Ising machines as hardware solvers of combinatorial optimization problems

Mohseni, Naeimeh; McMahon, Peter L.; Byrnes, Tim

doi:10.1038/s42254-022-00440-8

Cited by 242 publications

(100 citation statements)

References 180 publications

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“…From a fundamental vantage, our results show that polychromatic-driving can expand the range of localized structures that can be hosted and studied in dispersive Kerr resonators, with a plethora of new dynamics to be explored. Moreover, the bi-phase degeneracy of PDCSs make them attractive candidates for bits in all-optical random number generators [19][20][21] or coherent Ising machines [22,23], and our work could therefore pave the way for new and possibly improved approaches for realising such applications. Lastly, to the best of our knowledge, our work is the first to present and use an Ikeda-like map model that can account for driving fields associated with multiple frequencies with different detunings.…”

Section: Discussionmentioning

confidence: 94%

“…[13] realised suitable conditions using quadratic down-conversion, it is well-known that analogous phase-sensitive amplification can also be realised in pure Kerr resonators using appropriate driving configurations [14][15][16][17][18]. In fact, there has been considerable recent interest in leveraging phase-sensitive four-wave mixing to realise bi-phase (nonsolitonic) states in pure Kerr resonators driven by two lasers with different carrier frequencies; such systems have allowed for the realisation of novel random number generators [19][20][21] as well as coherent optical Ising machines [22,23]. A natural question that arises is: is it possible to generate parametricallydriven CSs in Kerr-only resonators with bichromatic driving?…”

Section: Introductionmentioning

confidence: 99%

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Parametrically-driven temporal cavity solitons in a bichromatically-driven pure Kerr resonator

Leonhardt¹,

Paligora²,

Englebert³

et al. 2022

Preprint

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Temporal cavity solitons (CSs) are pulses of light that can persist endlessly in dispersive, nonlinear optical resonators. They have been extensively studied in the context of resonators with purely cubic (Kerr-type) nonlinearity that are externally-driven with a monochromatic continuous wave laser -in such systems, the solitons manifest themselves as unique attractors whose carrier frequency coincides with that of the external driving field. Recent experiments have, however, shown that a qualitatively different type of temporal CS can arise via parametric down-conversion in resonators with simultaneous quadratic and cubic nonlinearity. In contrast to conventional CSs in pure-Kerr resonators, these parametrically-driven cavity solitons come in two different flavours with opposite phases, and they are spectrally centred at half of the frequency of the driving field. Here, we theoretically and numerically show that, under conditions of bichromatic driving, such parametricallydriven CSs can also arise in dispersive resonators with pure Kerr nonlinearity. In this case, the solitons arise through parametric four-wave mixing, come with two distinct phases, and have a carrier frequency in between the two external driving fields. We show that, when all waves are resonant, the solitons can experience longrange interactions due to their back-action on the intracavity fields at the pump frequencies, and we discuss the parameter requirements for the solitons' existence. Besides underlining the possibility of exciting a new type of cavity soliton in dispersive Kerr cavities, our work advances the theoretical modeling of resonators that are coherently-driven with polychromatic fields.

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Section: Discussionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Parametrically-driven temporal cavity solitons in a bichromatically-driven pure Kerr resonator

Leonhardt¹,

Paligora²,

Englebert³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…(For some practical applications of Ising machines and for recent reviews see Refs. [15,16]). This paper will show how to encode Diophantine problems of the kind described above onto such machines.…”

Section: Introductionmentioning

confidence: 99%

Ising Machines for Diophantine Problems in Physics

Abel¹,

Nutricati²

2022

Preprint

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Diophantine problems arise frequently in physics, in for example anomaly cancellation conditions, string consistency conditions and so forth. We present methods to solve such problems to high order on annealers that are based on the quadratic Ising Model. This is the intrinsic framework for both quantum annealing and for common forms of classical simulated annealing. We demonstrate the method on so-called Taxicab numbers (discovering some apparently new ones), and on the realistic problem of anomaly cancellation in U (1) extensions of the Standard Model.

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“…Quantum-inspired solvers are able to solve larger problems e.g the Digital Annealer (DA) which uses application speci c CMOS and is able to solve binary quadratic problems with up to 100,000 bits [Hiroshi et al, 2021]. A detailed analysis of hardware solvers within the context of Ising machines is presented in [Mohseni et al, 2022].…”

Section: Introductionmentioning

confidence: 99%

Comparing the Digital Annealer with Classical Evolutionary Algorithm

Ayodele¹

2022

Preprint

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In more recent years, there has been increasing research interest in exploiting the use of application speci c hardware for solving optimisation problems. Examples of solvers that use specialised hardware are IBM's Quantum System One and D-wave's Quantum Annealer (QA) and Fujitsu's Digital Annealer (DA). These solvers have been developed to optimise problems faster than traditional meta-heuristics implemented on general purpose machines. Previous research has shown that these solvers (can optimise many problems much quicker than exact solvers such as GUROBI and CPLEX. Such conclusions have not been made when comparing hardware solvers with classical evolutionary algorithms. Making a fair comparison between traditional evolutionary algorithms, such as Genetic Algorithm (GA), and the DA (or other similar solvers) is challenging because the later bene ts from the use of application speci c hardware while evolutionary algorithms are often implemented on generalpurpose machines. Moreover, quantum or quantum-inspired solvers are limited to solving problems in a speci c format. A common formulation used is Quadratic Unconstrained Binary Optimisation (QUBO). Many optimisation problems are however constrained and have natural representations that are non-binary. Converting such problems to QUBO can lead to more problem di culty and/or larger search space. The question addressed in this paper is whether quantum or quantum-inspired solvers can optimise QUBO transformations of combinatorial optimisation problems faster than classical evolutionary algorithms applied to the same problems in their natural representations. We show that the DA often present better average objective function values than GA on Travelling Salesman, Quadratic Assignment and Multi-dimensional Knapsack Problem instances.

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Ising machines as hardware solvers of combinatorial optimization problems

Cited by 242 publications

References 180 publications

Parametrically-driven temporal cavity solitons in a bichromatically-driven pure Kerr resonator

Parametrically-driven temporal cavity solitons in a bichromatically-driven pure Kerr resonator

Ising Machines for Diophantine Problems in Physics

Comparing the Digital Annealer with Classical Evolutionary Algorithm

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