QMA vs QCMA and Pseudorandomness
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3717823.3718296.pdf
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802.06 KB
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Author(s)
Liu, Jiahui
Mutreja, Saachi
Yuen, Henry
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
Jiahui Liu, Saachi Mutreja, and Henry Yuen. 2025. QMA vs QCMA and Pseudorandomness. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 1520–1531.
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Final published version
Abstract
We study a longstanding question of Aaronson and Kuperberg on whether there exists a classical oracle separating QMA from QCMA. Settling this question in either direction would yield insight into the power of quantum proofs over classical proofs. We show that such an oracle exists if a certain quantum pseudorandomness conjecture holds. Roughly speaking, the conjecture posits that quantum algorithms cannot, by making few queries, distinguish between the uniform distribution over permutations versus permutations drawn from so-called “dense” distributions.
Our result can be viewed as establishing a “win-win” scenario: either there is a classical oracle separation of QMA from QCMA, or there is quantum advantage in distinguishing pseudorandom distributions on permutations.
Description
STOC ’25, Prague, Czechia
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3717823.3718296
