Year: 2025
Type: article
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.
DOI: 10.1145/3773903
Authors: Nai-Hui Chia, Honghao Fu, Fang Song, Penghui Yao
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Awards: G1997119393, G2659216395, QLCI-CI: NSF Quantum Leap Challenge Institute for Present and Future Quantum Computing, G3095286837, Collaborative Research: FET: Small: Minimum Quantum Circuit Size Problems, Variants, and Applications, Collaborative Research: FET: Small: Minimum Quantum Circuit Size Problems, Variants, and Applications, G5414997189, G5528670684, G5684620518, G6061312510, G6123861678, G6652710192, G6671297155, G7347053913, FET: CAREER: Algorithms, cryptography and complexity meet quantum reductions
OpenAlex ID: W4415614691