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Fault-Tolerant Quantum Simulations of Chemistry in First Quantization

Su, Yuan and Berry, Dominic W. and Wiebe, Nathan and Rubin, Nicholas and Babbush, Ryan (2021) Fault-Tolerant Quantum Simulations of Chemistry in First Quantization. PRX Quantum, 2 (4). Art. No. 040332. ISSN 2691-3399. doi:10.1103/prxquantum.2.040332.

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Quantum simulations of chemistry in first quantization offer some important advantages over approaches in second quantization including faster convergence to the continuum limit and the opportunity for practical simulations outside of the Born-Oppenheimer approximation. However, since all prior work on quantum simulation of chemistry in first quantization has been limited to asymptotic analysis, it has been impossible to directly compare the resources required for these approaches to those required for the more commonly studied algorithms in second quantization. Here, we compile, optimize, and analyze the finite resources required to implement two first quantized quantum algorithms for chemistry from Babbush et al. [Npj Quantum Inf. 5, 92 (2019)] that realize block encodings for the qubitization and interaction-picture frameworks of Low et al. [Quantum 3, 163 (2019), arXiv:1805.00675 (2018)]. The two algorithms we study enable simulation with gate complexities of ˜O(η^(8/3)N^(1/3)t+η^(4/3)N^(2/3)t) and ˜O(η^(8/3)N^(1/3)t) where η is the number of electrons, N is the number of plane-wave basis functions, and t is the duration of time evolution (t is linearly inverse to target precision when the goal is to estimate energies). In addition to providing the first explicit circuits and constant factors for any first quantized simulation, and then introducing improvements, which reduce circuit complexity by about a thousandfold over naive implementations for modest sized systems, we also describe new algorithms that asymptotically achieve the same scaling in a real-space representation. Finally, we assess the resources required to simulate various molecules and materials and conclude that the qubitized algorithm will often be more practical than the interaction-picture algorithm. We demonstrate that our qubitization algorithm often requires much less surface-code space-time volume for simulating millions of plane waves than the best second quantized algorithms require for simulating hundreds of Gaussian orbitals.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Su, Yuan0000-0003-1144-3563
Berry, Dominic W.0000-0003-3446-1449
Wiebe, Nathan0000-0001-7642-1061
Rubin, Nicholas0000-0003-3963-1830
Babbush, Ryan0000-0001-6979-9533
Additional Information:© 2021 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 31 May 2021; accepted 4 October 2021; published 11 November 2021. The authors thank Garnet Kin-Lic Chan, Matthias Degroote, Craig Gidney, Cody Jones, Joonho Lee, Jarrod McClean, Yuval Sanders, Norm Tubman, and the quantum-computing team at BASF for helpful discussions. D.B. worked on this project under a sponsored research agreement with Google Quantum AI. D.B. is also supported by Australian Research Council Discovery Projects DP190102633 and DP210101367. N.W. is funded by a grant from Google Quantum AI as well as the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-Design Center for Quantum Advantage under contract number DE-SC0012704, which supported his work on the asymptotic analysis of the algorithms. Y.S. is partly supported by the National Science Foundation RAISE-TAQS 1839204. The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center PHY-1733907.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Australian Research CouncilDP190102633
Australian Research CouncilDP210101367
Department of Energy (DOE)DE-SC0012704
Issue or Number:4
Record Number:CaltechAUTHORS:20211117-230943225
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111940
Deposited By: Tony Diaz
Deposited On:17 Nov 2021 23:19
Last Modified:17 Nov 2021 23:19

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