QLunch: Faster quantum and classical SDP approximations for quadratic binary optimization

Speaker: Daniel Stilck França from QMATH

Title: Faster quantum and classical SDP approximations for quadratic binary optimization

Abstract: We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. The class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into constant factor approximations of the original quadratic optimization problem.

If time permits, I will also discuss applications of our algorithm to obtain faster algorithms for the tomography of low-rank quantum states.This is joint work with Fernando Brandao and Richard Kueng.