如何经典验证一个量子猫而不杀死它
How to Classically Verify a Quantum Cat without Killing It
AI总结：
本文提出了一种无需破坏量子见证态的经典验证量子计算协议，基于后量子LWE假设，实现了低错误率的验证
摘要：
现有用于经典验证量子计算（CVQC）的协议会消耗证人的见证态，需要为每次调用提供新的见证态。由于QMA见证态通常不能克隆，破坏输入见证态意味着通过重复来放大正确性和完备性需要许多见证态的副本。迄今为止，构建一个使用仅一个见证态副本且具有极低正确性错误率的CVQC仍是一个开放性问题。我们通过构造一个CVQC来解决这个问题，该CVQC使用一个QMA见证态副本，具有可忽略的正确性和错误率，并且不破坏其见证态。我们的CVQC的正确性基于后量子学习与错误（LWE）假设。为了获得这一结果，我们定义并构建了两个原始工具（基于后量子LWE假设），用于非破坏性地处理经典数据的叠加，我们认为这些工具具有独立的兴趣：- 一个保持状态的NP经典论证。- 具有状态恢复的双模式陷阱门函数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
