We present a generic compiler that converts any $\mathsf{MIP}^{*}$ protocol into a succinct interactive argument where the communication and the verifier are classical, and where post-quantum soundness relies on the post-quantum sub-exponential hardness of the Learning with Errors ($\mathsf{LWE}$) problem. Prior to this work, such a compiler for $\mathsf{MIP}^{*}$ was given by Kalai, Lombardi, Vaikuntanathan and Yang (STOC 2022), but the post-quantum soundness of this compiler is still under investigation. More generally, our compiler can be applied to any $\mathsf{QIP}$ protocol which is sound only against semi-malicious provers that follow the prescribed protocol, but with possibly malicious initial state. Our compiler consists of two steps. We first show that if a language $\mathcal{L}$ has a $\mathsf{QIP}$ with semi-malicious soundness, where the prover runs in time $T$, then $\mathcal{L} \in \mathsf{QMATIME}(T)$. Then we construct a succinct classical argument for any such language, where the communication complexity grows polylogarithmically with $T$, under the post-quantum sub-exponential hardness of $\mathsf{LWE}$. Note: After this work was finished, an independent and concurrent work (Baroni et al. 2025) resolved the question of quantum soundness of the KLVY compiler.

翻译：我们提出了一种通用编译器，可将任意 $\mathsf{MIP}^{*}$ 协议转换为一种简洁的交互式论证，其中通信和验证方均为经典的，且后量子安全性依赖于带错误学习（$\mathsf{LWE}$）问题的后量子亚指数级困难性。在本工作之前，Kalai、Lombardi、Vaikuntanathan 和 Yang（STOC 2022）已提出此类 $\mathsf{MIP}^{*}$ 编译器，但其后量子安全性仍在研究中。更一般地，我们的编译器可应用于任何仅对遵循规定协议但可能具有恶意初始状态的半恶意证明者具有安全性的 $\mathsf{QIP}$ 协议。我们的编译器包含两个步骤。首先，我们证明若语言 $\mathcal{L}$ 具有半恶意安全性的 $\mathsf{QIP}$，且证明者运行时间为 $T$，则 $\mathcal{L} \in \mathsf{QMATIME}(T)$。随后，我们在 $\mathsf{LWE}$ 的后量子亚指数级困难性假设下，为任何此类语言构建了一个简洁的经典论证，其通信复杂度随 $T$ 呈多对数增长。注：本工作完成后，一项独立且并行的研究（Baroni 等人，2025）已解决 KLVY 编译器的量子安全性问题。