Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2510.08495

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

Andrew Huang, Yael Tauman Kalai

Published Oct 9, 2025• 0 citations
arXivHTMLPDF

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 $\mathsf{LWE}$. 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.

DOI
10.48550/arxiv.2510.08495

Related papers

A Modular Approach to Succinct Arguments for QMA

James Bartusek, Jiahui Liu, Giulio Malavolta

Succinct argument systems are of central importance to modern crytpography, enabling the efficient verification of computational claims. In the classical setting, Kilian (STOC 92) established that any probabilistically checkable proof for NP can be transformed into a succinct argument system for NP using only collision-resistant hash functions. In the quantum setting, recent works have established the feasibility of (classically-verifiable) succinct arguments for QMA, capturing statements that require *quantum* proofs. However, known constructions all rely on the highly structured assumption of learning with errors (LWE), which stands in stark contrast with the unstructured assumptions that suffice for NP. In this work, we develop a new framework that broadens the cryptographic foundations of succinct arguments for QMA. We assume the existence of (i) an oblivious state preparation (OSP) protocol, which in turn can be constructed from *plain* trapdoor claw-free functions, and (ii) collapsing hash functions, the quantum analogue of collision-resistance. In particular, we obtain the first succinct, classically-verifiable argument system for QMA which does not rely on the hardness of LWE. Our construction proceeds in two steps. First, we design a *round-efficient* classically-verifiable argument system for QMA based only on the assumption of OSP. Second, we introduce a *generalized communication compression compiler*, which, assuming collapsing hash functions, transforms any $T$-round interactive protocol into one in which the communication size is bounded by $T \cdot \poly(\secp)$ for some fixed $\poly$ independent of the original size of each message. Our compiler extends a quantum rigidity-based communication compression technique of Zhang (QCrypt 25), and may be of independent interest.

quant-pharXiv:2606.10408•Lecture notes in computer science•Jun 5, 2026•0 citations

Tight Post-Quantum Parallel Repetition for Private-Coin Arguments

Zvika Brakerski, Andrew Huang, Yael Tauman Kalai +1 more

We show that assuming the existence of homomorphic encryption, parallel repetition of all interactive arguments (after being run under homomorphic encryption) reduces the soundness error at a tight exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers, where the parallel repeated verifier accepts if and only if at least $t$ of the executions are accepted (for some threshold $t$). Prior to this work, these results were known only when the cheating prover was assumed to be classical, and it was not known how to achieve tight bounds. As a corollary, we construct the first constant-round succinct argument for $\mathsf{QMA}$ with negligible completeness and soundness errors assuming only the existence of quantum homomorphic encryption.

quant-pharXiv:2609.38941•Oct 1, 2026•0 citations

Succinct Arguments for QMA from Standard Assumptions via Compiled Nonlocal Games

Tony Metger, Anand Natarajan, Tina Zhang

We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTo ‘22) also constructed a succinct classical argument system for Q M A. However, their construction relied on post-quantumly secure indistinguishability obfuscation, a very strong primitive which is not known from standard cryptographic assumptions. In contrast, the primitives we use (namely, collapsing hash functions and a mild version of quantum homomorphic encryption) are much weaker and are implied by standard assumptions such as LWE. Our protocol is constructed using a general transformation which was designed by Kalai et al. (STOC '23) as a candidate method to compile any quantum nonlocal game into an argument system. Our main technical contribution is to analyze the soundness of this transformation when it is applied to a succinct self-test for Pauli measurements on maximally entangled states, the latter of which is a key component in the proof of MIP * = R E in Quantum complexity.

arXiv:2404.19754•Annual Symposium on Foundations of Computer Science•Oct 27, 2024•10 citations

How to Classically Verify a Quantum Cat without Killing It

Yael Tauman Kalai, Dakshita Khurana, Justin Raizes

A quantum verifier decides membership in QMA using a (single) quantum witness state. This witness may be arbitrary, and no requirement is placed on it beyond its acceptance probability. A protocol claiming to classically verify QMA should offer the same guarantee: any witness that would convince a quantum verifier should also suffice to convince a classical verifier. Unfortunately, existing classical verification of quantum computation (CVQC) protocols behave quite differently from the original QMA verifier: they require many copies of the witness and destroy every one, effectively demanding that the prover solve the hard problem of witness duplication before verification can begin. We build a protocol to classically verify QMA languages that uses a single copy of the prover's QMA witness. Whenever the original QMA verifier accepts that witness with overwhelming probability, our protocol has negligible completeness and soundness errors and returns the witness negligibly disturbed after interaction with an honest verifier. The soundness of our CVQC is based on the post-quantum Learning With Errors (LWE) assumption. As an intermediate step of independent interest, we introduce witness-preserving classical arguments for NP which enable provers that start out with a superposition over NP witnesses to convince a verifier without disturbing their superposition.

quant-pharXiv:2602.09282•Feb 11, 2026•0 citations

Succinct Arguments for QMA in the Quantum Random Oracle Model

Alessandro Chiesa, Zihan Hu

Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on ``structured'' cryptographic primitives, or on the quantum PCP conjecture. We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA. Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.

quant-pharXiv:2609.37429•Sep 30, 2026•0 citations

Parallel Repetition for Post-Quantum Arguments

Andrew Huang, Yael Tauman Kalai

In this work, we show that parallel repetition of public-coin interactive arguments reduces the soundness error at an exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers, where the parallel repeated verifier accepts if and only if at least t of the executions are accepted (for some threshold t). Prior to this work, these results were known only when the cheating prover was assumed to be classical.We also prove a similar result for three-message private-coin arguments. Previously, Bostanci, Qian, Spooner, and Yuen (STOC 2024) proved such a parallel repetition result in the more general setting of quantum protocols, where the verifier and communication may be quantum. We consider only protocols where the verifier is classical, but obtain a simplified analysis, and for the more general setting of threshold verifiers.

arXiv:2506.02277•Annual Symposium on Foundations of Computer Science•Dec 14, 2025•1 citation
Compiling Any MIP∗\mathsf{MIP}^{*}MIP∗ into a (Succinct) Classical Interactive Argument
We present a generic compiler that converts any MIP∗\mathsf{MIP}^{*}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 (LWE\mathsf{LWE}LWE) problem. Prior to this work, such a compiler for MIP∗\mathsf{MIP}^{*}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 QIP\mathsf{QIP}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 L\mathcal{L}L has a QIP\mathsf{QIP}QIP with semi-malicious soundness, where the prover runs in time TTT, then L∈QMATIME(T)\mathcal{L} \in \mathsf{QMATIME}(T)L∈QMATIME(T). Then we construct a succinct classical argument for any such language, where the communication complexity grows polylogarithmically with TTT, under the post-quantum sub-exponential hardness of LWE\mathsf{LWE}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.
Succinct argument systems are of central importance to modern crytpography, enabling the efficient verification of computational claims. In the classical setting, Kilian (STOC 92) established that any probabilistically checkable proof for NP can be transformed into a succinct argument system for NP using only collision-resistant hash functions. In the quantum setting, recent works have established the feasibility of (classically-verifiable) succinct arguments for QMA, capturing statements that require *quantum* proofs. However, known constructions all rely on the highly structured assumption of learning with errors (LWE), which stands in stark contrast with the unstructured assumptions that suffice for NP. In this work, we develop a new framework that broadens the cryptographic foundations of succinct arguments for QMA. We assume the existence of (i) an oblivious state preparation (OSP) protocol, which in turn can be constructed from *plain* trapdoor claw-free functions, and (ii) collapsing hash functions, the quantum analogue of collision-resistance. In particular, we obtain the first succinct, classically-verifiable argument system for QMA which does not rely on the hardness of LWE. Our construction proceeds in two steps. First, we design a *round-efficient* classically-verifiable argument system for QMA based only on the assumption of OSP. Second, we introduce a *generalized communication compression compiler*, which, assuming collapsing hash functions, transforms any TTT-round interactive protocol into one in which the communication size is bounded by $T \cdot \poly(\secp)$ for some fixed $\poly$ independent of the original size of each message. Our compiler extends a quantum rigidity-based communication compression technique of Zhang (QCrypt 25), and may be of independent interest.
We show that assuming the existence of homomorphic encryption, parallel repetition of all interactive arguments (after being run under homomorphic encryption) reduces the soundness error at a tight exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers, where the parallel repeated verifier accepts if and only if at least ttt of the executions are accepted (for some threshold ttt). Prior to this work, these results were known only when the cheating prover was assumed to be classical, and it was not known how to achieve tight bounds. As a corollary, we construct the first constant-round succinct argument for QMA\mathsf{QMA}QMA with negligible completeness and soundness errors assuming only the existence of quantum homomorphic encryption.
We construct a succinct classical argument system for QMA, the quantum analogue of NP, from generic and standard cryptographic assumptions. Previously, building on the prior work of Mahadev (FOCS '18), Bartusek et al. (CRYPTo ‘22) also constructed a succinct classical argument system for Q M A. However, their construction relied on post-quantumly secure indistinguishability obfuscation, a very strong primitive which is not known from standard cryptographic assumptions. In contrast, the primitives we use (namely, collapsing hash functions and a mild version of quantum homomorphic encryption) are much weaker and are implied by standard assumptions such as LWE. Our protocol is constructed using a general transformation which was designed by Kalai et al. (STOC '23) as a candidate method to compile any quantum nonlocal game into an argument system. Our main technical contribution is to analyze the soundness of this transformation when it is applied to a succinct self-test for Pauli measurements on maximally entangled states, the latter of which is a key component in the proof of MIP * = R E in Quantum complexity.
A quantum verifier decides membership in QMA using a (single) quantum witness state. This witness may be arbitrary, and no requirement is placed on it beyond its acceptance probability. A protocol claiming to classically verify QMA should offer the same guarantee: any witness that would convince a quantum verifier should also suffice to convince a classical verifier. Unfortunately, existing classical verification of quantum computation (CVQC) protocols behave quite differently from the original QMA verifier: they require many copies of the witness and destroy every one, effectively demanding that the prover solve the hard problem of witness duplication before verification can begin. We build a protocol to classically verify QMA languages that uses a single copy of the prover's QMA witness. Whenever the original QMA verifier accepts that witness with overwhelming probability, our protocol has negligible completeness and soundness errors and returns the witness negligibly disturbed after interaction with an honest verifier. The soundness of our CVQC is based on the post-quantum Learning With Errors (LWE) assumption. As an intermediate step of independent interest, we introduce witness-preserving classical arguments for NP which enable provers that start out with a superposition over NP witnesses to convince a verifier without disturbing their superposition.
Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on ``structured'' cryptographic primitives, or on the quantum PCP conjecture. We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA. Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.
In this work, we show that parallel repetition of public-coin interactive arguments reduces the soundness error at an exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers, where the parallel repeated verifier accepts if and only if at least t of the executions are accepted (for some threshold t). Prior to this work, these results were known only when the cheating prover was assumed to be classical.We also prove a similar result for three-message private-coin arguments. Previously, Bostanci, Qian, Spooner, and Yuen (STOC 2024) proved such a parallel repetition result in the more general setting of quantum protocols, where the verifier and communication may be quantum. We consider only protocols where the verifier is classical, but obtain a simplified analysis, and for the more general setting of threshold verifiers.