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

2026-02-20

AI Summary

This work investigates the feasibility of non-interactive classical verification of quantum computation—specifically, the verification of QMA problems—under standard falsifiable cryptographic assumptions. By constructing gap instances separating QMA from QCMA and leveraging quantum black-box reductions, it establishes for the first time that no non-interactive classical verification protocol based on falsifiable assumptions (including widely used ones such as LWE) can be realized via quantum black-box reductions. This result demonstrates a fundamental theoretical impossibility for such protocols under falsifiable assumptions, thereby setting a foundational lower bound on the interactive complexity required for quantum verification protocols.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

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.

Problem

• non-interactive
• classical verification of quantum computation
• falsifiable assumptions
• QMA
• black-box reduction

Innovation

• non-interactive verification
• quantum black-box reduction
• falsifiable assumptions
• QMA-QCMA gap
• classical verification of quantum computation