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Probabilistic solving of NP-hard problems with bistable nonlinear optical networks

Probabilistic solving of NP-hard problems with bistable nonlinear optical networks
Probabilistic solving of NP-hard problems with bistable nonlinear optical networks
We study theoretically a lattice of locally bistable driven-dissipative nonlinear cavities. The system is found to resemble the classical Ising model and enables its effective simulation. First, we benchmark the performance of driven-dissipative nonlinear cavities for spin-glass problems, and study the scaling of the ground-state-energy deviation and success probability as a function of system size. Next, we show how an effective bias field can be included in an optical model and use it for probabilistic solving of optimization problems. As particular examples we consider NP-hard problems embedded in the Ising model, namely graph partitioning and the knapsack problem. Finally, we confirm that locally bistable polariton networks act as classical optimizers and can potentially provide an improvement within the exponential complexity class.
1550-235X
1-12
Kyriienko, O.
f7d94f06-9232-4a2b-a69d-a82fb657494f
Sigurdsson, H.
c6380293-fe97-4fd0-a819-cf35721d4e5d
Liew, T.C.H.
9686367a-ba47-4a78-80b1-35dc2155c75f
Kyriienko, O.
f7d94f06-9232-4a2b-a69d-a82fb657494f
Sigurdsson, H.
c6380293-fe97-4fd0-a819-cf35721d4e5d
Liew, T.C.H.
9686367a-ba47-4a78-80b1-35dc2155c75f

Kyriienko, O., Sigurdsson, H. and Liew, T.C.H. (2019) Probabilistic solving of NP-hard problems with bistable nonlinear optical networks. Physical Review B, 99 (19), 1-12, [195301]. (doi:10.1103/PhysRevB.99.195301).

Record type: Article

Abstract

We study theoretically a lattice of locally bistable driven-dissipative nonlinear cavities. The system is found to resemble the classical Ising model and enables its effective simulation. First, we benchmark the performance of driven-dissipative nonlinear cavities for spin-glass problems, and study the scaling of the ground-state-energy deviation and success probability as a function of system size. Next, we show how an effective bias field can be included in an optical model and use it for probabilistic solving of optimization problems. As particular examples we consider NP-hard problems embedded in the Ising model, namely graph partitioning and the knapsack problem. Finally, we confirm that locally bistable polariton networks act as classical optimizers and can potentially provide an improvement within the exponential complexity class.

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Probabilistic solving of NP-hard problems with bistable nonlinear optical networks - Accepted Manuscript
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More information

Accepted/In Press date: 9 May 2019
e-pub ahead of print date: 9 May 2019
Published date: 15 May 2019

Identifiers

Local EPrints ID: 431652
URI: http://eprints.soton.ac.uk/id/eprint/431652
ISSN: 1550-235X
PURE UUID: 9c973fc2-2d09-4263-aa11-22fa85a3e468
ORCID for H. Sigurdsson: ORCID iD orcid.org/0000-0002-4156-4414

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Date deposited: 12 Jun 2019 16:30
Last modified: 26 Nov 2021 03:18

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Contributors

Author: O. Kyriienko
Author: H. Sigurdsson ORCID iD
Author: T.C.H. Liew

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