The complexity of NISQ

Journal Article · Tue Sep 26 00:00:00 EDT 2023 · Nature Communications

DOI:https://doi.org/10.1038/s41467-023-41217-6· OSTI ID:2006532

Chen, Sitan; Cotler, Jordan ; Huang, Hsin-Yuan ; Li, Jerry

Abstract The recent proliferation of NISQ devices has made it imperative to understand their power. In this work, we define and study the complexity class , which encapsulates problems that can be efficiently solved by a classical computer with access to noisy quantum circuits. We establish super-polynomial separations in the complexity among classical computation, , and fault-tolerant quantum computation to solve some problems based on modifications of Simon’s problems. We then consider the power of for three well-studied problems. For unstructured search, we prove that cannot achieve a Grover-like quadratic speedup over classical computers. For the Bernstein-Vazirani problem, we show that only needs a number of queries logarithmic in what is required for classical computers. Finally, for a quantum state learning problem, we prove that is exponentially weaker than classical computers with access to noiseless constant-depth quantum circuits.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0007870
• OSTI ID: 2006532
• Journal Information: Nature Communications, Journal Name: Nature Communications Vol. 14 Journal Issue: 1; ISSN 2041-1723
• Publisher: Nature Publishing Group
• Country of Publication: United Kingdom
• Language: English