On Exponential-Time Hypotheses, Derandomization, and Circuit Lower Bounds: Extended Abstract

Quantum learning algorithms imply circuit lower bounds

“…This is because B computes a promise natural property, and we cannot easily estimate the exact probability that B accepts a string to consistently compute the "first" such string.3 Indeed, this has happened in practice, where techniques employed to design a better PRG also led to a new learning-to-lower-bound connection[CRTY20]. Our work shows that this is not a coincidence, i.e., better PRGs lead to better connections in a black-box way.…”