We study the power of quantum witnesses under perfect completeness. We construct a classical oracle relative to which a language lies in $\mathsf{QMA}_1$ but not in $\mathsf{QCMA}$ when the $\mathsf{QCMA}$ verifier is only allowed polynomially many adaptive rounds and exponentially many parallel queries per round. Additionally, we derandomize the permutation-oracle separation of Fefferman and Kimmel, obtaining an in-place oracle separation between $\mathsf{QMA}_1$ and $\mathsf{QCMA}$. Furthermore, we focus on $\mathsf{QCMA}$ and $\mathsf{QMA}$ with an exponentially small gap, where we show a separation assuming the gap is fixed, but not when it may be arbitrarily small. Finally, we derive consequences for approximate ground-state preparation from sparse Hamiltonian oracle access, including a bounded-adaptivity frustration-free variant.

翻译：我们研究了完美完备性条件下量子见证的力量。我们构建了一个经典Oracle，在该Oracle下存在一门语言属于$\mathsf{QMA}_1$，但不在$\mathsf{QCMA}$中，其中$\mathsf{QCMA}$验证器仅被允许进行多项式次自适应轮次，且每轮最多进行指数次并行查询。此外，我们对Fefferman和Kimmel的置换Oracle分离进行了去随机化，得到了一个$\mathsf{QMA}_1$与$\mathsf{QCMA}$之间的原位Oracle分离。进一步地，我们聚焦于带指数小间隙的$\mathsf{QCMA}$和$\mathsf{QMA}$，并证明当该间隙固定时存在分离，但间隙可任意小时则不然。最后，我们推导了基于稀疏哈密顿量Oracle访问的近似基态制备的相关结论，包括一个有界自适应无挫败变体。