A Cryptographic Perspective on the Verifiability of Quantum Advantage

Fuente: arXiv
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Main Authors: Chia, Nai-Hui, Fu, Honghao, Song, Fang, Yao, Penghui
Format: Preprint
Published: 2023
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author Chia, Nai-Hui
Fu, Honghao
Song, Fang
Yao, Penghui
author_facet Chia, Nai-Hui
Fu, Honghao
Song, Fang
Yao, Penghui
contents 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 paper 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 ($\mathsf{EFI}$), pseudorandom states ($\mathsf{PRS}$), and variants of minimum circuit size problems ($\mathsf{MCSP}$). Specifically, we prove that a) a sampling-based quantum advantage is either verifiable or can be used to build $\mathsf{EFI}$ and even $\mathsf{PRS}$ and b) polynomial-time algorithms for a variant of $\mathsf{MCSP}$ 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.
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id arxiv_https___arxiv_org_abs_2310_14464
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle A Cryptographic Perspective on the Verifiability of Quantum Advantage
Chia, Nai-Hui
Fu, Honghao
Song, Fang
Yao, Penghui
Quantum Physics
Cryptography and Security
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 paper 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 ($\mathsf{EFI}$), pseudorandom states ($\mathsf{PRS}$), and variants of minimum circuit size problems ($\mathsf{MCSP}$). Specifically, we prove that a) a sampling-based quantum advantage is either verifiable or can be used to build $\mathsf{EFI}$ and even $\mathsf{PRS}$ and b) polynomial-time algorithms for a variant of $\mathsf{MCSP}$ 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.
title A Cryptographic Perspective on the Verifiability of Quantum Advantage
topic Quantum Physics
Cryptography and Security
url https://arxiv.org/abs/2310.14464