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Designing Ising machines with higher order spin interactions and their application in solving combinatorial

Mohammad Khairul Bashar1, Nikhil Shukla2

  • 1Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA.

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|June 12, 2023
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Summary
This summary is machine-generated.

This study introduces higher-order interactions in Ising spin-based dynamical systems for solving complex combinatorial optimization problems (COPs). This expands the capabilities of physics-inspired computing for tackling problems on hypergraphs.

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Area of Science:

  • Computational physics
  • Theoretical computer science
  • Applied mathematics

Background:

  • The Ising model is a powerful tool for mapping computationally hard combinatorial optimization problems (COPs).
  • Dynamical systems minimizing Ising Hamiltonians show promise for solving COPs, but typically focus on quadratic interactions.
  • Higher-order interactions in Ising spin systems for computing are largely unexplored.

Purpose of the Study:

  • To propose and develop Ising spin-based dynamical systems incorporating higher-order interactions (> 2).
  • To enable the direct computation of solutions for COPs involving higher-order interactions, such as those on hypergraphs.
  • To extend the applicability of physics-inspired computing paradigms.

Main Methods:

  • Development of novel dynamical systems modeling Ising spins with higher-order interactions.
  • Application of these systems to solve specific computational problems, including Boolean NAE-K-SAT and Max-K-Cut on hypergraphs.
  • Theoretical analysis and simulation of the proposed dynamical systems.

Main Results:

  • Successful formulation of dynamical systems capable of handling higher-order Ising interactions.
  • Demonstration of the systems' efficacy in solving Boolean NAE-K-SAT (K ≥ 4) and Max-K-Cut problems on hypergraphs.
  • Validation of the proposed approach for tackling complex COPs.

Conclusions:

  • The proposed higher-order Ising spin-based dynamical systems offer a new computational framework for solving challenging COPs.
  • This work significantly advances the potential of physics-inspired computing for optimization problems on hypergraphs.
  • The findings open new avenues for designing specialized hardware and algorithms for complex computational tasks.