Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines

• URL: http://arxiv.org/abs/2407.09161v2
• Date: Thu, 3 Oct 2024 07:14:15 GMT
• Title: Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines
• Authors: Jason Sakellariou, Alexis Askitopoulos, Georgios Pastras, Symeon I. Tsintzos,
• Abstract summary: We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected values and then proceed to solve both the unweighted and weighted graph problems. Our approach greatly expands the applicability of SPIMs for real-world applications without sacrificing any of the inherent advantages of the system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising Machines have proven to be advantageous for simulating fully connected large-scale spin systems. However, fine control of a general interaction matrix $J$ has so far only been accomplished through eigenvalue decomposition methods that either limit the scalability or increase the execution time of the optimization process. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, enabling the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected values and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach greatly expands the applicability of SPIMs for real-world applications without sacrificing any of the inherent advantages of the system, and paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models, on SPIM devices.

Related papers

• Efficient Computation Using Spatial-Photonic Ising Machines: Utilizing Low-Rank and Circulant Matrix Constraints [0.0]
  spatial-photonic Ising machines (SPIMs) address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically affected by the rank and precision of the coupling matrices.
  arXiv  Detail & Related papers  (2024-06-03T15:03:31Z)
• L0-regularized compressed sensing with Mean-field Coherent Ising Machines [0.8292466835099597]
  We propose the mean-field CIM model, which is a physics-inspired solver without quantum noise. Our results indicate that the proposed model has similar performance to physically accurate SDEs in both artificial and magnetic resonance imaging data.
  arXiv  Detail & Related papers  (2024-05-01T07:43:26Z)
• A Multi-Grained Symmetric Differential Equation Model for Learning Protein-Ligand Binding Dynamics [74.93549765488103]
  In drug discovery, molecular dynamics simulation provides a powerful tool for predicting binding affinities, estimating transport properties, and exploring pocket sites. We propose NeuralMD, the first machine learning surrogate that can facilitate numerical MD and provide accurate simulations in protein-ligand binding. We show the efficiency and effectiveness of NeuralMD, with a 2000$times$ speedup over standard numerical MD simulation and outperforming all other ML approaches by up to 80% under the stability metric.
  arXiv  Detail & Related papers  (2024-01-26T09:35:17Z)
• Smoothing Methods for Automatic Differentiation Across Conditional Branches [0.0]
  Smooth interpretation (SI) approximates the convolution of a program's output with a Gaussian kernel, thus smoothing its output in a principled manner. We combine SI with automatic differentiation (AD) to efficiently compute gradients of smoothed programs. We propose a novel Monte Carlo estimator that avoids the underlying assumptions by estimating the smoothed programs' gradients through a combination of AD and sampling.
  arXiv  Detail & Related papers  (2023-10-05T15:08:37Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching [55.28394191394675]
  We develop an adaptive inexact Newton method for equality-constrained nonlinear, nonIBS optimization problems. We demonstrate the superior performance of our method on benchmark nonlinear problems, constrained logistic regression with data from LVM, and a PDE-constrained problem.
  arXiv  Detail & Related papers  (2023-05-28T06:33:37Z)
• Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machine [0.44040106718326594]
  We propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions.
  arXiv  Detail & Related papers  (2023-03-27T08:36:37Z)
• Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems [4.280301926296439]
  In this work, we explore the idea of multiscale modeling with machine learning and employ DeepONet, a neural operator, as an efficient surrogate of the expensive solver. DeepONet is trained offline using data acquired from the fine solver for learning the underlying and possibly unknown fine-scale dynamics. We present various benchmarks to assess accuracy and speedup, and in particular we develop a coupling algorithm for a time-dependent problem.
  arXiv  Detail & Related papers  (2022-02-25T20:46:08Z)
• Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
  We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations. Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
  arXiv  Detail & Related papers  (2021-09-07T20:01:22Z)
• Optimization on manifolds: A symplectic approach [127.54402681305629]
  We propose a dissipative extension of Dirac's theory of constrained Hamiltonian systems as a general framework for solving optimization problems. Our class of (accelerated) algorithms are not only simple and efficient but also applicable to a broad range of contexts.
  arXiv  Detail & Related papers  (2021-07-23T13:43:34Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.