Ising accelerator with a reconfigurable interferometric photonic processor

TL;DR

This work introduces a reconfigurable interferometric photonic processor to implement a photonic Ising machine on a hexagonal programmable mesh. By diagonalizing the coupling matrix $J$ as $J=Q^{T}\Lambda Q$ and encoding $\sqrt{D}Q\sigma$ in the optical domain, the system performs fast, on-chip matrix-vector multiplications to evaluate the Ising Hamiltonian $H(\sigma)$, while spins are updated electronically via a probabilistic annealing algorithm. The authors demonstrate 3-node and 4-node benchmark problems with high fidelity and near-unity success, and show scalable performance in simulations up to $N=50$, examining the influence of phase and coupling errors on solution quality. The work indicates a practical, energy-efficient path to large-scale photonic Ising solvers on silicon photonics, with potential impact on combinatorial optimization tasks across engineering and science. Overall, the programmable photonic Ising machine combines optical acceleration with electronic control to enable rapid exploration of complex energy landscapes at scale.

Abstract

The general-purpose programmable photonic processors offer a scalable and reconfigurable solution for a wide range of RF and optical applications. Therefore, implementing photonic Ising machines using programmable processors leverages the advantages of high speed and parallelism, enabling efficient hardware acceleration for finding ground-state solutions to combinatorial optimization problems. In this work, we demonstrate a novel programmable photonic Ising solver based on a hexagonal mesh general-purpose programmable photonic platform. The integrated system allows reconfigurable matrix multiplication and computes the Hamiltonian iteratively using an annealing algorithm that facilitates spin updates and effectively searches for the ground state. As a proof of concept, we experimentally solve two benchmark optimization problems, a fundamental three-node ferromagnetic coupling problem with external bias that demonstrates nontrivial spin interactions, and a four-node Max-Cut problem with arbitrary coupling matrices. Furthermore, to establish a large-scale capability, we emulated Ising problems with sizes up to N = 50, achieving success probabilities exceeding 80\%. Additionally, we examined the impact of errors, such as phase and coupling, on the performance of the programmable photonic Ising machine. Our general-purpose photonic Ising machine paves the way for implementing large-scale, programmable architectures for solving optimization problems.

Figures (6)

• Figure 1: a. An example of a combinatorial optimization problem, the Ising model mapping with its energy landscape and the schematic of a photonic-electronic integrated-based Ising solver. The Ising solver works as a phase encoding and intensity detection annealer where the coupling matrix $J$ is decomposed into its eigenvectors and eigenvalues $J = Q^{T}DQ$. The product $A = \sqrt{D}Q$ is encoded in the optical matrix-vector multiplier (MVM) with the spin state $\sigma$. After photo-detection, the Hamiltonian is calculated, and the new spin state is obtained. The spin state of the optical MVM is updated, and the process is repeated during $N$ iterations. b Representation of the general-purpose photonic processor with a hexagonal topology. The green path represents a splitter tree used to divide light among the input paths where spin encoding is carried out. The orthogonal matrix $Q$ is implemented using the rectangular (Clements) configuration for unitary matrix multiplication, where the MZIs in orange are in a fixed state while the blue MZIs are tunable. Finally, an ancillary array of MZIs is used to encode the diagonal matrix $D$.
• Figure 2: a. Image of the programmable photonic chip in the Smartlight processor. b Experimental fidelity and weight distribution of 1500 random unitary matrices with 3x3 (blue) and 4x4 (orange) sizes. c. Comparison between the real and measured Hamiltonian for different random coupling matrices and spin configurations d. Difference between the real and measured Hamiltonian for different random coupling matrices and spin configurations.
• Figure 3: Example of the evolution of the Hamiltonian (orange lines) during the annealing algorithm for 1000 models and 100 iterations. The dotted horizontal line represents the ground state of the problem. Results are presented for a. 3-Node problem with $J_{1} = J_{2} = 1$ and $\alpha = \frac{J_{3}}{J_{1}}= 1.5$. Inset graph represents the probability distribution of the solutions for the 1000 models and shows in green the optimal solution. b. Max-Cut problem with 4 nodes. The green line represents the mean of Hamiltonian evolution and the blue dotted line the evolution of the cut value.
• Figure 4: Performance simulations of the programmable Ising machine: a. Max-Cut with varying phase errors and problem sizes, b. Max-Cut with varying coupling errors and problem sizes, c. Möbius ladder with $N=20$ under different phase and coupling errors, d. Hamiltonian evolution for the ideal case of the Möbius ladder with $N=20$, and e. Hamiltonian evolution for the Möbius ladder with $N=100$.
• Figure 5: (a) Stability Analysis via measurement of fidelity, (b) Temperature variation monitoring, (c) Impact of System noise during hamiltonian measurement