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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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

Shaomeng Wang, Wenjia Zhang, Xin Ye

|June 10, 2024

Summary

This summary is machine-generated.

A new spatial photonic Ising machine can now solve complex optimization problems by using eigendecomposition to map arbitrary problems. This method significantly reduces errors and improves the probability of finding optimal solutions.

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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.