Optical Potts machine through networks of three-photon down-conversion oscillators

Honari-Latifpour, Mostafa; Miri, Mohammad‐Ali

doi:10.1515/nanoph-2020-0256

Cited by 18 publications

(8 citation statements)

References 28 publications

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“…Similar behavior was also observed in the polarization states of nano-laser arrays [16]. Furthermore, networks of parametric three-photon down-conversion oscillators have been suggested for implementing a three-state Potts machine [19].…”

supporting

confidence: 60%

“…Recently, there has been a growing interest in emulating spin models with nonlinear driven-damped optical systems [7][8][9][10][11][12][13][14][15][16][17][18][19]. In particular, networks of coherently coupled degenerate optical parametric oscillators were used for implementing a binary spin system in analogy with the Ising model and utilized for solving NP-hard problems [8,9].…”

mentioning

confidence: 99%

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Mapping the XY Hamiltonian onto a Network of Coupled Lasers

Honari-Latifpour,

Miri

2020

Preprint

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In recent years there has been a growing interest in the physical implementation of classical spin models through networks of optical oscillators. However, a key missing step in this mapping is to formally prove that the dynamics of such a nonlinear dynamical system is toward minimizing a global cost function which is equivalent with the spin model Hamiltonian. Here, we introduce a minimal dynamical model for a network of dissipatively coupled optical oscillators and prove that the dynamics of such a system is governed by a Lyapunov function that serves as a cost function for the system. This cost function is in general a function of both phases and intensities

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supporting

confidence: 60%

mentioning

confidence: 99%

Mapping the XY Hamiltonian onto a Network of Coupled Lasers

Honari-Latifpour,

Miri

2020

Preprint

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“…Our system can be further generalized by considering an anti-ferromagnetic or random twobody spin interactions and including other higher-order spin interactions through sum frequency generation, four-wave mixing, and high harmonic generations. It can be used for the study of q-state Potts model 56,57 and the development of self-learning Monte-Carlo algorithm 58 , etc.…”

Section: Discussionmentioning

confidence: 99%

Observation of distinct phase transitions in a nonlinear optical Ising machine

Kumar

et al. 2023

Commun Phys

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Optical Ising machines promise to solve complex optimization problems with an optical hardware acceleration advantage. Here we study the ground state properties of a nonlinear optical Ising machine realized by spatial light modulator, Fourier optics, and second-harmonic generation in a nonlinear crystal. By tuning the ratio of the light intensities at the fundamental and second-harmonic frequencies, we experimentally observe two distinct ferromagnetic-to-paramagnetic phase transitions: a second-order phase transition where the magnetization changes to zero continuously and a first-order phase transition where the magnetization drops to zero abruptly as the effective temperature increases. Our experimental results are corroborated by a numerical simulation based on the Monte Carlo Metropolis-Hastings algorithm, and the physical mechanism for the distinct phase transitions can be understood with a mean-field theory. Our results showcase the flexibility of the nonlinear optical Ising machine, which may find potential applications in solving combinatorial optimization problems.

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“…It can be used for the study of q-state Potts model 56,57 and the development of self-learning Monte-Carlo algorithm 58 , etc.…”

Section: Discussionmentioning

confidence: 99%

Observation of Distinct Phase Transitions in a Nonlinear Optical Ising Machine

Kumar

et al. 2022

Preprint

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Optical Ising machines promise to solve complex optimization problems with an optical hardware acceleration advantage. Here we study the ground state properties of a nonlinear optical Ising machine realized by spatial light modulator, Fourier optics, and second harmonic generation in a nonlinear crystal. By tuning the ratio of the light intensities at the fundamental and second-harmonic frequencies, we experimentally observe two distinct ferromagnetic-to-paramagnetic phase transitions: a second-order phase transition where the magnetization changes to zero continuously and a first-order phase transition where the magnetization drops to zero abruptly as the effective temperature increases. Our experimental results are corroborated by a numerical simulation based on the Monte Carlo Metropolis-Hastings algorithm, and the physical mechanism for the distinct phase transitions can be understood with a mean-field theory. Our results showcase the great flexibility of the nonlinear optical Ising machine, which may find important potential applications in solving combinatorial optimization problems.

show abstract

Optical Potts machine through networks of three-photon down-conversion oscillators

Cited by 18 publications

References 28 publications

Mapping the XY Hamiltonian onto a Network of Coupled Lasers

Mapping the XY Hamiltonian onto a Network of Coupled Lasers

Observation of distinct phase transitions in a nonlinear optical Ising machine

Observation of Distinct Phase Transitions in a Nonlinear Optical Ising Machine

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