# Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems

@article{Goto2019CombinatorialOB, title={Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems}, author={Hayato Goto and Kosuke Tatsumura and Alexander Dixon}, journal={Science Advances}, year={2019}, volume={5} }

Combinatorial optimization problems are ubiquitous but difficult to solve. [... ] Key Result Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new… Expand

## 112 Citations

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This work reformulated a broad range of combinatorial optimization problems with a general graph-based data structure called the Ising model, and utilized a new heuristic algorithm, simulated bifurcation, to search for solutions.

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FPGA-Based Simulated Bifurcation Machine

- Computer Science2019 29th International Conference on Field Programmable Logic and Applications (FPL)
- 2019

This work implements the SB algorithm on FPGAs by designing massively parallel custom circuits, and compares the FPGA-based SB machines with a state-of-the-art machine called a coherent Ising machine (CIM), a highly optimized implementation of simulated annealing (SA), and GPU-basedSB machines.

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- 2021

This article reviews the recent works on the design and implementation of high-performance FPGA-based accelerators for SB and their applications toward innovative real-time systems that make optimal responses to ever-changing situations and shows a scale-out architecture for SB-based Ising machines with all-to-all spin-spin couplings.

Scaling out Ising machines using a multi-chip architecture for simulated bifurcation

- Computer Science
- 2021

A scale-out architecture for Ising machines that provides enlarged machine sizes and enhanced processing speeds by using multiple connected chips and relies on an autonomous synchronization mechanism that is implemented in the information exchange processes between neighbouring chips and leads to scalability of computational throughput.

High-performance combinatorial optimization based on classical mechanics

- Computer ScienceScience Advances
- 2021

This work proposes an algorithm based on classical mechanics, which is obtained by modifying a previously proposed algorithm called simulated bifurcation, which 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.

Dynamical Systems Theory and Algorithms for NP-hard Problems

- Computer ScienceArXiv
- 2020

This article surveys a range of examples that illustrate the use of dynamical systems theory in the context of computational complexity analysis and novel algorithm construction and summarizes a novel approach for clustering graphs using the wave equation partial differential equation.

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