Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Ryan Babbush (), William J. Huggins, Dominic W. Berry, Shu Fay Ung, Andrew Zhao, David R. Reichman, Hartmut Neven, Andrew D. Baczewski and Joonho Lee ()
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Ryan Babbush: Google Quantum AI
William J. Huggins: Google Quantum AI
Dominic W. Berry: Macquarie University
Shu Fay Ung: Columbia University
Andrew Zhao: Google Quantum AI
David R. Reichman: Columbia University
Hartmut Neven: Google Quantum AI
Andrew D. Baczewski: Sandia National Laboratories
Joonho Lee: Google Quantum AI

Nature Communications, 2023, vol. 14, issue 1, 1-9

Abstract: Abstract Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree–Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree–Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

Date: 2023
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DOI: 10.1038/s41467-023-39024-0

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