Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields

A monolithically integrated optical Ising machine

The growing demand for enhanced computational power and energy efficiency has driven the development of optical Ising machines for solving combinatorial optimization problems. However, existing implementations face challenges in integration density and energy efficiency. Here, we propose a monolithically integrated four-spin Ising machine based on optoelectronic coupled oscillators. This system integrates a custom-designed Mach-Zehnder interferometer (MZI) symmetric matrix with a high-efficiency optical-electrical coupled (OEC) nonlinear unit. The OEC unit has an ultra-compact 0.01 mm² footprint and achieves a power efficiency of 4 mW per unit, ensuring scalability. The reconfigurable real-valued coupling matrix achieves a mean fidelity of 0.986. The spin evolution time is measured as 150 ns, with a 1.71 ns round-trip time confirmed through bandwidth measurements. The system successfully finds ground states for various four-spin Ising problems, demonstrating its effectiveness. This work represents a significant step toward monolithic integration of all-optical physical annealing systems, minimizing footprint, power consumption, and convergence time.

Fully Programmable Spatial Photonic Ising Machine by Focal Plane Division

Ising machines are an emerging class of hardware that promises ultrafast and energy-efficient solutions to NP-hard combinatorial optimization problems. Spatial photonic Ising machines (SPIMs) exploit optical computing in free space to accelerate the computation, showcasing parallelism, scalability, and low power consumption. However, current SPIMs can implement only a restricted class of problems. This partial programmability is a critical limitation that hampers their benchmark. Achieving full programmability of the device while preserving its scalability is an open challenge. Here, we report a fully programmable SPIM achieved through a novel operation method based on the division of the focal plane. In our scheme, a general Ising problem is decomposed into a set of Mattis Hamiltonians, whose energies are simultaneously computed optically by measuring the intensity on different regions of the camera sensor. Exploiting this concept, we experimentally demonstrate the computation with high success probability of ground-state solutions of up to 32-spin Ising models on unweighted maximum cut graphs with and without ferromagnetic bias. Simulations of the hardware prove a favorable scaling of the accuracy with the number of spin. Our fully programmable SPIM enables the implementation of many quadratic unconstrained binary optimization problems, further establishing SPIMs as a leading paradigm in non-von Neumann hardware.

Spatial Optical Simulator for Classical Statistical Models

Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a variety of classical statistical systems, including the clock, XY, Potts, and Heisenberg models, utilizing a digital micromirror device composed of a large number of tiny mirrors. Spins, with desired amplitudes or phases of the statistical models, are precisely encoded by a patch of mirrors with a superpixel approach. Then, by modulating the light field in a sequence of designed patterns, the spin-spin interaction is realized in such a way that the Hamiltonian symmetries are preserved. We successfully simulate statistical systems on a fully connected network, with ferromagnetic or Mattis-type random interactions, and observe the corresponding phase transitions between the paramagnetic and the ferromagnetic or spin-glass phases. Our results largely extend the research scope of spatial optical simulators and their versatile applications.

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

The spatial photonic Ising machine has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly map an arbitrary problem to the Ising model. In this paper, we propose a general spatial photonic Ising machine based on the interaction matrix eigendecomposition method. The arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as ∼65% of the eigenvalues are required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this percentage decreases to below ∼20% for near-zero probability. The 4-spin experiments and error analysis demonstrate the Hamiltonian linear mapping and ergodic optimization. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of the multi-dimensional optical property.

Spatial-photonic Ising machine by space-division multiplexing with physically tunable coefficients of a multi-component model

This paper proposes a space-division multiplexed spatial-photonic Ising machine (SDM-SPIM) that physically calculates the weighted sum of the Ising Hamiltonians for individual components in a multi-component model. Space-division multiplexing enables tuning a set of weight coefficients as an optical parameter and obtaining the desired Ising Hamiltonian at a time. We solved knapsack problems to verify the system's validity, demonstrating that optical parameters impact the search property. We also investigated a new dynamic coefficient search algorithm to enhance search performance. The SDM-SPIM would physically calculate the Hamiltonian and a part of the optimization with an electronics process.