Compiler Creates Succinct Classical Interactive Arguments with Post-Soundness Relying on Learning with Errors

The challenge of verifying complex computations securely underpins much of modern cryptography, and researchers continually seek methods to prove the correctness of these processes with minimal communication. Andrew Huang and Yael Tauman Kalai, both from MIT’s Computer Science and Artificial Intelligence Laboratory, now present a new compiler that transforms any computational protocol into a succinct interactive argument, ensuring verification can occur efficiently with classical computers. This achievement overcomes limitations in previous approaches, which relied on unproven assumptions about post-quantum security, and establishes a framework where the security of the verification process depends on the well-studied post-sub-exponential hardness of the Learning with Errors problem. By enabling succinct and classically verifiable proofs for any protocol, this work represents a significant step towards practical and robust cryptographic systems.

Lombardi, Vaikuntanathan and Yang previously presented work at STOC 2022, but the post-quantum soundness of that compiler remains under investigation. This compiler applies to any Quantum Interactive Proof (QIP) protocol sound only against semi-malicious provers, even with a potentially malicious initial state. The compiler operates in two steps, first demonstrating that if a language L has a QIP with semi-malicious soundness, and the prover runs in time T, then L belongs to the complexity class QMATIME(T). Subsequently, the team constructs a succinct classical argument for any such language, where the communication required to verify the proof grows very slowly with the computation time T, relying on the post-quantum sub-exponential hardness of the Learning with Errors (LWE) problem.

Quantum Verification Without Problem Specificity

Scientists have achieved a breakthrough in quantum verification by developing a method to verify quantum computations without needing specific knowledge of the input. This instance-independent protocol is a crucial step towards building practical and reliable quantum computers. The team addresses the challenge of verifying problems within the complexity class QMA, where a quantum prover attempts to convince a quantum verifier of the correctness of a solution. The core innovation lies in constructing a Hamiltonian, a mathematical operator describing the energy of a quantum system, that encodes the verification problem.

This Hamiltonian is carefully designed to be local, meaning it only acts on a small number of qubits, simplifying the quantum computation. The Hamiltonian comprises components for initialization, computation regulation, the computation itself, and final result checking. Crucially, the Hamiltonian is constructed to be Y-free, involving only specific quantum operators, which further simplifies the computation. The team adapts the Morimae-Fitzsimons protocol, achieving instance independence by removing the need for random numbers and using a fixed basis for measurement. The resulting verification protocol efficiently verifies the computation, contributing to the development of practical quantum verification protocols, enhancing the security of quantum systems, and advancing our understanding of the complexity class QMA.

Succinct Classical Arguments for Quantum Interactive Proofs

Scientists have developed a new compiler that transforms any interactive protocol into a succinct interactive argument, where both the prover and verifier operate classically. This breakthrough establishes a strong foundation for secure computation and addresses which quantum computations can be efficiently and succinctly verified by a classical system. The team demonstrates that if a language has a Quantum Interactive Proof (QIP) with semi-malicious soundness, and the prover operates within a time limit of T, then that language belongs to the complexity class QMATIME(T). Subsequently, they construct a succinct classical argument for any such language, achieving a communication complexity that grows very slowly with the computation time T, relying on the post-quantum sub-exponential hardness of the Learning with Errors (LWE) problem.

This work builds upon prior advancements, offering a generic transformation applicable to any MIP∗ protocol, even those that are not succinct or involve multiple provers. Experiments confirm that the compiled protocol’s soundness approaches the commuting operator value of the underlying nonlocal game, offering a pathway to more robust and verifiable quantum computations. This work delivers a significant step towards bridging the gap between quantum computation and classical verification, potentially enabling the widespread adoption of secure quantum technologies.

Succinct Arguments From Any Protocol Compiler

Scientists have presented a new compiler that transforms any protocol into a succinct interactive argument, ensuring security relies on the difficulty of solving the Learning with Errors problem, even when the initial state of the prover is potentially malicious. The researchers demonstrate that if a language possesses a proof system with semi-malicious soundness, then a succinct classical argument can be constructed for it, with the complexity of the argument growing at a polylogarithmic rate. This achievement builds upon prior work, offering a compiler with stronger security guarantees grounded in a well-studied computational hardness assumption. The team’s compiler is broadly applicable, extending to protocols initially sound only against honest provers, by accommodating potentially malicious initial states. This versatility represents a significant step forward in the field of cryptographic protocols, offering a method to enhance the security of a wide range of systems.