Solving the max-3-cut problem using synchronized dissipative networks

Abstract

Many computational problems are intractable through classical computing and, as Moore's law is drawing to a halt, demand for finding alternative methods in tackling these problems is growing. Here, we realize a liquid light machine for the NP-hard max-3-cut problem based on a network of synchronized exciton-polariton condensates. We overcome the binary limitation of the decision variables in Ising machines using the continuous-phase degrees of freedom of a coherent network of polariton condensates. The condensate network dynamical transients provide optically-fast annealing of the XY Hamiltonian. We apply the Goemans and Williamson random hyperplane technique, discretizing the XY ground state spin configuration to serve as ternary decision variables for an approximate optimal solution to the max-3-cut problem. Applications of the presented coherent network are investigated in image-segmentation tasks and in circuit design.

12 pages, 8 figures

References in corpus (7)

• Excitations in a non-equilibrium Bose-Einstein condensate of exciton-polaritons
• Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
• Large-scale photonic Ising machine by spatial light modulation
• A Scalable Photonic Computer Solving the Subset Sum Problem
• A Polariton Graph Simulator
• Engineering spatial coherence in lattices of polariton condensates
• Polariton condensation in a planar microcavity with InGaAs quantum wells

Cited by in corpus (5)

• Spin-polarized antichiral exciton-polariton edge states
• Next nearest neighbour coupling with spinor polariton condensates
• Spatial Optical Simulator for Classical Statistical Models
• Direct comparison of stochastic driven nonlinear dynamical systems for combinatorial optimization
• Minor embedding with Stuart-Landau oscillator networks