Unconditional proofs of quantumness between small-space machines

A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers. Existing approaches to provide proofs of quantumness depend on unpr...

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Bibliographic Details
Published in:arXiv.org 2024-12
Main Authors: Say, A C Cem, M Utkan Gezer
Format: Article
Language:English
Subjects:
Memory devices
Polynomials
Turing machines
Online Access:Get full text
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Summary:A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device, with comparable time and memory resources, is performing a computation that is impossible for classical computers. Existing approaches to provide proofs of quantumness depend on unproven assumptions about some task being impossible for machines of a particular model under certain resource restrictions. We study a setup where both devices have space bounds \(\mathit{o}(\log \log n)\). Under such memory budgets, it has been unconditionally proven that probabilistic Turing machines are unable to solve certain computational problems. We formulate a new class of problems, and show that these problems are polynomial-time solvable for quantum machines, impossible for classical machines, and have the property that their solutions can be "proved" by a small-space quantum machine to a classical machine with the same space bound. These problems form the basis of our newly defined protocol, where the polynomial-time verifier's verdict about the tested machine's quantumness is not conditional on an unproven weakness assumption.
ISSN:2331-8422