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Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle

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

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LIPIcs.ITCS.2024.72.pdf
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ACM Subject Classification
  • Theory of computation → Complexity classes
  • Theory of computation → Quantum computation theory
Keywords
  • quantum computation
  • computational complexity

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Abstract

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.

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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) https://doi.org/10.4230/LIPIcs.ITCS.2024.72

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

Funding

  • Liu, Qipeng: supported in part by the Simons Institute for the Theory of Computing, through a Quantum Postdoctoral Fellowship, by the DARPA SIEVE-VESPA grant No.HR00112020023 and by the NSF QLCI program through grant number OMA-2016245.
  • Pelecanos, Angelos: supported by DARPA under Agreement No. HR00112020023.

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