Topological defect formation in 1D and 2D spin chains realized by network of optical parametric oscillators

Abstract

A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this "Ising machine" for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice, and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear "growth stage" and a nonlinear "saturation stage". These predictions are compared against recent data for a 10,000-spin 1D Ising machine. arXiv:1605.08121v1 [physics.optics] 26 May 2016 J 1 =0.2,J 2 =0.3 J 1 =0.35,J 2 =0.15 J 1 =0.15,J 2 =0.35 0 50 100 150 J 1 =0.3,J 2 =0.2 50 100 150 Pulse i Topological defect formation in 1D and 2D spin chains realized by network of OPOs 21 J 1 =0.45,J 2 =0.05

Coherent Ising machines—optical neural networks operating at the quantum limit

“…23 The success probability as a function of system size N normalized by the correlation length x 0 and pump rate p normalized by the threshold pump rate p 0 agrees fairly well with the theoretical model 48 as shown in Fig. 8b.…”

Experimental investigation of performance differences between coherent Ising machines and a quantum annealer

“…The formula is derived by solving the nonlinear field equations [28, Sec. 2.2] in a χ (2) medium [38,Eq. (8)].…”

Synchronously-pumped OPO coherent Ising machine: benchmarking and prospects

“…The c-SDE model, which resembles noisy mean-field annealing, 21 can accurately predict the CIM's performance for the problems studied here. 17,20 Fig. 3(a) shows the success probability and time to solution of the CIM (c-SDE simulations) for dense MAX-CUT problems.…”

“…17,18 The CIM solves Ising problems through the gain-dissipative bifurcation dynamics of OPOs. 14,[19][20][21][22] Fundamentally, this is based on the OPO bifurcation from a below-threshold (quantum) squeezed state to an abovethreshold (classical) coherent state ( Fig. 1(b)).…”