Oracle Separation of QMA and QCMA with Bounded Adaptivity

Authors Shalev Ben-David , Srijita Kundu



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Author Details

Shalev Ben-David
  • Institute for Quantum Computing, University of Waterloo, Canada
Srijita Kundu
  • Institute for Quantum Computing, University of Waterloo, Canada

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Shalev Ben-David and Srijita Kundu. Oracle Separation of QMA and QCMA with Bounded Adaptivity. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 21:1-21:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ICALP.2024.21

Abstract

We give an oracle separation between QMA and QCMA for quantum algorithms that have bounded adaptivity in their oracle queries; that is, the number of rounds of oracle calls is small, though each round may involve polynomially many queries in parallel. Our oracle construction is a simplified version of the construction used recently by Li, Liu, Pelecanos, and Yamakawa (2023), who showed an oracle separation between QMA and QCMA when the quantum algorithms are only allowed to access the oracle classically. To prove our results, we introduce a property of relations called slipperiness, which may be useful for getting a fully general classical oracle separation between QMA and QCMA.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum computing
  • computational complexity

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