ArticleScience advances2021
High-performance combinatorial optimization based on classical mechanics.
Article in Science advances, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 24 papers.
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Who cites it
24 citing papers in PubMed.
- Analytical Prediction of Critical Transitions in Oscillator Networks With Non-Local Links.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- Real-time black-box optimization for dynamic discrete environments using embedded Ising machines.Nature communications · 2026Article
- Precision meets speed through an FPGA-based natively sparse Ising machine for combinatorial optimization.Nature communications · 2026Article
- Towards higher order oscillatory Ising machines.Scientific reports · 2026Article
- Machine learning-assisted high-speed combinatorial optimization with Ising machines for dynamically changing problems.Nature communications · 2026Article
- Factorization machine with quadratic-optimization annealing for RNA inverse folding and evaluation of binary-integer encoding and nucleotide assignment.Scientific reports · 2026Article
- Higher-order neuromorphic Ising machines-autoencoders and Fowler-Nordheim annealers are all you need for scalability.Nature communications · 2026Article
- Quantum-Inspired Fast Algorithm and Circuit Realization for Constrained Combinatorial Optimization Problem.Research (Washington, D.C.) · 2026Article
- Enhancing vehicle-mountable multiple object tracking systems with embeddable Ising machines.Nature communications · 2025Article
- Finding independent sets in large-scale graphs with a coherent Ising machine.Science advances · 2025Article
- Collaborative filtering based on nonnegative/binary matrix factorization.Frontiers in big data · 2025Article
- A rapid-convergent particle swarm optimization approach for multiscale design of high-permeance seawater reverse osmosis systems.Communications engineering · 2024Article
- Hybrid quantum-classical computation for automatic guided vehicles scheduling.Scientific reports · 2024Article
- Point convolutional neural network algorithm for Ising model ground state research based on spring vibration.Scientific reports · 2024Article
- A quantum-inspired probabilistic prime factorization based on virtually connected Boltzmann machine and probabilistic annealing.Scientific reports · 2023Article
- Effective implementation of [Formula: see text]-regularised compressed sensing with chaotic-amplitude-controlled coherent Ising machines.Scientific reports · 2023Article
- Efficient combinatorial optimization by quantum-inspired parallel annealing in analogue memristor crossbar.Nature communications · 2023Article
- Bifurcation behaviors shape how continuous physical dynamics solves discrete Ising optimization.Nature communications · 2023Article
- Highly reconfigurable oscillator-based Ising Machine through quasiperiodic modulation of coupling strength.Scientific reports · 2023Article
- Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning.Nature communications · 2022Article
Corrections and comments
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Authors and funding
9 authors.
Funding
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Abstract
Quickly obtaining optimal solutions of combinatorial optimization problems has tremendous value but is extremely difficult. Thus, various kinds of machines specially designed for combinatorial optimization have recently been proposed and developed. Toward the realization of higher-performance machines, here, we propose an algorithm based on classical mechanics, which is obtained by modifying a previously proposed algorithm called simulated bifurcation. Our proposed algorithm allows us to achieve not only high speed by parallel computing but also high solution accuracy for problems with up to one million binary variables. Benchmarking shows that our machine based on the algorithm achieves high performance compared to recently developed machines, including a quantum annealer using a superconducting circuit, a coherent Ising machine using a laser, and digital processors based on various algorithms. Thus, high-performance combinatorial optimization is realized by massively parallel implementations of the proposed algorithm based on classical mechanics.
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