Photonic Hopfield neural network for the Ising problem

Area of Science:

• * Physics and Engineering
• * Computational Science

Background:

• * The Ising problem is a critical combinatorial optimization challenge, difficult for traditional Von Neumann architectures at scale.
• * Existing physical architectures (quantum, electronic, optical) and Hopfield networks with simulated annealing show promise but face resource limitations.
• * Solving large-scale optimization problems efficiently remains a significant challenge in computing.

Purpose of the Study:

• * To propose and demonstrate an accelerated Hopfield network using a photonic integrated circuit.
• * To leverage photonic integrated circuits for efficient and high-probability solutions to combinatorial optimization problems.
• * To enhance the speed and reduce resource consumption for solving the Ising problem and related tasks.

Main Methods:

• * Implementation of a Photonic Hopfield Neural Network (PHNN) using arrays of Mach-Zehnder interferometers.
• * Utilizing the inherent parallelism and ultrafast iteration rates of photonic integrated circuits.
• * Testing the PHNN on combinatorial optimization problems, including MaxCut and Spin-glass.

Main Results:

• * The PHNN converges to stable ground state solutions with high probability.
• * Achieved average success probabilities exceeding 80% for MaxCut (N=100) and Spin-glass (N=60) problems.
• * Demonstrated inherent robustness against on-chip component noise.

Conclusions:

• * The proposed PHNN architecture offers a powerful and efficient method for solving large-scale combinatorial optimization problems.
• * Photonic integrated circuits provide a viable platform for accelerating neural network computations.
• * The PHNN demonstrates significant potential for applications requiring fast and reliable optimization solutions.