Compiling Any mathsf{MIP}^* into a (Succinct) Classical Interactive Argument

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.