arXiv:2308.02329 · Physical Review Letters

Hyperscaling in the Coherent Hyperspin Machine

Marcello Calvanese Strinati, Claudio Conti

Published Jan 3, 2024• 19 citations

Abstract

Classical and quantum systems are used to simulate the Ising Hamiltonian, an essential component in large-scale optimization and machine learning. However, as the system size increases, devices like quantum annealers and coherent Ising machines face an exponential drop in their success rate. Here, we introduce a novel approach involving high-dimensional embeddings of the Ising Hamiltonian and a technique called "dimensional annealing" to counteract the decrease in performance. This approach leads to an exponential improvement in the success rate and other performance metrics, slowing down the decline in performance as the system size grows. A thorough examination of convergence dynamics in high-performance computing validates the new methodology. Additionally, we suggest practical implementations using technologies like coherent Ising machines, all-optical systems, and hybrid digital systems. The proposed hyperscaling heuristics can also be applied to other quantum or classical Ising devices by adjusting parameters such as nonlinear gain, loss, and nonlocal couplings.

DOI: 10.1103/physrevlett.132.017301

Related papers

Multidimensional hyperspin machine

Marcello Calvanese Strinati, Claudio Conti

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.

arXiv:2203.16190Nature CommunicationsNov 25, 202234 citations

Ising Machine by Dimensional Collapse of Nonlinear Polarization Oscillators

Salvatore Chiavazzo, Marcello Calvanese Strinati, Claudio Conti +1 more

Ising machines show promise as ultrafast hardware for optimizations encoded in Ising Hamiltonians but fall short in terms of success rate and performance scaling. Here, we propose a novel Ising machine that exploits the three-dimensional nature of nonlinear polarization oscillators to counteract these limitations. Based on the evolution of the optical polarization in third-order nonlinear media, the high-dimensional machine reaches the Ising ground state by the mechanism of "dimensional collapse": the dynamics on the Poincaré sphere undergoes a self-induced collapse into polarization fixed points mapping an Ising spin. Collapse from a spherical to a binary spin occurs when the polarization oscillator experiences iterative loss and anisotropic feedback. The photonic setup consists of polarization modulated pulses in a χ^{(3)} crystal subject to measurement and feedback. We numerically demonstrate the polarization machine achieves enhanced success probability on benchmark graphs and an exponential improvement in performance scaling with respect to coherent Ising machines due to its high-dimensional operation. The proposed Ising machine paves the way for a new class of Ising solvers with enhanced computing capabilities.

arXiv:2504.08695Physical Review LettersJul 14, 20258 citations

Ising Hamiltonian minimization: Gain-based computing with manifold reduction of soft spins vs quantum annealing

James Cummins, Hayder Salman, Natalia G. Berloff

We investigate the minimization of Ising Hamiltonians, comparing the performance of gain-based computing paradigms based on the dynamics of semiclassical soft-spin models with quantum annealing. We systematically analyze how the energy landscape for the circulant couplings of a Möbius graph evolves with increased annealing parameters. Our findings indicate that these semiclassical models face challenges due to a widening dimensionality landscape. To counteract this issue, we introduce the manifold reduction method, which restricts the soft-spin amplitudes to a defined phase space region. Concurrently, quantum annealing demonstrates a natural capability to navigate the Ising Hamiltonian's energy landscape due to its operation within the comprehensive Hilbert space. Our study indicates that physics-inspired or physics-enhanced optimizers will likely benefit from combining classical and quantum annealing techniques.

arXiv:2311.17359Physical Review ResearchFeb 11, 202514 citations

Beyond Optimization: Harnessing Quantum Annealer Dynamics for Machine Learning

Akitada Sakurai, Aoi Hayashi, Tadayoshi Matsumori +3 more

Quantum annealing is typically regarded as a tool for combinatorial optimization, but its coherent dynamics also offer potential for machine learning. We present a model that encodes classical data into an Ising Hamiltonian, evolves it on a quantum annealer, and uses the resulting probability distributions as feature maps for classification. Experiments on the quantum annealer machine with the Digits dataset, together with simulations on MNIST, demonstrate that short annealing times yield higher classification accuracy, while longer times reduce accuracy but lower sampling costs. We introduce the participation ratio as a measure of the effective model size and show its strong correlation with generalization.

quant-pharXiv:2601.09938Jan 16, 20260 citations

Annealing by simulating the coherent Ising machine

Egor S. Tiunov, Alexander E. Ulanov, Alexander I. Lvovsky

The coherent Ising machine (CIM) enables efficient sampling of low-lying energy states of the Ising Hamiltonian with all-to-all connectivity by encoding the spins in the amplitudes of pulsed modes in an optical parametric oscillator (OPO). The interaction between the pulses is realized by means of measurement-based optoelectronic feedforward, which enhances the gain for lower-energy spin configurations. We present an efficient method of simulating the CIM on a classical computer that outperforms the CIM itself, as well as the noisy mean-field annealer in terms of both the quality of the samples and the computational speed. It is furthermore advantageous with respect to the CIM in that it can handle Ising Hamiltonians with arbitrary real-valued node coupling strengths. These results illuminate the nature of the faster performance exhibited by the CIM and may give rise to a new class of quantum-inspired algorithms of classical annealing that can successfully compete with existing methods.

arXiv:1901.08927Optics ExpressMar 28, 201989 citations

Quantum-Inspired Optimization for Large-Scale Machine Learning

Jincheng Zhang

The rapid growth of machine learning (ML) has been accompanied by a significant challenge: the scaling of optimization algorithms to handle the immense parameter spaces of modern models, such as deep neural networks. Traditional optimization methods, including gradient descent and its variants, often encounter difficulties in efficiently exploring these spaces, leading to slow training times and potential stagnation. This paper investigates the application of quantum-inspired optimization techniques to address this scaling problem. We explore algorithms inspired by quantum annealing and other quantum phenomena, adapting their core principles to classical computation. Specifically, we propose a novel optimization framework utilizing a stochastic search strategy based on quantum superposition and measurement, designed to navigate high-dimensional parameter spaces more effectively. The efficacy of this approach is evaluated through theoretical analysis and conceptual simulations, demonstrating its potential to accelerate the training of large-scale machine learning models. We demonstrate how these methods can improve convergence speed and potentially escape local minima more effectively than conventional techniques. The core contribution lies in providing a theoretical foundation and a practical framework for applying quantum-inspired concepts to optimization within the context of machine learning.

Sep 6, 20260 citations