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, groundstate 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 groundstate quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.
This content will become publicly available on July 1, 2025
 Award ID(s):
 2142846
 NSFPAR ID:
 10529156
 Publisher / Repository:
 Cell
 Date Published:
 Journal Name:
 Cell Reports Physical Science
 ISSN:
 26663864
 Page Range / eLocation ID:
 102105
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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