Networks of non-equilibrium condensates for global optimization

• Published in: New journal of physics Vol. 20; no. 11; pp. 113023 - 113029
• Main Authors: Kalinin, Kirill P, Berloff, Natalia G
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 14.11.2018
• Subjects: Bose-Einstein condensates; coherent network computing; Computer simulation; exciton-polariton; global optimisation; Global optimization; non-equilibrium condensates; Nonlinear programming; Optical communication; Optical Parametric Oscillators; Parametric amplifiers; Physics; polariton networks; Simulators; spin Hamiltonians
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/aae8ae

Recently several gain-dissipative platforms based on the networks of optical parametric oscillators, lasers and various non-equilibrium Bose-Einstein condensates have been proposed and realised as analogue Hamiltonian simulators for solving large-scale hard optimisation problems. However, in these realisations the parameters of the problem depend on the node occupancies that are not known a priori, which limits the applicability of the gain-dissipative simulators to the classes of problems easily solvable by classical computations. We show how to overcome this difficulty and formulate the principles of operation of such simulators for solving the NP-hard large-scale optimisation problems such as constant modulus continuous quadratic optimisation and quadratic binary optimisation for any general matrix. To solve such problems any gain-dissipative simulator has to implement a feedback mechanism for the dynamical adjustment of the gain and coupling strengths.