Solving the max-3-cut problem with coherent networks
Solving the max-3-cut problem with coherent networks
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.
Coupled oscillators, Exciton Polariton, Optical computing, XY model, optimisation problem
Harrison, Stella, Louise
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Sigurdsson, Helgi
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Alyatkin, Sergey
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Toepfer, Julian, Dominic
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Lagoudakis, Pavlos
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24 February 2022
Harrison, Stella, Louise
9c747e27-dc04-40d3-b982-0674c0154048
Sigurdsson, Helgi
c6380293-fe97-4fd0-a819-cf35721d4e5d
Alyatkin, Sergey
485bddd5-8eb7-4045-911b-86b0d401bdd4
Toepfer, Julian, Dominic
f3e89749-2912-4907-b712-6052b732dfb1
Lagoudakis, Pavlos
ea50c228-f006-4edf-8459-60015d961bbf
Harrison, Stella, Louise, Sigurdsson, Helgi, Alyatkin, Sergey, Toepfer, Julian, Dominic and Lagoudakis, Pavlos
(2022)
Solving the max-3-cut problem with coherent networks.
Physical Review Applied, 17 (2), [024063].
(doi:10.1103/PhysRevApplied.17.024063).
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.
Text
XU10552N
- Accepted Manuscript
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Published date: 24 February 2022
Additional Information:
Funding Information:
S.L.H., H.S., J.D.T., and P.G.L. acknowledge the support of the UK’s Engineering and Physical Sciences Research Council (Grant No. EP/M025330/1 on Hybrid Polaritonics), and S.A. acknowledges the funding of the Russian Foundation for Basic Research (RFBR) within the joint RFBR and CNR Project No. 20-52-7816. H.S. and P.G.L. also acknowledge the European Union’s Horizon 2020 program, through a FET Open Research and Innovation Action under the Grant Agreement No. 899141 (PoLLoC). H.S. acknowledges the Icelandic Research Fund (Rannis), Grant No. 217631-051. S.L.H. acknowledges the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work.
Publisher Copyright:
© 2022 American Physical Society.
Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.
Keywords:
Coupled oscillators, Exciton Polariton, Optical computing, XY model, optimisation problem
Identifiers
Local EPrints ID: 456051
URI: http://eprints.soton.ac.uk/id/eprint/456051
ISSN: 2331-7019
PURE UUID: 0bf8068e-1c84-42c3-ae91-3e2ee3f46d6f
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Date deposited: 25 Apr 2022 16:37
Last modified: 11 Nov 2024 20:40
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