Separating Non-Interactive Classical Verification of Quantum Computation from Falsifiable Assumptions

• URL: http://arxiv.org/abs/2602.18034v1
• Date: Fri, 20 Feb 2026 07:27:25 GMT
• Title: Separating Non-Interactive Classical Verification of Quantum Computation from Falsifiable Assumptions
• Authors: Mohammed Barhoush, Tomoyuki Morimae, Ryo Nishimaki, Takashi Yamakawa,
• Abstract summary: Mahadev introduced the first protocol for classical verification of quantum computation based on the Learning-with-Errors assumption.<n>This breakthrough naturally raised the question of whether fewer messages are possible in the plain model.<n>We prove that there is no quantum black-box reduction of non-interactive classical verification of quantum computation of $textsfQMA$ to any falsifiable assumption.
• Score: 11.346579815543075
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Mahadev [SIAM J. Comput. 2022] introduced the first protocol for classical verification of quantum computation based on the Learning-with-Errors (LWE) assumption, achieving a 4-message interactive scheme. This breakthrough naturally raised the question of whether fewer messages are possible in the plain model. Despite its importance, this question has remained unresolved. In this work, we prove that there is no quantum black-box reduction of non-interactive classical verification of quantum computation of $\textsf{QMA}$ to any falsifiable assumption. Here, "non-interactive" means that after an instance-independent setup, the protocol consists of a single message. This constitutes a strong negative result given that falsifiable assumptions cover almost all standard assumptions used in cryptography, including LWE. Our separation holds under the existence of a $\textsf{QMA} \text{-} \textsf{QCMA}$ gap problem. Essentially, these problems require a slightly stronger assumption than $\textsf{QMA}\neq \textsf{QCMA}$. To support the existence of such problems, we present a construction relative to a quantum unitary oracle.

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