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

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…

• NS
  National Science Foundation

  Awards: Grant No. NSF PHY-1748958, 2016245, OAC-1550456, OMA-2016245, PHY-1733907, NA0003525, 1733907, 2102505, DE-NA0003525, CHE-2102505, 1748958, 1550456
• UD
  U.S. Department of Energy

  Awards: SC0018140, DE-SC0020290, DE-SC0019390, DE-NA0003525, SC0019390, NSF PHY-1748958, NA0003525, -NA0003525, DE-SC0017867
• SF
  Simons Foundation
• OO
  Office of Science

  Awards: DE-SC0019390, DE-NA0003525, DE-SC0020290, DE-SC0017867, DOE-SC0018140, DE-SC0019374, SC0018140
• DO
  Division of Chemistry

  Awards: 1550456, CHE-2102505
• KI
  Kavli Institute for Theoretical Physics, University of California, Santa Barbara

  Awards: 1748958, NSF PHY-1748958, PHY-1748958