All-Optical Scalable Spatial Coherent Ising Machine

Strinati, Marcello Calvanese; Pierangeli, Davide; Conti, Claudio

doi:10.1103/physrevapplied.16.054022

Cited by 17 publications

(12 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This means that the PO network deterministically solves the selected optimization problem when driven above the threshold. Such a phenomenology allows to conclude that the optimization problem belongs to the polynomial (P) class of computational complexity 49 , 68 , because finding the ground state of Eq. ( 3 ) reduces to finding the eigenvector of C with maximal eigenvalue.…”

Section: Resultsmentioning

confidence: 99%

“…The design of the hyperspin machine with POs opens the future perspective to experimentally realize fully optical, scalable, and size-independent continuous spin simulators, extending recent proposals with an optical cavity with a nonlinear medium and spatial light modulators, similar to that in ref. 49 for the Ising model.…”

Section: Discussionmentioning

confidence: 99%

“…The choice of POs as fundamental constituents of an hyperspin is motivated by the fact that they furnish a versatile platform to realize artificial spin devices at room temperature. POs grant an extraordinary degree of control and the prospect to realize scalable systems of coupled all-optical POs with size-independent ultra-fast equilibration times 49 . However, despite their potential use as physical hardware, we show here that even only the software implementation of an hyperspin machine enables a novel strategy for annealing that we call “dimensional annealing”, which increases the probability to optimize hard models in a wide range of parameters.…”

Section: Introductionmentioning

confidence: 99%

“…However, the way to physically realize hyperspins and dimensional annealing has yet to be considered. Authors reported on proposals relying on nonlinear POs [17,18] and the first observation of hyperspin dynamics [19].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Multidimensional hyperspin machine

Strinati

Conti

2022

Nat Commun

Self Cite

View full text Add to dashboard Cite

From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and show that the hyperspin machine finds to a very good approximation the ground state of complex graphs. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call “dimensional annealing”. When interpolating between the XY and the Ising model, the dimensional annealing substantially increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Multidimensional hyperspin machine

Strinati

Conti

2022

Nat Commun

Self Cite

View full text Add to dashboard Cite

show abstract

“…Alternative approaches based on the encoding of problems into the dynamics of physical systems have been proposed, drawing inspiration from the Hopfield and Hopfield-Tank neural networks 12 – 14 from the 1980’s, with more general dynamics and control mechanisms, allowing for stronger scalability and convergence properties 15 – 22 . As experimental realizations of so-called Ising machines deem challenging 18 , 23 – 26 , the system dynamics have commonly been simulated on conventional computers 23 , 27 – 30 . Such approach has proven successful for medium- to large-scale optimizations of up to hundreds of thousand variables 19 , 28 , 31 , 32 , and even lead to special-purpose chip hardware implementations 33 – 37 .…”

Section: Introductionmentioning

confidence: 99%

Bifurcation behaviors shape how continuous physical dynamics solves discrete Ising optimization

et al. 2023

View full text Add to dashboard Cite

Simulating physical dynamics to solve hard combinatorial optimization has proven effective for medium- to large-scale problems. The dynamics of such systems is continuous, with no guarantee of finding optimal solutions of the original discrete problem. We investigate the open question of when simulated physical solvers solve discrete optimizations correctly, with a focus on coherent Ising machines (CIMs). Having established the existence of an exact mapping between CIM dynamics and discrete Ising optimization, we report two fundamentally distinct bifurcation behaviors of the Ising dynamics at the first bifurcation point: either all nodal states simultaneously deviate from zero (synchronized bifurcation) or undergo a cascade of such deviations (retarded bifurcation). For synchronized bifurcation, we prove that when the nodal states are uniformly bounded away from the origin, they contain sufficient information for exactly solving the Ising problem. When the exact mapping conditions are violated, subsequent bifurcations become necessary and often cause slow convergence. Inspired by those findings, we devise a trapping-and-correction (TAC) technique to accelerate dynamics-based Ising solvers, including CIMs and simulated bifurcation. TAC takes advantage of early bifurcated “trapped nodes” which maintain their sign throughout the Ising dynamics to reduce computation time effectively. Using problem instances from open benchmark and random Ising models, we validate the superior convergence and accuracy of TAC.

show abstract