Emergent Equilibrium in All-Optical Single Quantum-Trajectory Ising Machines

Area of Science:

• Quantum optics
• Nonlinear optics
• Quantum information science

Background:

• Investigating complex dynamics in multimode optical systems is crucial for advancing quantum technologies.
• Understanding the role of quantum noise and nonlocal losses is essential for controlling optical system behavior.

Purpose of the Study:

• To explore the dynamics of multimode optical systems driven by two-photon processes under nonlocal losses and Gaussian quantum noise.
• To determine if these systems can achieve thermal equilibrium and function as Boltzmann samplers.
• To assess their potential for combinatorial optimization and machine learning.

Main Methods:

• Analysis of quantum trajectories in multimode optical systems.
• Incorporation of two-photon processes and nonlocal loss mechanisms.
• Gaussian noise modeling at the quantum level.
• Investigation of emergent thermal equilibrium governed by an Ising Hamiltonian.

Main Results:

• Observed emergent thermal equilibrium in a single Gaussian quantum trajectory.
• Identified an Ising Hamiltonian encoded in the dissipative coupling between modes.
• Established that the system's effective temperature depends on driving strength relative to the oscillation threshold.
• Demonstrated the potential for ultrafast Boltzmann sampling due to ultrashort timescales.

Conclusions:

• Multimode optical systems with specific driving and loss mechanisms can exhibit thermal equilibrium.
• These systems can operate as ultrafast Boltzmann samplers, leveraging their inherent dynamics.
• The findings open avenues for efficient hardware realization for combinatorial optimization and machine learning tasks.