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*.

翻译：现有的量子计算经典验证（CVQC）协议会消耗证明者的见证态，每次调用都需要新的见证态。由于QMA见证态通常不可克隆，销毁输入见证态意味着通过重复进行可靠性与完备性放大需要多个见证副本。迄今为止，构建仅使用*单份*见证副本且具有低可靠性误差的CVQC一直是一个悬而未决的问题。我们通过构造一种CVQC解决了该问题，该协议仅使用单份QMA见证态副本，具有可忽略的完备性与可靠性误差，且*不会*销毁其见证态。我们CVQC的可靠性基于后量子学习错误（LWE）假设。为实现这一结果，我们定义并构建了两种用于非破坏性处理经典数据叠加态的基元（基于后量子LWE假设），我们相信这些基元具有独立的研究价值：- 一种*状态保持*的NP经典论证方案。- 具有*状态恢复*功能的双模陷门函数。