Ising Machine by Dimensional Collapse of Nonlinear Polarization Oscillators

Area of Science:

• Quantum computing
• Nonlinear optics
• Computational physics

Background:

• Ising machines offer ultrafast optimization but struggle with success rates and scaling.
• Current Ising machines face limitations in performance for complex computational tasks.

Purpose of the Study:

• To propose a novel Ising machine architecture that overcomes limitations in success rate and performance scaling.
• To leverage the three-dimensional dynamics of nonlinear polarization oscillators for enhanced Ising computation.

Main Methods:

• Exploiting optical polarization evolution in third-order nonlinear media.
• Utilizing a "dimensional collapse" mechanism for high-dimensional Ising ground state attainment.
• Employing a photonic setup with polarization-modulated pulses in a nonlinear crystal with feedback.

Main Results:

• The proposed polarization machine demonstrates enhanced success probability on benchmark graphs.
• Achieved exponential improvement in performance scaling compared to coherent Ising machines.
• The high-dimensional operation is key to improved computational capabilities.

Conclusions:

• The novel polarization-based Ising machine offers a new class of solvers for optimization problems.
• This approach significantly enhances computing capabilities for Ising Hamiltonian-based optimizations.
• The "dimensional collapse" mechanism provides a pathway to overcome existing Ising machine limitations.