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On the Power of Nonstandard Quantum Oracles

Authors Roozbeh Bassirian, Bill Fefferman, Kunal Marwaha

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Author Details

Roozbeh Bassirian
  • University of Chicago, IL, USA
Bill Fefferman
  • University of Chicago, IL, USA
Kunal Marwaha
  • University of Chicago, IL, USA

Funding

  • Bassirian, Roozbeh: AFOSR (YIP number FA9550-18-1-0148 and FA9550-21-1-0008); NSF under Grant CCF-2044923 (CAREER); U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers; DOE QuantISED grant DE-SC0020360.
  • Fefferman, Bill: AFOSR (YIP number FA9550-18-1-0148 and FA9550-21-1-0008); NSF under Grant CCF-2044923 (CAREER); U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers; DOE QuantISED grant DE-SC0020360.
  • Marwaha, Kunal: NSF Graduate Research Fellowship Program under Grant No. DGE-1746045

Acknowledgements

Thanks to Casey Duckering, Juspreet Singh Sandhu, Peter Shor, and Justin Yirka for collaborating on early stages of this project. KM thanks many others for engaging discussions, including Adam Bouland, Antares Chen, Aram Harrow, Matt Hastings, Eric Hester, Neng Huang, Robin Kothari, Brian Lawrence, Yi-Kai Liu, Patrick Lutz, Tushant Mittal, Abhijit Mudigonda, Chinmay Nirkhe, and Aaron Potechin. Thanks to Chinmay Nirkhe for feedback on a previous version of this manuscript.

Cite As Get BibTex

Roozbeh Bassirian, Bill Fefferman, and Kunal Marwaha. On the Power of Nonstandard Quantum Oracles. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 11:1-11:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.TQC.2023.11

Abstract

We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function f, and present f in different oracle models. We first give a one-query QMA protocol to test if a graph encoded in f has a small disconnected subset. We then use representation theory to show that no classical witness can help a quantum verifier efficiently decide this problem relative to an in-place oracle. Perhaps surprisingly, a simple modification to the standard oracle prevents a quantum verifier from efficiently deciding this problem, even with access to an unbounded witness.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • quantum complexity
  • QCMA
  • expander graphs
  • representation theory

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