All-Optical Scalable Spatial Coherent Ising Machine

Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the collective nonlinear dynamics of coupled oscillators can drive the system close to the global minimum of the classical Ising Hamiltonian, encoded in the coupling matrix of the network. To date, realizations of large-scale CIMs have been demonstrated using hybrid optical-electronic setups, where optical oscillators simulating different spins are subject to electronic feedback mechanisms emulating their mutual interaction. While the optical evolution ensures an ultrafast computation, the electronic coupling represents a bottleneck that causes the computational time to severely depend on the system size. Here, we propose an all-optical scalable CIM with fully programmable coupling. Our setup consists of an optical parametric amplifier with a spatial light modulator (SLM) within the parametric cavity. The spin variables are encoded in the binary phases of the optical wave front of the signal beam at different spatial points, defined by the pixels of the SLM. We first discuss how different coupling topologies can be achieved by different configurations of the SLM, and then benchmark our setup with a numerical simulation that mimics the dynamics of the proposed machine. In our proposal, both the spin dynamics and the coupling are fully performed in parallel, paving the way towards the realization of size-independent ultrafast optical hardware for large-scale computation purposes.

https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.16.054022

https://arxiv.org/abs/2111.06737

Phase space machine learning for multi-particle event optimization in Gaussian boson sampling

We use neural networks to represent the characteristic function of many-body Gaussian states in the quantum phase space. By a pullback mechanism, we model transformations due to unitary operators as linear layers that can be cascaded to simulate complex multi-particle processes. We use the layered neural networks for non-classical light propagation in random interferometers, and compute boson pattern probabilities by automatic differentiation. We also demonstrate that multi-particle events in Gaussian boson sampling can be optimized by a proper design and training of the neural network weights. The results are potentially useful to the creation of new sources and complex circuits for quantum technologies.

https://arxiv.org/abs/2102.12142

Official code

Experiments on adiabatic evolution in Ising machines in Optica

Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware. Novel optical platforms, known as coherent or photonic Ising machines, are attracting considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-known technique based on adiabatic evolution for finding optimal solutions in classical and quantum systems made by atoms, electrons, or photons. Although various Ising machines employ annealing in some form, adiabatic computing on optical settings has been only partially investigated. Here, we realize the adiabatic evolution of frustrated Ising models with 100 spins programmed by spatial light modulation. We use holographic and optical control to change the spin couplings adiabatically, and exploit experimental noise to explore the energy landscape. Annealing enhances the convergence to the Ising ground state and allows to find the problem solution with probability close to unity. Our results demonstrate a photonic scheme for combinatorial optimization in analogy with adiabatic quantum algorithms and classical annealing methods but enforced by optical vector-matrix multiplications and scalable photonic technology.

https://www.osapublishing.org/optica/fulltext.cfm?uri=optica-7-11-1535&id=442147

See also https://arxiv.org/abs/2005.08690

The Artificial Intelligence of Waves

In a paper published in Physical Review Letters, with title

Theory of Neuromorphic Computing by Waves: Machine Learning by Rogue Waves, Dispersive Shocks and Solitons

we study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layered model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximating mathematical functions, real-world datasets, and universal Boolean gates.
The rank of the transmission matrix has a fundamental role in assessing the learning abilities of the wave.
For a given set of training points, a threshold nonlinearity for universal interpolation exists. When considering the nonlinear Schrödinger equation, the use of highly nonlinear regimes implies that solitons, rogue, and shock waves do have a leading role in training and computing. Our results may enable the realization of novel machine learning devices by using diverse physical systems, as nonlinear optics, hydrodynamics, polaritonics, and Bose-Einstein condensates. The application of these concepts to photonics opens the way to
a large class of accelerators and new computational paradigms. In complex wave systems, as multimodal fibers, integrated optical circuits, random, topological devices, and metasurfaces, nonlinear waves can be employed to perform computation and solve complex combinatorial optimization.

The paper was selected as Editors’Suggestion and Featured in Physics

See also

https://arxiv.org/abs/1912.07044