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

arXiv:1311.2696 · Physical Review A

Coherent Ising machine based on degenerate optical parametric oscillators

Zhe Wang, Alireza Marandi, Kai Wen, Robert L. Byer, Y. Yamamoto

Published Dec 30, 2013• 391 citations
arXivHTMLPDF

Abstract

A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and the inherent preference of the network in selecting oscillation modes with the minimum photon decay rate. Computational experiments are performed on all instances reducible to the NP-hard MAX-CUT problems on cubic graphs of order up to 20. The numerical results reasonably suggest the effectiveness of the proposed network.

DOI
10.1103/physreva.88.063853

Related papers

Network of femtosecond degenerate OPOs for solving NP-Hard Ising problems

Alireza Marandi, Kenta Takata, Zhe Wang +2 more

We report implementation of a configurable network of four degenerate optical parametric oscillators as an Ising spin system using time-multiplexed femtosecond pulses. This coherent Ising machine solves an instance of NP-hard MAXCUT problem without error.

•Jan 1, 2014•0 citations

A 16-bit Coherent Ising Machine for One-Dimensional Ring and Cubic Graph Problems

Kenta Takata, Alireza Marandi, Ryan Hamerly +6 more

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.

arXiv:1605.03847•Scientific Reports•Sep 23, 2016•82 citations

Combinatorial Optimization with Coherent Ising Machines based on Degenerate Optical Parametric Oscillators

Y. Yamamoto

The basic concept, principle and implementation of coherent Ising machines are presented. A fully programmable 100 spin machine with all-to-all connections solves ground states and randomly samples low-energy excited states of NP-hard Ising problems.

Frontiers in Optics•Jan 1, 2016•0 citations

Solving large-scale optimization problems with coherent Ising machine

Hiroki Takesue, Takahiro Inagaki, Kensuke Inaba +1 more

We report a coherent Ising machine (CIM), which is a network of degenerate optical parametric oscillators for simulating the Ising model. Using a long-distance fiber cavity that includes a telecom-band phase sensitive amplifier, we generated large number of degenerate optical parametric oscillator (DOPO) pulses multiplexed in time domain, which represent the Ising spins. By using a measurement and feedback scheme, we could implement all-to-all coupling among 2048 DOPOs. We experimentally confirmed that the CIM could find solutions to maximum cut problems for graphs with as many as 2000 nodes.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Jul 1, 2017•1 citation

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

A coherent Ising machine based on a network of 100,000 degenerate optical parametric oscillator pulses

Toshimori Honjo, Kensuke Inaba, Takahiro Inagaki +3 more

Coherent Ising machines (CIMs) are increasingly anticipated as a new computer that can solve combinatorial optimization problems. CIMs use degenerate optical parametric oscillator pulses as artificial spins. We constructed a 100,512-spin coherent Ising machine, the world's largest. Our CIM can find good solutions to maximum cut problems of 100,000-node graphs ~1000 times faster than simulated annealing. Furthermore, it provides both very good scores and a broad distribution when we operate it near the phase transition point.

IEEE International Conference on Nanotechnology (IEEE-NANO)•Jul 4, 2022•6 citations
A degenerate optical parametric oscillator network is proposed to solve the NP-hard problem of finding a ground state of the Ising model. The underlying operating mechanism originates from the bistable output phase of each oscillator and the inherent preference of the network in selecting oscillation modes with the minimum photon decay rate. Computational experiments are performed on all instances reducible to the NP-hard MAX-CUT problems on cubic graphs of order up to 20. The numerical results reasonably suggest the effectiveness of the proposed network.
Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to finding a ground state of the Ising Hamiltonian, thus various physical systems have been studied to emulate and solve this Ising problem. Recently, networks of mutually injected optical oscillators, called coherent Ising machines, have been developed as promising solvers for the problem, benefiting from programmability, scalability and room temperature operation. Here, we report a 16-bit coherent Ising machine based on a network of time-division-multiplexed femtosecond degenerate optical parametric oscillators. The system experimentally gives more than 99.6% of success rates for one-dimensional Ising ring and nondeterministic polynomial-time (NP) hard instances. The experimental and numerical results indicate that gradual pumping of the network combined with multiple spectral and temporal modes of the femtosecond pulses can improve the computational performance of the Ising machine, offering a new path for tackling larger and more complex instances.
We report a coherent Ising machine (CIM), which is a network of degenerate optical parametric oscillators for simulating the Ising model. Using a long-distance fiber cavity that includes a telecom-band phase sensitive amplifier, we generated large number of degenerate optical parametric oscillator (DOPO) pulses multiplexed in time domain, which represent the Ising spins. By using a measurement and feedback scheme, we could implement all-to-all coupling among 2048 DOPOs. We experimentally confirmed that the CIM could find solutions to maximum cut problems for graphs with as many as 2000 nodes.
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.
Coherent Ising machines (CIMs) are increasingly anticipated as a new computer that can solve combinatorial optimization problems. CIMs use degenerate optical parametric oscillator pulses as artificial spins. We constructed a 100,512-spin coherent Ising machine, the world's largest. Our CIM can find good solutions to maximum cut problems of 100,000-node graphs ~1000 times faster than simulated annealing. Furthermore, it provides both very good scores and a broad distribution when we operate it near the phase transition point.