Solving the Max-3-Cut Problem with Coherent 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.

Qubit gate operations in elliptically trapped polariton condensates

“…In particular, these optically induced potentials can be flexibly designed with the use of spatial light modulators (SLMs). Their shape may be varied on demand from one experiment to another, permitting the realization of polariton XY 37 , 38 or Ising simulators 39 , 40 .…”

Spin-polarized antichiral exciton-polariton edge states

“…Exciton-polaritons are quasi particles that arise due to the strong coupling between quantum well excitons and microcavity photons [19][20][21]. Due to their excitonic component, polaritons exhibit strong nonlinearity, which has lead to a variety of optical devices [22,23], optical computation [24][25][26][27], and others [28,29]. The finite lifetime of the photons gives rise to interesting non-Hermitian physics.…”