Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Science and Technology

Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

Y Takeda, Shuhei Tamate, Y. Yamamoto, Hiroki Takesue, Takahiro Inagaki, Shoko Utsunomiya

Published Oct 10, 2017• 51 citations
Publisher

Abstract

We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.

DOI
10.1088/2058-9565/aa923b

Related papers

Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

Yutaka Takeda, Shuhei Tamate, Y. Yamamoto +3 more

We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.

arXiv:1705.03611•May 10, 2017•9 citations

Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

Yutaka Takeda, Shuhei Tamate, Y. Yamamoto +3 more

We built a non-degenerate optical parametric oscillator (NOPO) network to simulate a one-dimensional XY model in thermal equilibrium. We experimentally found that the effective temperature can be controlled via an external noise injection.

Frontiers in Optics•Jan 1, 2017•5 citations

10-GHz-clock time-multiplexed non-degenerate optical parametric oscillator network with a variable planar lightwave circuit interferometer

Yuya Yonezu, Kensuke Inaba, Yasuhiro Yamada +4 more

A coherent XY machine (CXYM) is a physical spin simulator that can simulate the XY model by mapping XY spins onto the continuous phases of non-degenerate optical parametric oscillators (NOPOs). Here, we demonstrated a large-scale CXYM with >47,000 spins by generating 10-GHz-clock time-multiplexed NOPO pulses via four-wave mixing in a highly nonlinear fiber inside a fiber ring cavity. By implementing a unidirectional coupling from the ith pulse to the (i + 1)th pulse with a variable 1-pulse delay planar lightwave circuit interferometer, we successfully controlled the effective temperature of a one-dimensional XY spin network within two orders of magnitude.

arXiv:2307.03333•Optics Letters•Oct 6, 2023•5 citations

Combinatorial optimization with a network of degenerated optical parametric oscillators

Takahiro Inagaki, Kensuke Inaba, Toshimori Honjo +4 more

Various artificial spin systems with networked physical devices are now emerging as a way to simulate the Ising model. Combinatorial optimization problems for many applications can be mapped onto ground state search problems of the Ising model and solved efficiently with the artificial spin system. Here, we report a coherent Ising machine based on 2,048 networked degenerate optical parametric oscillators. All-to-all couplings were achieved with a measurement and feedback scheme to implement arbitrary graph structures with up to 2,048 nodes. The coherent Ising machine can simulate large-scale Ising model and obtain good solutions for the optimization of a 2,000-node complete graph.

OSA Advanced Photonics Congress•Jan 1, 2019•0 citations

Steady-state squeezing and entanglement in a dissipatively coupled NOPO network

Inui, Yoshitaka, Y. Yamamoto

We investigate the steady-state photon-number squeezing and quantum entanglement in a network of nondegenerate optical parametric oscillators (NOPOs). We treat each NOPO with Shen's Raman laser model, whose lasing mode provides a photon-number-squeezed state. Two dissipatively coupled NOPOs satisfy Hillery-Zubairy's $HZ1$ entanglement criterion if they are pumped far above the threshold and the dissipative coupling is sufficiently larger than the NOPO cavity loss.

arXiv:1906.12044•Jun 28, 2019•1 citation

Distributions of steady states in a network of degenerate optical parametric oscillators in solving combinatorial optimization problems

Ryoji Miyazaki, Masayuki Ohzeki

We investigate a network of degenerate optical parametric oscillators (DOPOs) as a model of the coherent Ising machine, an architecture for solving Ising problems. The network represents the interaction in the Ising model, which is a generalization of a previously proposed one for the two-DOPO case. Dynamics of the DOPOs is described by the Fokker-Planck equation in the positive $P$ representation. We obtain approximate distribution of steady states for arbitrary Ising problems under some ansatz. Using the method of statistical mechanics, we analytically demonstrate that the most probable states in a particular range of the parameters correspond to the true optimal states for two rather simple problems, i.e., fully connected ferromagnetic coupling without or with binary random fields. In particular, for the random-field problem, the distribution correctly detects the phase transition that occurs in the target Ising model with varying the magnitude of the fields.

arXiv:1808.10643•Physical Review A•Nov 21, 2018•0 citations
We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.
We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.
A coherent XY machine (CXYM) is a physical spin simulator that can simulate the XY model by mapping XY spins onto the continuous phases of non-degenerate optical parametric oscillators (NOPOs). Here, we demonstrated a large-scale CXYM with >47,000 spins by generating 10-GHz-clock time-multiplexed NOPO pulses via four-wave mixing in a highly nonlinear fiber inside a fiber ring cavity. By implementing a unidirectional coupling from the ith pulse to the (i + 1)th pulse with a variable 1-pulse delay planar lightwave circuit interferometer, we successfully controlled the effective temperature of a one-dimensional XY spin network within two orders of magnitude.
Various artificial spin systems with networked physical devices are now emerging as a way to simulate the Ising model. Combinatorial optimization problems for many applications can be mapped onto ground state search problems of the Ising model and solved efficiently with the artificial spin system. Here, we report a coherent Ising machine based on 2,048 networked degenerate optical parametric oscillators. All-to-all couplings were achieved with a measurement and feedback scheme to implement arbitrary graph structures with up to 2,048 nodes. The coherent Ising machine can simulate large-scale Ising model and obtain good solutions for the optimization of a 2,000-node complete graph.
We investigate the steady-state photon-number squeezing and quantum entanglement in a network of nondegenerate optical parametric oscillators (NOPOs). We treat each NOPO with Shen's Raman laser model, whose lasing mode provides a photon-number-squeezed state. Two dissipatively coupled NOPOs satisfy Hillery-Zubairy's HZ1HZ1HZ1 entanglement criterion if they are pumped far above the threshold and the dissipative coupling is sufficiently larger than the NOPO cavity loss.
We investigate a network of degenerate optical parametric oscillators (DOPOs) as a model of the coherent Ising machine, an architecture for solving Ising problems. The network represents the interaction in the Ising model, which is a generalization of a previously proposed one for the two-DOPO case. Dynamics of the DOPOs is described by the Fokker-Planck equation in the positive PPP representation. We obtain approximate distribution of steady states for arbitrary Ising problems under some ansatz. Using the method of statistical mechanics, we analytically demonstrate that the most probable states in a particular range of the parameters correspond to the true optimal states for two rather simple problems, i.e., fully connected ferromagnetic coupling without or with binary random fields. In particular, for the random-field problem, the distribution correctly detects the phase transition that occurs in the target Ising model with varying the magnitude of the fields.