SIAM Journal on Computing, Volume 49, Issue 2, Page 245-283, January 2020.
Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result representing a further quantum generalization of this fact, which is that every problem in the complexity class QMA has a quantum zero-knowledge proof system. More specifically, assuming the existence of an unconditionally binding and quantum computationally concealing commitment scheme, we prove that every problem in the complexity class QMA has a quantum interactive proof system that is zero-knowledge with respect to efficient quantum computations. Our QMA proof system is sound against arbitrary quantum provers, but only requires an honest prover to perform polynomial-time quantum computations, provided that it holds a quantum witness for a given instance of the QMA problem under consideration. The proof system relies on a new variant of the QMA-complete local Hamiltonian problem in which the local terms are described by Clifford operations and standard basis measurements. We believe that the QMA-completeness of this problem may have other uses in quantum complexity.

中文翻译：

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QMA的零知识证明系统

SIAM计算杂志，第49卷，第2期，第245-283页，2020年1月。
先前的工作已经确定，NP中的所有问题都可以使用经典的零知识证明系统，并且在进行量子计算的合理硬度假设下，可以使这些证明系统抵抗量子攻击。我们证明了代表这一事实的进一步量子概括的结果，即复杂度类QMA中的每个问题都有一个量子零知识证明系统。更具体地说，假设存在无条件绑定和量子计算隐藏承诺方案，我们证明了复杂度类QMA中的每个问题都有一个相对于有效量子计算为零知识的量子交互证明系统。我们的QMA证明系统可以抵御任意量子证明，但是只需要诚实的证明者即可执行多项式时间量子计算，前提是它拥有要考虑的QMA问题给定实例的量子见证。证明系统依赖于QMA完全局部哈密顿量问题的新变体，其中通过Clifford运算和标准基础测量来描述局部项。我们认为，此问题的QMA完整性可能在量子复杂度方面还有其他用途。