Abstract
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.
Highlights
To cite this article: Kirill P Kalinin and Natalia G Berloff 2018 New J
Several gain-dissipative platforms based on the networks of optical parametric oscillators, Any further distribution of lasers and various non-equilibrium Bose–Einstein condensates have been proposed and realised as this work must maintain attribution to the analogue Hamiltonian simulators for solving large-scale hard optimisation problems
In the last five years we have seen the rapid emergence of a new field at the intersection of laser and condensed matter physics, engineering and complexity theories which aims to develop quantum devices to simulate classical spin problems faster than on classical von Neumann architecture using a gain-dissipative principle of operation
Summary
To cite this article: Kirill P Kalinin and Natalia G Berloff 2018 New J. Different densities at the threshold even if the steady state and phase synchronisation is achieved imply that the system reached the minimum of the XY Hamiltonian the coupling coefficients DiijnjKij are replaced by DiijnjKij rj ri where ρi and ρj are not known a priori.
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