How to Classically Verify a Quantum Cat without Killing It

2026-02-09

AI Summary

This work proposes the first non-destructive classical verification protocol for quantum computations that achieves negligible completeness and soundness errors while using only a single copy of a QMA witness state. Existing classical verification protocols typically consume the witness state, making it challenging to simultaneously ensure reusability and low error rates with just one copy. The key innovations include an NP-based classical argument system with state-preserving properties constructed under the post-quantum Learning With Errors (LWE) assumption, and a dual-mode trapdoor function enabling state recovery. This protocol enables efficient, repeatable, and secure classical verification using a single QMA witness, resolving a long-standing open problem in the field.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Computer Vision: Multi-modal Vision

Application Category

• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Existing protocols for classical verification of quantum computation (CVQC) consume the prover's witness state, requiring a new witness state for each invocation. Because QMA witnesses are not generally clonable, destroying the input witness means that amplifying soundness and completeness via repetition requires many copies of the witness. Building CVQC with low soundness error that uses only *one* copy of the witness has remained an open problem so far. We resolve this problem by constructing a CVQC that uses a single copy of the QMA witness, has negligible completeness and soundness errors, and does *not* destroy its witness. The soundness of our CVQC is based on the post-quantum Learning With Errors (LWE) assumption. To obtain this result, we define and construct two primitives (under the post-quantum LWE assumption) for non-destructively handling superpositions of classical data, which we believe are of independent interest: - A *state preserving* classical argument for NP. - Dual-mode trapdoor functions with *state recovery*.

Problem

• classical verification of quantum computation
• QMA witness
• non-destructive verification
• soundness amplification
• witness preservation

Innovation

• classical verification of quantum computation
• QMA witness
• state-preserving
• dual-mode trapdoor functions
• post-quantum LWE