Large-scale coherent Ising machine based on optoelectronic parametric oscillator

Abstract

Ising machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.

Photonic Spatial-Euler Ising Machine for Solving 20000-node Max-cut Problem

“…Efficiently solving large-scale Max-cut problems. Compared to most solutions [44,34,45,46], we comfortably solve Max-cut problems with size over 20,000, approaching the highest reported record so far [24]. In fact, we take the adjacent 10×10 pixels as an operation unit for the same encoding to ensure the consistency of the Ising system in our experiments, thus do not maximise the use of all pixel points.…”

“…Flexible mapping of (non)fully connected Max-cut problems with arbitrary amplitude. Considering experimental setups, many schemes prefer to demonstrate the process of solving the benchmark sparse unweighted Max-cut problem [34,24,45]. Obviously, being unweighted reduces the complexity, and fully connected problems are of more practical value and harder to implement than sparse ones [44].…”

“…Therefore, for large instances, we choose to employ another classical greedy heuristic algorithm called the Sahni-Gonzales (SG) method, which is known to find approximate solutions to large Max-cut problems in polynomial time, comparable to the GW-SDP [24,36]. Using this method, a set of [34] Easy All-to-all,Unweighted 100-node 63 ns per-step CIM with DOPO [24] Very hard All-to-all,Unweighted 100000-node 785 µs CIM with OEPO [45] Hard Sparse,Unweighted 56-node 4.5 µs D-wave 2000Q [46,36] Very Furthermore, we carried out five simulations of the same problem in MATLAB to approximate the operation of the photonic Ising machine. As shown in Fig.…”

An Ising machine based on networks of subharmonic electrical resonators

“…These beyond-traditional hardware approaches [16][17][18] , as well as alloptical passive computing architectures with a similar principle of in-memory computing [19][20][21][22] , are naturally suitable for highly parallel calculations and offer orders-of-magnitude higher energy efficiency than classical devices. Many more physical systems are under intense investigation as quadratic unconstrained binary optimisation (QUBO) solvers in the post-CMOS era including lasers [23][24][25][26] , photonic simulators 27 , trapped ions 28 , photon and polariton condensates 29,30 , QED 31,32 , and others [33][34][35] .…”

“…One of the challenges in assessing the potential optimisation performance of such platforms is caused by the choice of instances of NP-hard problems. For example, minimising the Ising spin Hamiltonian on unweighted 3-regular graphs is proven to be NP-hard 37 , while for a subclass of Möbius ladder graphs, which are often chosen for testing non-traditional computing platforms 7,15,[33][34][35][38][39][40] , the Ising model can be minimized in polynomial time 41 .…”