We show that a mild derandomization assumption together with the
worst-case hardness of NP implies the average-case hardness of a
language in non-deterministic quasi-polynomial time. Previously such
connections were only known for high classes such as EXP and
PSPACE.

There has been a long line of research trying to explain ... more >>>

Let m,q > 1 be two integers that are co-prime and A be any subset of Z_m. Let P be any multi-linear polynomial of degree d in n variables over Z_m. We show that the MOD_q boolean function on n variables has correlation at most exp(-\Omega(n/(m2^{m-1})^d)) with the boolean function ... more >>>

Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a state using a number of measurements that grows only linearly with n. Besides possible ... more >>>