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.

翻译：Mahadev [SIAM J. Comput. 2022] 基于带误差学习（LWE）假设，首次提出了量子计算的经典验证协议，实现了一个4轮交互方案。这一突破自然引出了一个核心问题：在标准模型中，是否可能使用更少的交互轮数？尽管该问题至关重要，但一直未得到解决。本文证明，不存在从$\textsf{QMA}$类量子计算的非交互式经典验证到任何可证伪假设的量子黑盒归约。此处“非交互式”指在完成与实例无关的初始化阶段后，协议仅包含单轮消息传递。考虑到可证伪假设涵盖了密码学中几乎所有标准假设（包括LWE），这一结果构成了强有力的否定性结论。我们的分离结果建立在存在$\textsf{QMA} \text{-} \textsf{QCMA}$间隙问题的前提下。本质上，这类问题所需的假设条件略强于$\textsf{QMA}\neq \textsf{QCMA}$。为支持此类问题的存在性，我们给出了相对于量子酉预言机的一个构造方案。