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Bulletin of the American Physical Society

A fully programmable 100-spin coherent Ising machine with all-to-all connections

Peter L. McMahon, Alireza Marandi, Yoshitaka Haribara, Ryan Hamerly, Carsten Langrock, Shuhei Tamate, Takahiro Inagaki, Hiroki Takesue, Shoko Utsunomiya, Kazuyuki Aihara, Robert L. Byer, M. M. Fejer, Hideo Mabuchi, Y. Yamamoto

Published Mar 13, 2017• 0 citations
OpenAlex

Abstract

Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.

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Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.

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Programmable optical differential Ising machines

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Optical Ising machines provide a hardware approach for combinatorial optimization and physical-system emulation, but their scalability is limited by redundant matrix operations and analog modulation precision. Here we show a programmable optical differential Ising machine that directly evaluates Hamiltonian changes rather than the full Hamiltonian. Numerical simulations from 60 to 2000 spins show that 6-bit analog–digital conversion and 5-bit digital–analog conversion are sufficient to obtain solution quality close to high-precision digital references, with a phase-error tolerance of about 0.3–0.4 rad. Experiments on a dual-channel fiber-optic prototype reproduce phase-transition behavior in representative Ising models and solve MaxCut benchmarks through a multi-spin parallel tempering (PT) routine. The system reaches the best-known cut for the 800-spin G1 instance and 99.66% of the best-known cut for the 2000-spin G22 instance within fewer than 500 PT iterations. These results establish differential optical feedback as a route for scalable Ising-model computation. The authors develop a programmable optical differential Ising machine that directly computes Hamiltonian variations to eliminate redundant full-matrix calculations for Ising combinatorial optimization and physical system emulation. Simulations and fiber-optic prototype experiments verify that the hardware only requires 5-bit DACs and 6-bit ADCs with a phase-error tolerance of 0.3–0.4 rad, and it yields optimal MaxCut solutions for the 800-spin benchmark and 99.66% of the known optimum for the 2000-spin instance via multi-spin parallel tempering.

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100,000-spin coherent Ising machine

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Computers based on physical systems are increasingly anticipated to overcome the impending limitations on digital computer performance. One such computer is a coherent Ising machine (CIM) for solving combinatorial optimization problems. Here, we report a CIM with 100,512 degenerate optical parametric oscillator pulses working as the Ising spins. We show that the CIM delivers fine solutions to maximum cut problems of 100,000-node graphs drastically faster than standard simulated annealing. Moreover, the CIM, when operated near the phase transition point, provides some extremely good solutions and a very broad distribution. This characteristic will be useful for applications that require fast random sampling such as machine learning.

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Ising machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.

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A fully programmable 100-spin coherent Ising machine with all-to-all connections

Peter L. McMahon, Alireza Marandi, Yoshitaka Haribara +11 more

Taking the pulse of optimization Finding the optimum solution of multiparameter or multifunctional problems is important across many disciplines, but it can be computationally intensive. Many such problems defined as computationally difficult can be mathematically mapped onto the so-called Ising problem, which looks at finding the minimum energy configuration for an array of coupled spins. Inagakiet al.and McMahonet al.show that an optical processing approach based on a network of coupled optical pulses in a ring fiber can be used to model and optimize large-scale Ising systems. Such a scalable architecture could help to optimize solutions to a wide range of complex problems. Science, this issue pp. 603 and 614

Science•Oct 21, 2016•703 citations
Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.
Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.
Optical Ising machines provide a hardware approach for combinatorial optimization and physical-system emulation, but their scalability is limited by redundant matrix operations and analog modulation precision. Here we show a programmable optical differential Ising machine that directly evaluates Hamiltonian changes rather than the full Hamiltonian. Numerical simulations from 60 to 2000 spins show that 6-bit analog–digital conversion and 5-bit digital–analog conversion are sufficient to obtain solution quality close to high-precision digital references, with a phase-error tolerance of about 0.3–0.4 rad. Experiments on a dual-channel fiber-optic prototype reproduce phase-transition behavior in representative Ising models and solve MaxCut benchmarks through a multi-spin parallel tempering (PT) routine. The system reaches the best-known cut for the 800-spin G1 instance and 99.66% of the best-known cut for the 2000-spin G22 instance within fewer than 500 PT iterations. These results establish differential optical feedback as a route for scalable Ising-model computation. The authors develop a programmable optical differential Ising machine that directly computes Hamiltonian variations to eliminate redundant full-matrix calculations for Ising combinatorial optimization and physical system emulation. Simulations and fiber-optic prototype experiments verify that the hardware only requires 5-bit DACs and 6-bit ADCs with a phase-error tolerance of 0.3–0.4 rad, and it yields optimal MaxCut solutions for the 800-spin benchmark and 99.66% of the known optimum for the 2000-spin instance via multi-spin parallel tempering.
Computers based on physical systems are increasingly anticipated to overcome the impending limitations on digital computer performance. One such computer is a coherent Ising machine (CIM) for solving combinatorial optimization problems. Here, we report a CIM with 100,512 degenerate optical parametric oscillator pulses working as the Ising spins. We show that the CIM delivers fine solutions to maximum cut problems of 100,000-node graphs drastically faster than standard simulated annealing. Moreover, the CIM, when operated near the phase transition point, provides some extremely good solutions and a very broad distribution. This characteristic will be useful for applications that require fast random sampling such as machine learning.
Ising machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.
Taking the pulse of optimization Finding the optimum solution of multiparameter or multifunctional problems is important across many disciplines, but it can be computationally intensive. Many such problems defined as computationally difficult can be mathematically mapped onto the so-called Ising problem, which looks at finding the minimum energy configuration for an array of coupled spins. Inagakiet al.and McMahonet al.show that an optical processing approach based on a network of coupled optical pulses in a ring fiber can be used to model and optimize large-scale Ising systems. Such a scalable architecture could help to optimize solutions to a wide range of complex problems. Science, this issue pp. 603 and 614