We study one-way quantum communication lower bounds for search problems.Unlike decision problems, search problems can have many valid outputs, which pose a fundamental barrier to standard quantum lower-bound techniques. We overcome this by developing a novel method based on matrix discrepancy, which allows us to bound the output measurements of ... more >>>

We explore the torus polynomial approximation based approach towards a long-standing question: whether AND can be computed by $CC^0$ circuits - the class of constant-depth polynomial size circuits containing $MOD_m$ gates for some natural number $m$.
Bhrushundi, Hosseini, Lovett and Rao (ITCS 2019) introduced torus polynomial approximations as an approach ... more >>>

We prove an $\tilde{\Omega}(n^2)$ lower bound for read-once parity branching programs computing an explicit boolean function on $n$ variables. The previous best lower bound was $\tilde{\Omega}(n^{1.5})$. Our lower bound is proved by reducing the problem to a lower bound in algebraic circuit complexity.

more >>>