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Bifurcation behaviors shape how continuous physical dynamics solves discrete Ising optimization.

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Summary
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Simulated physical solvers can solve discrete optimization problems, especially Coherent Ising Machines (CIMs), by analyzing bifurcation behaviors. A new trapping-and-correction technique accelerates these solvers, improving convergence and accuracy for Ising models.

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Area of Science:

  • Computational Physics
  • Optimization Theory
  • Quantum Computing

Background:

  • Simulating physical dynamics is effective for combinatorial optimization.
  • Continuous dynamics in these systems may not guarantee optimal discrete solutions.
  • The exact conditions under which simulated physical solvers succeed remain an open question, particularly for Coherent Ising Machines (CIMs).

Purpose of the Study:

  • Investigate the conditions for simulated physical solvers to correctly solve discrete optimization problems.
  • Focus on the dynamics of Coherent Ising Machines (CIMs) and their mapping to discrete Ising optimization.
  • Develop methods to accelerate dynamics-based Ising solvers.

Main Methods:

  • Established an exact mapping between Coherent Ising Machine (CIM) dynamics and discrete Ising optimization.
  • Analyzed two distinct bifurcation behaviors: synchronized and retarded bifurcations.
  • Developed a trapping-and-correction (TAC) technique to accelerate solvers.

Main Results:

  • Identified synchronized bifurcation as a condition for exact Ising problem solutions when nodal states are bounded away from zero.
  • Demonstrated that violated mapping conditions lead to slower convergence due to subsequent bifurcations.
  • Validated that the TAC technique effectively reduces computation time and improves convergence and accuracy.

Conclusions:

  • Coherent Ising Machine (CIM) dynamics can precisely solve discrete Ising optimization under specific synchronized bifurcation conditions.
  • The developed trapping-and-correction (TAC) technique offers a significant improvement for dynamics-based optimization solvers.
  • This work provides a theoretical framework and practical method for enhancing simulated physical solvers for combinatorial optimization.