We present a distribution $D$ over inputs in $\{-1,1\}^{2N}$, such that:
(1) There exists a quantum algorithm that makes one (quantum) query to the input, and runs in time $O(\log N)$, that distinguishes between $D$ and the uniform distribution with advantage $\Omega(1/\log N)$.
(2) No Boolean circuit of $\mathrm{quasipoly}(N)$ ... more >>>

Given the polygonal schema embedding of an $O(log n)$ genus graph $G$ and two vertices
$s$ and $t$ in $G$, we show that deciding if there is a path from $s$ to $t$ in $G$ is in unambiguous
logarithmic space.

more >>>

We show that any language in nondeterministic time $\exp(\exp(\cdots\exp(n)))$, where the number of iterated exponentials is an arbitrary function $R(n)$, can be decided by a multiprover interactive proof system with a classical polynomial-time verifier and a constant number of quantum entangled provers, with completeness $1$ and soundness $1 - \exp(-C\exp(\cdots\exp(n)))$, ... more >>>