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Three coupled Kerr parametric oscillators (KPOs) can simulate Ising Hamiltonians for analog computation. This work simplifies finding conditions for successful optimization algorithms, relevant for quantum systems.

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Area of Science:

  • Nonlinear dynamics
  • Quantum optics
  • Analog computation

Background:

  • Coupled Kerr parametric oscillators (KPOs) show promise for analog computation, particularly for solving Ising Hamiltonians.
  • The complex state space of strongly coupled KPO networks complicates their application in optimization algorithms.
  • Existing challenges include phase diagrams with an inappropriate number of states or states unmappable to Ising configurations.

Purpose of the Study:

  • To demonstrate the use of three strongly coupled KPOs as a simulator for an Ising Hamiltonian.
  • To estimate the ground state of an Ising Hamiltonian using Boltzmann sampling measurements.
  • To simplify the conditions required for successful analog optimization algorithms.

Main Methods:

  • Utilized a network of three strongly coupled Kerr parametric oscillators.
  • Employed Boltzmann sampling measurements to estimate the ground state.
  • Focused on a classical simulation approach directly relevant to quantum systems.

Main Results:

  • Successfully demonstrated the simulation of an Ising Hamiltonian using three coupled KPOs.
  • Estimated the ground state of the Ising Hamiltonian via Boltzmann sampling.
  • Provided a method to navigate the complex state space of KPO networks for optimization.

Conclusions:

  • Strongly coupled KPOs can effectively simulate Ising Hamiltonians for analog computation.
  • The proposed method simplifies the process of finding optimal conditions for analog optimization.
  • Findings are relevant for advancing classical and quantum analog computation, especially for systems operating on coherent states.