Ryan O'Donnell (CMU)
Title: Mean Estimation When You Have The Source Code; or, Quantum Monte Carlo Methods
Abstract: Suppose y is a real random variable, and one is given access to "the code" that generates it (for example, a randomized or quantum circuit whose output is y). We give a quantum procedure that runs the code O(n) times and returns an estimate for E[y] with optimal dependence on n for quantum algorithms. The central subroutine for our result is essentially Grover's algorithm but with complex phases.
Joint work with Robin Kothari (Microsoft).