A network‐theoretical perspective on oscillator‐based Ising machines

Abstract

Summary The standard van Neumann computer excels at many things. However, it can be very inefficient in solving optimization problems with a large solution space. For that reason, a novel analog approach, the oscillator‐based Ising machine, has been proposed as a better alternative for dealing with such problems. In this work, we review the concept of oscillator‐based Ising machine and address how optimization problems can be mapped onto such machines when the quadratic unconstrained binary optimization (QUBO) formulation is given. Furthermore, we provide an ideal circuit that can be used in combination with the wave digital concept for real‐time simulated annealing. The functionality of this circuit is explained on the basis of a Lyapunov stability analysis. The latter also provides an answer for the decision‐making question: When has the Ising machine solved a mapped problem? At the end, we provide emulation results demonstrating the correlation between functionality and stability. Our results are based on an eigenvalue analysis of the linearized system and demonstrate that all eigenvalues converge to the left complex half plane, once an optimization problem has been optimally solved. This implies that the system enters an attractor region and is hence forced to eventually converge to the optimal solution.

Oscillator networks with N‐shaped nonlinearities: Electrical modeling and wave digital emulation

“…Importantly, all NP-problems can be mapped to it. 37,5,3 A well-known problem of the sort is the max-cut problem. Solving it requires to partition the nodes of a graph into two sets such that the sum of the cut (weighted) edges is maximized.…”

“…Finding the ground state of the Ising Hamiltonian is called the Ising problem. Importantly, all NP‐problems can be mapped to it 37,5,3 . A well‐known problem of the sort is the max‐cut problem.…”

“…Computational paradigms based on oscillator networks have been gaining popularity as a promising energy‐efficient supplementation to the classical von Neumann computer 1,2 . These networks are usually large and consist of many oscillators performing computations in parallel 3 . One prominent example are Oscillator‐based Ising Machines (OIMs).…”

“…Ising machines are systems that are governed by the Ising Hamiltonian and evolve towards its ground state. They are of interest because all NP‐problems can be mapped to them 4,5,3 . Here, NP stands for Non‐deterministic Polynomial‐time, referring to a set of computational problems for which there is no known algorithm to compute the solution in polynomial‐time.…”