Recent works have demonstrated that quantum oracles have subtle behavior, as access to inverse, conjugate or controlled queries can exponentially change the query complexity of certain tasks. Inspired by these works, we introduce the notion of meta-complexity of quantum relativization. We ask: for any two quantum compl...
S. Aaronson, Adam Bouland, Jordan Docter et al.· 0 citations
The planted clique problem is a promising candidate for quantum advantage with a wide computational-statistical gap and substantial evidence for classical hardness. We study two quantum encodings of classical samples, a natural binary phase state encoding and symmetry-adapted measurements, and determine if they preserv...
Vojtěch Havlíček, Jordan Docter, Subhash Khot· 0 citations
One of the most basic conjectures in quantum complexity theory states that every $t$-query quantum algorithm can be simulated on most inputs by a $\mathrm{poly}(t)$-query classical algorithm. If true, this would provide broad justification for the need for structure in quantum speedups. We settle this conjecture for pa...
Guy Blanc, Jordan Docter, Carmen Strassle et al.· 1 citation· ⚡1
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