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Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems.

Hayato Goto1, Kosuke Tatsumura1, Alexander R Dixon1

  • 1Corporate Research and Development Center, Toshiba Corporation, 1, Komukai-Toshiba-cho, Saiwai-ku, Kawasaki 212-8582, Japan.

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We introduce simulated bifurcation (SB), a novel algorithm for solving complex combinatorial optimization problems. SB, implemented on a field-programmable gate array, achieves significant speedups for large-scale problems.

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Area of Science:

  • Computational physics
  • Optimization algorithms
  • Hardware acceleration

Background:

  • Combinatorial optimization problems are widespread and computationally challenging.
  • Current hardware solutions, including quantum computing, are being explored.
  • Quantum adiabatic optimization using nonlinear oscillators inspired this work.

Purpose of the Study:

  • To propose a new classical algorithm, simulated bifurcation (SB), for combinatorial optimization.
  • To leverage adiabatic and chaotic dynamics of nonlinear Hamiltonian systems.
  • To demonstrate SB's efficiency on specialized hardware.

Main Methods:

  • Simulated bifurcation (SB) algorithm based on adiabatic and ergodic evolutions of nonlinear Hamiltonian systems.
  • Parallel computing approach with simultaneous updating.
  • Implementation on a field-programmable gate array (FPGA).

Main Results:

  • SB machine successfully obtained approximate solutions for a 2000-node MAX-CUT problem.
  • Achieved a solution time of 0.5 ms.
  • Demonstrated a speedup approximately 10 times faster than a coherent Ising machine.

Conclusions:

  • SB offers a powerful new method for accelerating large-scale combinatorial optimization.
  • This approach effectively harnesses digital computer technologies.
  • SB presents novel applications in computational and mathematical physics.