Three Strongly Coupled Kerr Parametric Oscillators Forming a Boltzmann Machine

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.