Classical Commitments to Quantum States
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3717823.3718264.pdf
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Author(s)
Gunn, Sam
Tauman Kalai, Yael
Natarajan, Anand
Vill?nyi, ?gi
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
Sam Gunn, Yael Tauman Kalai, Anand Natarajan, and Ági Villányi. 2025. Classical Commitments to Quantum States. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 234–244.
Version
Final published version
Abstract
We define the notion of a classical commitment scheme to quantum states, which allows a quantum prover to compute a classical commitment to a quantum state, and later open each qubit of the state in either the standard or the Hadamard basis. Our notion is a strengthening of the measurement protocol from Mahadev (STOC 2018). We construct such a commitment scheme from the post-quantum Learning With Errors (LWE) assumption, and more generally from any noisy trapdoor claw-free function family that has the distributional strong adaptive hardcore bit property (a property that we define in this work).
Our scheme is succinct in the sense that the running time of the verifier in the commitment phase depends only on the security parameter (independent of the size of the committed state), and its running time in the opening phase grows only with the number of qubits that are being opened (and the security parameter). As a corollary we obtain a classical succinct argument system for QMA under the post-quantum LWE assumption. Previously, this was only known assuming post-quantum secure indistinguishability obfuscation. As an additional corollary we obtain a generic way of converting any X/Z quantum PCP into a succinct argument system under the quantum hardness of LWE.
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-Noncommercial
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DOI of Published Version
https://doi.org/10.1145/3717823.3718264
