Unconditional proofs of quantumness between small-space machines

• URL: http://arxiv.org/abs/2412.02662v1
• Date: Tue, 03 Dec 2024 18:37:07 GMT
• Title: Unconditional proofs of quantumness between small-space machines
• Authors: A. C. Cem Say, M. Utkan Gezer,
• Abstract summary: A proof of quantumness is a protocol through which a classical machine can test whether a purportedly quantum device is performing a computation that is impossible for classical computers.
• Score: 0.0
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• Abstract: 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.

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