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Nearly tight Trotterization of interacting electrons

Su, Yuan and Huang, Hsin-Yuan and Campbell, Earl T. (2020) Nearly tight Trotterization of interacting electrons. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210408-131650720

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Abstract

We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting the commutativity of Hamiltonian, the sparsity of interactions, and the prior knowledge of initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of Hamiltonian terms within the η-electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use O(n^(5/3)/η^(2/3)+n^(4/3)η^(2/3)) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and η electrons up to a negligible factor, improving the best previous result in second quantization while outperforming the first-quantized simulation when n=O(η²). We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2012.09194arXivDiscussion Paper
ORCID:
AuthorORCID
Su, Yuan0000-0003-1144-3563
Huang, Hsin-Yuan0000-0001-5317-2613
Additional Information:We thank Fernando Brand˜ao for inspiring discussions during the initial stages of this work. YS thanks Nathan Wiebe, Guang Hao Low, Ryan Babbush, Minh Cong Tran, Kunal Sharma, John Preskill, and Andrew Childs for helpful discussions. He is supported by the National Science Foundation RAISE-TAQS 1839204 and Amazon Web Services, AWS Quantum Program. HH is supported by the J. Yang & Family Foundation. 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
J. Yang Family and FoundationUNSPECIFIED
NSFPHY-1733907
Record Number:CaltechAUTHORS:20210408-131650720
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210408-131650720
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108662
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:09 Apr 2021 18:33
Last Modified:09 Apr 2021 18:33

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