Abstract
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.
Highlights
Scalable implementations of Ising machines are of paramount importance because many of the most challenging combinatorial optimization problems in science, engineering, and social life can be cast in terms of an Ising model [1, 2]
Minimizing the difference between the image detected on the camera and a chosen target image IT is equivalent to minimizing an Ising Hamiltonian with couplings determined by the amplitude values set by SLM1 and by IT [48]
We have realized adiabatic computing schemes on a spatial-photonic Ising machine showing that ground states are found with enhanced success probability
Summary
Ising machines are physical devices aimed to accelerate the minimization of Ising Hamiltonians. Finding the ground state of the Ising spin system gives the solution to the optimization, but requires resources growing exponentially with the problem size. For this reason, intense research focuses on unconventional architectures that use computational units such as light pulses [3], superconducting [4] and magnetic junctions [5], electromechanical modes [6], lasers and nonlinear waves [7– 12], or polariton and photon condensates [13, 14]. Annealing is a form of adiabatic computing at non-zero temperatures in which classical, quantum, or nonlinear perturbations enable the exploration of the complex energy landscape [21–24]. Recently large interest is centred on the the realization of non-electronic annealing devices that can exploits classical nonlinear and photonic properties
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