QuICS Special Seminar
Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the global effect of quantum tunneling. Specifically, we introduce a quantum algorithm termed the quantum tunneling walk (QTW) and apply it to nonconvex problems where local minima are approximately global minima. We show that QTW achieves quantum speedup over classical stochastic gradient descents (SGD) when the barriers between different local minima are high but thin and the minima are flat. Based on this observation, we construct a specific double-well landscape, where classical algorithms cannot efficiently hit one target well knowing the other well but QTW can when given proper initial states near the known well. Finally, we corroborate our findings with numerical experiments.
This is a joint work with Yizhou Liu and Weijie J. Su. The full version of the paper can be found at https://quantum-journal.org/papers/q-2023-06-02-1030/.
ATL 3100A and Virtual Via Zoom.
*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*