Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry

Seunghoon Lee, Joonho Lee, Huanchen Zhai, Yu Tong, Alexander M. Dalzell, Ashutosh Kumar, Phillip Helms, Johnnie Gray, Zhi-Hao Cui, Wenyuan Liu, Michael Kastoryano, Ryan Babbush, John Preskill, David R. Reichman, Earl T. Campbell, Edward F. Valeev, Lin Lin and Garnet Kin-Lic Chan ()
Additional contact information
Seunghoon Lee: California Institute of Technology
Joonho Lee: Columbia University
Huanchen Zhai: California Institute of Technology
Yu Tong: University of California
Alexander M. Dalzell: AWS Center for Quantum Computing
Ashutosh Kumar: Virginia Tech
Phillip Helms: California Institute of Technology
Johnnie Gray: California Institute of Technology
Zhi-Hao Cui: California Institute of Technology
Wenyuan Liu: California Institute of Technology
Michael Kastoryano: AWS Center for Quantum Computing
Ryan Babbush: Google Quantum AI
John Preskill: AWS Center for Quantum Computing
David R. Reichman: Columbia University
Earl T. Campbell: Riverlane
Edward F. Valeev: Virginia Tech
Lin Lin: University of California
Garnet Kin-Lic Chan: California Institute of Technology

Nature Communications, 2023, vol. 14, issue 1, 1-7

Abstract: Abstract Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.

Date: 2023
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DOI: 10.1038/s41467-023-37587-6

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