Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators.

Area of Science:

• Quantum physics
• Artificial intelligence
• Computational complexity

Background:

• A network of Kerr-non-linear parametric oscillators was proposed for combinatorial optimization using quantum adiabatic evolution.
• The behavior of the quantum bifurcation machine (QbM) in the presence of dissipation was not previously understood.

Purpose of the Study:

• To investigate the impact of dissipation on the quantum bifurcation machine.
• To determine if dissipative QbMs can be used for Boltzmann sampling.

Main Methods:

• Numerical simulations of a dissipative network of Kerr-non-linear parametric oscillators.
• Generalization of quantum heating concepts to coupled nonlinear oscillators.

Main Results:

• The output probability distribution of the dissipative QbM was found to be Boltzmann-like.
• The energy in the Boltzmann distribution corresponds to the cost function of the optimization problem.
• A theoretical explanation for the Boltzmann distribution was provided by generalizing quantum heating.

Conclusions:

• Dissipative quantum bifurcation machines can generate Boltzmann-like distributions relevant to optimization problems.
• Driven dissipative nonlinear oscillator networks show potential for Boltzmann sampling applications.
• This research bridges quantum computing approaches with machine learning techniques in artificial intelligence.