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Can Nonlinear Parametric Oscillators Solve Random Ising Models?

Marcello Calvanese Strinati1,2, Leon Bello3, Emanuele G Dalla Torre1

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Coherent Ising machines, networks of parametric oscillators, do not inherently solve Ising models near threshold. Driving them above threshold enables them to find ground-state solutions with finite probability.

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Area of Science:

  • Physics
  • Quantum Computing
  • Computational Science

Background:

  • Coherent Ising machines (CIMs) utilize networks of parametric oscillators to solve complex problems.
  • The Ising model is a fundamental model in statistical mechanics, often used to represent magnetic materials and other complex systems.
  • CIMs aim to find the ground state of Ising models by leveraging mode competition in oscillator networks.

Purpose of the Study:

  • To investigate the efficacy of coherent Ising machines as heuristic solvers for random Ising models.
  • To determine if the steady state of parametric oscillator networks reliably corresponds to the ground state of Ising models.
  • To identify the operating regimes where CIMs can accurately solve Ising models.

Main Methods:

  • Analysis of large networks of parametric oscillators.
  • Simulation and theoretical study of frustrated Ising models.
  • Examination of oscillator behavior near and above the lasing threshold.

Main Results:

  • Networks of parametric oscillators near threshold do not generically find the ground state of Ising models.
  • The most efficient mode in these networks does not necessarily correspond to the Ising model's ground state.
  • Driving oscillators sufficiently above threshold, where nonlinearities dominate, allows convergence to the ground state with finite probability.

Conclusions:

  • Coherent Ising machines are not intrinsically Ising solvers when operating close to threshold.
  • Nonlinear dynamics become crucial for enabling CIMs to find ground-state solutions.
  • The effectiveness of CIMs as Ising solvers depends on operating parameters, specifically driving the oscillators well above threshold.