On the power of nonstandard quantum oracles
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 onequery 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 inplace 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2212.00098
 arXiv:
 arXiv:2212.00098
 Bibcode:
 2022arXiv221200098B
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity
 EPrint:
 22+13 pages