Is there evidence for exponential quantum advantage in quantum chemistry?

TL;DR

This paper reviews the evidence for exponential quantum advantage in quantum chemistry, specifically in ground-state energy estimation, and concludes that such advantage has not yet been demonstrated across chemical space.

Contribution

It critically assesses existing claims of exponential quantum advantage in quantum chemistry and finds no conclusive evidence for it so far.

Findings

No evidence of exponential advantage in ground-state energy estimation

Quantum computers may still be useful but not exponentially faster for this task

Assumption of no generic exponential speedup in quantum chemistry is prudent

Abstract

The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through quantum computation, as a potential ``killer application''. Indications of potential exponential quantum advantage in artificial tasks have increased interest in this application, thus, 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. 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 quantum chemistry, it may be prudent to assume exponential speedups are not generically available for this problem.