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. This 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. Such instances include approximating the ground state of spin glasses and MaxCut on Erdös-Rényi graphs. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into approximations of the original quadratic optimization problem.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 20, 2022
- Source ID
- 10.22331/q-2022-01-20-625
Entities
People
- Daniel Stilck França
- Fernando G.s L. Brandão
- Richard Kueng
Organizations
- California Institute of Technology
- Johannes Kepler University Linz
- Office of Naval Research
- Technical University of Munich
- University of Copenhagen
- Villum Foundation