Year: 2022
Type: article
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.
Source: Quantum
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
Funders: National Science Foundation, California Institute of Technology, Villum Fonden, European Commission, Technische Universität München, Samsung, Institute for Quantum Information and Matter, California Institute of Technology, Elitenetzwerk Bayern, Graduate School, Technische Universität München, Office of Naval Research, Army Research Office
Awards: G1658625161, TUM-IAS Fellowships for the cooperative development of high risk new fields in technology and science, G2403330605, G2958415499, G4504108201, The Institute for Quantum Information and Matter: Advancing the Entanglement Frontier, G5259259942, G7352392636, G8345540293, G8876996369, G961819192
OpenAlex ID: W2972992123