Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle

Authors Xingjian Li , Qipeng Liu , Angelos Pelecanos , Takashi Yamakawa

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Author Details

Xingjian Li
  • Tsinghua University, Beijing, China
Qipeng Liu
  • University of California at San Diego, La Jolla, CA, USA
Angelos Pelecanos
  • University of California at Berkeley, CA, USA
Takashi Yamakawa
  • NTT Social Informatics Laboratories, Tokyo, Japan

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Xingjian Li, Qipeng Liu, Angelos Pelecanos, and Takashi Yamakawa. Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 72:1-72:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly ≠ BQP/poly or QMA ≠ QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly ≠ BQP/poly and QMA ≠ QCMA. Here, classically-accessible classical oracles are oracles that can be accessed only classically even for quantum algorithms. Based on a similar technique, we also show an alternative proof for the separation of QMA and QCMA relative to a distributional quantumly-accessible classical oracle, which was recently shown by Natarajan and Nirkhe.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
  • Theory of computation → Quantum computation theory
  • quantum computation
  • computational complexity


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