Is there evidence for exponential quantum advantage in quantum chemistry?

Authors:
  • SLSeunghoon Lee
    Seunghoon Lee
  • JLJoonho Lee
    Joonho Lee
  • HZHuanchen Zhai
    Huanchen Zhai
  • YTYu Tong
    Yu Tong
  • ADAlexander M. Dalzell
    Alexander M. Dalzell
  • AKAshutosh Kumar
    Ashutosh Kumar
  • PHPhillip Helms
    Phillip Helms
  • JGJohnnie Gray
    Johnnie Gray
  • ZCZhi-Hao Cui
    Zhi-Hao Cui
  • WLWenyuan Liu
    Wenyuan Liu
  • MKMichael Kastoryano
    Michael Kastoryano
  • RBRyan Babbush
    Ryan Babbush
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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 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.