Gain-dissipative simulators for large-scale hard classical optimisation
Kirill P. Kalinin, Natalia G. Berloff · arXiv (Cornell University) · 2018
Recently several gain-dissipative platforms based on the network of optical parametric oscillators, lasers and various non-equilibrium Bose-Einstein condensates have been proposed as analog Hamiltonian simulators for solving large-scale hard optimisation problems. The parameters of such problems depend on the node occupancies that are not a priory known, 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 algorithms for solving the NP-hard large-scale optimisation problems such as constant modulus continuous quadratic optimisation for any general matrix. We show that to solve such problems any gain-dissipative simulator has to implement a feedback mechanism for the dynamical adjustment of the gain, so that occupancy of each node is the same. Based on the principle of operation of such simulators we propose a novel class of classical gain-dissipative algorithms and show its advantage in comparison with classical algorithms. The estimates of the time operation of the physical implementation of the gain-dissipative simulators for large matrices show the speed-up of the several orders of magnitude in comparison with classical computations.