发表机构
Department of Computer Science and Engineering, Pennsylvania State University（宾夕法尼亚州立大学计算机科学与工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入非均匀量子多项式时间层级QCPH/mpoly，证明其坍缩当且仅当QCPH坍缩，并给出coQCMA包含于QCMA/mpoly时QCPH坍缩的充分条件，类比经典PH坍缩结果。
AI 中文摘要
尽管非均匀多项式时间层级（PH/poly）在经典复杂性理论中对于理解多项式时间层级（PH）的坍缩条件具有重要意义，但文献中尚未研究PH/poly的量子对应物。我们引入了非均匀计算量子多项式时间层级（QCPH/mpoly），即PH/poly的量子对应物，并证明当且仅当QCPH（由Gharibian等人（comput. complex. 2022）引入的PH的量子对应物）也坍缩时，QCPH/mpoly才坍缩。我们还证明了如果coQCMA包含于QCMA/mpoly中，则QCPH坍缩。这些结果类似于Yap（TCS 1983）在经典复杂性中常用于引发PH坍缩的结果。QCPH/mpoly类似于具有非均匀量子验证器电路的QCPH。
英文摘要
Despite the importance of the non-uniform Polynomial-Time Hierarchy (PH/poly) in classical complexity understanding the collapse conditions of the Polynomial-Time Hierarchy (PH), a quantum equivalent of PH/poly has yet to be studied in the literature. We introduce the non-uniform computational Quantum Polynomial-Time Hierarchy (QCPH/mpoly), the quantum equivalent of PH/poly, and show that it collapses if and only if QCPH, the quantum equivalent of PH introduced by Gharibian et al. (comput. complex. 2022), also collapses. We also show that QCPH collapses if coQCMA is contained in QCMA/mpoly. These results are analogous to those of Yap (TCS 1983) commonly used to invoke the collapse of PH in classical complexity. QCPH/mpoly is analogous to QCPH with non-uniform quantum verifier circuits.
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