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arXiv · 2212.00098

On the power of nonstandard quantum oracles

Roozbeh Bassirian·Bill Fefferman·Kunal Marwaha
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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.

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Roozbeh Bassirian, Bill Fefferman, Kunal Marwaha. 2022-11-30. On the power of nonstandard quantum oracles. https://doi.org/10.4230/lipics.tqc.2023.11

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