Sponsor
NHC was supported by NSF award FET-2243659, Google Scholar Award, and DOE award DE-SC0024301. HF was supported by the US National Science Foundation QLCI program (grant OMA-2016245). FS was supported in part by the US National Science Foundation grants CCF-2054758 (CAREER) and CCF-2224131. P.Y. were supported by National Natural Science Foundation of China (Grant No. 62332009, 12347104), Quantum Science and Technology-National Science and Technology Major Project (Grant No. 2021ZD0302901), NSFC/RGC Joint Research Scheme (Grant no. 12461160276) and Natural Science Foundation of Jiangsu Province (No. BK20243060).
Published In
ACM Transactions on Quantum Computing
Document Type
Article
Publication Date
3-1-2026
Subjects
Theory of computation -- Cryptographic primitives, Quantum complexity theory
Abstract
In recent years, achieving verifiable quantum advantage on a NISQ device has emerged as an important open problem in quantum information. The sampling-based quantum advantages are not known to have efficient verification methods. This article investigates the verification of quantum advantage from a cryptographic perspective. We establish a strong connection between the verifiability of quantum advantage and cryptographic and complexity primitives, including efficiently samplable, statistically far but computationally indistinguishable pairs of (mixed) quantum states (EFI), pseudorandom states (PRS), and variants of minimum circuit size problems (MCSP). Specifically, we prove that a) a sampling-based quantum advantage is either verifiable or can be used to build EFI and even PRS and b) polynomial-time algorithms for a variant of MCSP would imply efficient verification of quantum advantages. Our work shows that the quest for verifiable quantum advantages may lead to applications of quantum cryptography, and the construction of quantum primitives can provide new insights into the verifiability of quantum advantages.
Rights
Copyright (c) 2025 The Authors
This work is licensed under a Creative Commons Attribution 4.0 International License.
DOI
10.1145/3773903
Persistent Identifier
https://archives.pdx.edu/ds/psu/44454
Citation Details
Chia, N.-H., Fu, H., Song, F., & Yao, P. (2025). A Cryptographic Perspective on the Verifiability of Quantum Advantage. ACM Transactions on Quantum Computing, 7(1), 1–20.