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Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian

McArdle, Sam and Campbell, Earl and Su, Yuan (2022) Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian. Physical Review A, 105 (1). Art. No. 012403. ISSN 2469-9926. doi:10.1103/physreva.105.012403. https://resolver.caltech.edu/CaltechAUTHORS:20220118-839577000

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Abstract

Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number information in the implementation of Trotter-based approaches and overestimated the quantum-computer runtime as a result. They also depended on numerical procedures that are computationally too expensive to scale up to large systems of practical interest. Here we propose techniques that solve both problems by using various factorized decompositions of the electronic structure Hamiltonian. We showcase our techniques for the uniform electron gas, finding substantial (over 100×) improvements in Trotter error for low-filling fraction and pushing to much higher numbers of orbitals than is possible with existing methods. Finally, we calculate the T-count to perform phase estimation on Jellium. In the low-filling regime, we observe improvements in gate complexity of over 10× compared to the best Trotter-based approach reported to date. We also report gate counts competitive with qubitization-based approaches for Wigner-Seitz values of physical interest.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.105.012403DOIArticle
https://arxiv.org/abs/2107.07238arXivDiscussion Paper
ORCID:
AuthorORCID
McArdle, Sam0000-0003-4994-5964
Campbell, Earl0000-0002-3903-2734
Su, Yuan0000-0003-1144-3563
Additional Information:© 2022 American Physical Society. (Received 26 August 2021; revised 3 December 2021; accepted 9 December 2021; published 3 January 2022) We thank Hsin-Yuan (Robert) Huang, Fernando Brandao, Mario Berta, and Michael Kastoryano for discussions during this project. Y.S.'s contribution to this project was made while at Caltech. He was supported in part by the National Science Foundation RAISE-TAQS 1839204 and Amazon Web Services, AWS Quantum Program. The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center PHY-1733907.
Group:AWS Center for Quantum Computing, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFCCF-1839204
Amazon Web ServicesUNSPECIFIED
NSFPHY-1733907
Issue or Number:1
DOI:10.1103/physreva.105.012403
Record Number:CaltechAUTHORS:20220118-839577000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220118-839577000
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112968
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:19 Jan 2022 16:13
Last Modified:19 Jan 2022 16:13

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