-04
- Pages
- 361-384
- ISSN
- 1533-7146 (ISSN-L)
- OpenAlex
- W2950522577
- Cited by
- 159
- References
- 2
- Citations by year
- 2026: 6 · 2025: 12 · 2024: 10 · 2023: 15 · 2022: 13 · 2021: 17 · 2020: 19 · 2019: 15 · 2018: 26 · 2017: 6 · 2016: 11 · 2015: 7 · 2014: 2
- FWCI
- 16.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Quantum Information and Computation (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
- Keywords
- quantum simulation of molecules, quantum chemistry, scaling analysis, quantum circuit complexity
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