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Researchers developed a new gauge transformation scheme for Ising machines, enabling arbitrary spin interactions. This photonic Ising machine simulates complex spin systems and solves optimization problems like Max-Cut efficiently.

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Area of Science:

  • Quantum Computing and Optimization
  • Photonic Systems for Computation

Background:

  • Ising spin Hamiltonians are crucial for solving combinatorial optimization problems.
  • Implementing arbitrary spin-spin interactions in unconventional Ising machines remains a significant challenge.

Purpose of the Study:

  • To propose a general gauge transformation scheme for enabling arbitrary spin-spin interactions and external magnetic fields in Ising machines.
  • To develop and demonstrate a programmable spatial photonic Ising machine (SPIM) capable of general spin coupling.

Main Methods:

  • A novel gauge transformation scheme decomposes Ising Hamiltonians into multiple Mattis-type interactions.
  • A wavelength-division multiplexing spatial photonic Ising machine (SPIM) was engineered to implement programmable general spin coupling.
  • Simulations of ±J models, Sherrington-Kirkpatrick models, and J1-J2 models were conducted to observe phase transitions.

Main Results:

  • The developed SPIM successfully demonstrated programmable general spin coupling interactions.
  • Simulations revealed phase transitions in various spin systems.
  • The SPIM was utilized for ground-state searches to solve the Max-Cut problem.

Conclusions:

  • The proposed gauge transformation scheme effectively enables arbitrary spin-spin interactions and external fields in Ising machines.
  • The wavelength-division multiplexing SPIM offers a powerful platform for simulating complex spin systems and tackling optimization problems.
  • This work paves the way for ultrafast, high-power efficiency Boltzmann sampling for generalized large-scale Ising models.