General spatial photonic Ising machine based on the interaction matrix eigendecomposition method

Area of Science:

• Quantum computing
• Photonic systems
• Combinatorial optimization

Background:

• Spatial photonic Ising machines show promise for solving complex optimization problems.
• A key limitation is the difficulty in mapping arbitrary problems to the Ising model.

Purpose of the Study:

• To propose a general spatial photonic Ising machine capable of flexibly mapping arbitrary problems.
• To utilize eigendecomposition of the interaction matrix for problem configuration.

Main Methods:

• Employing a two-dimensional Fourier transformation-based spatial photonic Ising model.
• Configuring the arbitrary interaction matrix using eigenvalues from matrix eigendecomposition.
• Analyzing error reduction with an increasing number of utilized eigenvalues.

Main Results:

• The error in Hamiltonian structural representation decreases as more eigenvalues are used.
• For a 20-vertex graph Max-cut problem, ~65% of eigenvalues guarantee optimal solutions, decreasing to <20% for near-zero probability.
• 4-spin experiments validated Hamiltonian linear mapping and ergodic optimization.

Conclusions:

• The proposed method offers a viable approach for spatial photonic Ising machines to tackle arbitrary combinatorial optimization problems.
• Leveraging multi-dimensional optical properties enhances the capability of these machines.