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

2025-10-09

AI Summary

This work addresses the problem of compiling arbitrary $mathsf{MIP}^*$ protocols into succinct interactive arguments with *classical communication and classical verifiers*, while achieving *post-quantum security*. Methodologically, it introduces the first generic compiler for $mathsf{QIP}$—requiring only semi-malicious security—and integrates subexponentially hard LWE-based assumptions, quantum interactive proofs, and succinct argument techniques to achieve classical verification. Key contributions are: (1) the first post-quantum secure compilation framework transforming $mathsf{MIP}^*$ protocols into classical succinct arguments; (2) communication complexity of $mathrm{polylog}(T)$, substantially improving upon prior constructions; and (3) efficient verification with provable security under standard post-quantum hardness assumptions—namely, the subexponential hardness of LWE.

Technology Category

• Machine Learning: Quantum Machine Learning
• Natural Language Processing: Discourse, Pragmatics & Argument Mining
• Multiagent Systems: Agreement, Argumentation & Negotiation

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

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 $mathsf{LWE}$.

Problem

• Converting quantum MIP* protocols into classical interactive arguments
• Achieving post-quantum security through LWE problem hardness
• Enabling succinct classical verification of quantum computations

Innovation

• Compiler transforms MIP* to succinct classical arguments
• Relies on post-quantum LWE hardness for security
• Handles semi-malicious provers in QIP protocols