We study the relative advantage of classical and quantum distinguishers of bounded query complexity over $n$-bit strings, focusing on the case of a single quantum query. A construction of Aaronson and Ambainis (STOC 2015) yields a pair of distributions that is $\epsilon$-distinguishable by a one-query quantum algorithm, but $O(\epsilon k/\sqrt{n})$-indistinguishable ... more >>>

In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an information-theoretically secure) streaming proof with a quantum logspace prover and a classical logspace verifier. The prover provides a polynomial-length proof that is streamed to ... more >>>

What is the $\Sigma_3^2$-circuit complexity (depth 3, bottom-fanin 2) of the $2n$-bit inner product function? The complexity is known to be exponential $2^{\alpha_n n}$ for some $\alpha_n=\Omega(1)$. We show that the limiting constant $\alpha=\limsup \alpha_n$ satisfies
\[
0.847... ~\leq~ \alpha ~\leq~ 0.965...\ .
\]
Determining $\alpha$ is one of the ... more >>>