A distribution testing oracle separation between QMA and QCMA

Quantum 8, 1377 (2024).

https://doi.org/10.22331/q-2024-06-17-1377

It is a long-standing open question in quantum complexity theory whether the definition of $non-deterministic$ quantum computation requires quantum witnesses (QMA) or if classical witnesses suffice (QCMA). We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes. Previous separations [3], [13] required a quantum unitary oracle. The separating problem is deciding whether a distribution supported on regular un-directed graphs either consists of multiple connected components (yes instances) or consists of one expanding connected component (no instances) where the graph is given in an adjacency-list format by the oracle. Therefore, the oracle is a distribution over $n$-bit boolean functions.