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Conference on Lasers and Electro-Optics

Photonic Recurrent Ising Sampler

Charles Roques‐Carmes, Yichen Shen, Cristian Zanoci, Mihika Prabhu, Fadi Atieh, Li Jing, Tena Dubček, Vladimir Čeperić, John D. Joannopoulos, Dirk Englund, Marin Soljacic A

Published Jan 1, 2019• 9 citations
Publisher

Abstract

We present the Photonic Recurrent Ising Sampler (PRIS), an algorithm tailored for photonic parallel networks, that can sample distributions of arbitrary Ising problems. The PRIS finds the ground state of general Ising problems and probes critical exponents of universality classes.
DOI
10.1364/cleo_qels.2019.ftu4c.2

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Photonic Recurrent Ising Sampler

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We present the Photonic Recurrent Ising Sampler (PRIS), an algorithm tailored for photonic parallel networks, that can sample distributions of arbitrary Ising problems. The PRIS finds the ground state of general Ising problems and probes critical exponents of universality classes. © 2019 The Author(s)

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The failure of conventional electronic architectures to solve large combinatorial problems motivates the development of novel computational architectures. There has been much effort recently in developing photonic networks which can exploit fundamental properties enshrined in the wave nature of light and of its interaction with matter: high-speed, low-power, optical passivity, and parallelization. However, unleashing the true potential of photonic architectures requires the development of featured algorithms which largely exploit these fundamental properties. We here present the Photonic Recurrent Ising Sampler (PRIS), an algorithm tailored for photonic parallel networks that can sample combinatorially hard distributions of Ising problems, in a fast and efficient manner. The PRIS finds the ground state of general ising problems and is able to probe critical behaviors of universality classes and their critical exponents. In addition to the attractive features of photonic networks, the PRIS relies on intrinsic dynamic noise to find ground states more efficiently.

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The failure of conventional electronic architectures to solve large combinatorial problems motivates the development of novel computational architectures. There has been much effort recently in developing photonic networks which can exploit fundamental properties enshrined in the wave nature of light and of its interaction with matter: high-speed, low-power, optical passivity, and parallelization. However, unleashing the true potential of photonic architectures requires the development of featured algorithms which largely exploit these fundamental properties. We here present the Photonic Recurrent Ising Sampler (PRIS), an algorithm tailored for photonic parallel networks that can sample combinatorially hard distributions of Ising problems, in a fast and efficient manner. The PRIS finds the ground state of general ising problems and is able to probe critical behaviors of universality classes and their critical exponents. In addition to the attractive features of photonic networks, the PRIS relies on intrinsic dynamic noise to find ground states more efficiently.
The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort toward developing application-specific hardware across many different fields of engineering, such as integrated circuits, memristors, and photonics. However, unleashing the potential of such architectures requires the development of algorithms which optimally exploit their fundamental properties. Here, we present the Photonic Recurrent Ising Sampler (PRIS), a heuristic method tailored for parallel architectures allowing fast and efficient sampling from distributions of arbitrary Ising problems. Since the PRIS relies on vector-to-fixed matrix multiplications, we suggest the implementation of the PRIS in photonic parallel networks, which realize these operations at an unprecedented speed. The PRIS provides sample solutions to the ground state of Ising models, by converging in probability to their associated Gibbs distribution. The PRIS also relies on intrinsic dynamic noise and eigenvalue dropout to find ground states more efficiently. Our work suggests speedups in heuristic methods via photonic implementations of the PRIS.
Combinatorial problems, such as the Ising problem, are hard to solve with conventional electronics. Photonic systems have recently been proposed as an efficient platform to solve these problems faster and more efficiently, thus calling for the development of featured algorithms to run on photonic machines. A few recent findings, including the Photonic Recurrent Ising Sampler, a photonic machine that recurrently solves arbitrary Ising problems, will be presented in this talk, along with their experimental realizations in various platforms.
Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks, which are encountered in fundamental areas and real-world practical problems including logistics, social networks, and cryptography. Physical machines have recently been proposed and implemented as an alternative to conventional exact and heuristic solvers for the Ising problem, one such optimization task that requires finding the ground state spin configuration of an arbitrary Ising graph. However, these physical approaches usually suffer from decreased ground state convergence probability or universality for high edge-density graphs or arbitrary graph weights, respectively. We experimentally demonstrate a proof-of-principle integrated nanophotonic recurrent Ising sampler (INPRIS) capable of converging to the ground state of various 4-spin graphs with high probability. The INPRIS exploits experimental physical noise as a resource to speed up the ground state search. By injecting additional extrinsic noise during the algorithm iterations, the INPRIS explores larger regions of the phase space, thus allowing one to probe noise-dependent physical observables. Since the recurrent photonic transformation that our machine imparts is a fixed function of the graph problem, and could thus be implemented with optoelectronic architectures that enable GHz clock rates (such as passive or non-volatile photonic circuits that do not require reprogramming at each iteration), our work paves a way for orders-of-magnitude speedups in exploring the solution space of combinatorially hard problems.
Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks such as the Ising problem, which requires finding the ground state spin configuration of an arbitrary Ising graph. Physical Ising machines have recently been developed as an alternative to conventional exact and heuristic solvers; however, these machines typically suffer from decreased ground state convergence probability or universality for high edge-density graphs or arbitrary graph weights, respectively. We experimentally demonstrate a proof-of-principle integrated nanophotonic recurrent Ising sampler (INPRIS), using a hybrid scheme combining electronics and silicon-on-insulator photonics, that is capable of converging to the ground state of various four-spin graphs with high probability. The INPRIS results indicate that noise may be used as a resource to speed up the ground state search and to explore larger regions of the phase space, thus allowing one to probe noise-dependent physical observables. Since the recurrent photonic transformation that our machine imparts is a fixed function of the graph problem and therefore compatible with optoelectronic architectures that support GHz clock rates (such as passive or non-volatile photonic circuits that do not require reprogramming at each iteration), this work suggests the potential for future systems that could achieve orders-of-magnitude speedups in exploring the solution space of combinatorially hard problems.