QIP $ \subseteq $ AM(2QCFA)

• URL: http://arxiv.org/abs/2508.21020v1
• Date: Thu, 28 Aug 2025 17:22:31 GMT
• Title: QIP $ \subseteq $ AM(2QCFA)
• Authors: Abuzer Yakaryılmaz,
• Abstract summary: We show that $mathsfPSPACE$ is subset of $mathsfAM (2QCFA)$, the class of languages having Arthur-Merlin proof systems.<n>Our protocols use only rational-valued quantum transitions and run in double-exponential expected time.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The class of languages having polynomial-time classical or quantum interactive proof systems ($\mathsf{IP}$ or $\mathsf{QIP}$, respectively) is identical to $\mathsf{PSPACE}$. We show that $\mathsf{PSPACE}$ (and so $\mathsf{QIP}$) is subset of $\mathsf{AM(2QCFA)}$, the class of languages having Arthur-Merlin proof systems where the verifiers are two-way finite automata with quantum and classical states (2QCFAs) communicating with the provers classically. Our protocols use only rational-valued quantum transitions and run in double-exponential expected time. Moreover, the member strings are accepted with probability 1 (i.e., perfect-completeness).

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