Order-of-magnitude differences in computational performance of analog Ising machines induced by the choice of nonlinearity

Ising machines based on nonlinear analog systems are a promising method to accelerate computation of NP-hard optimization problems. Yet, their analog nature is also causing amplitude inhomogeneity which can deteriorate the ability to find optimal solutions. Here, we investigate how the system's nonlinear transfer function can mitigate amplitude inhomogeneity and improve computational performance. By simulating Ising machines with polynomial, periodic, sigmoid and clipped transfer functions and benchmarking them with MaxCut optimization problems, we find the choice of transfer function to have a significant influence on the calculation time and solution quality. For periodic, sigmoid and clipped transfer functions, we report order-of-magnitude improvements in the time-to-solution compared to conventional polynomial models, which we link to the suppression of amplitude inhomogeneity induced by saturation of the transfer function. This provides insights into the suitability of systems for building Ising machines and presents an efficient way for overcoming performance limitations

Distributed Kerr Nonlinearity in a Coherent All-Optical Fiber-Ring Reservoir Computer

We investigate, both numerically and experimentally, the usefulness of a distributed nonlinearity in a passive coherent photonic reservoir computer. This computing system is based on a passive coherent optical fiber-ring cavity in which part of the nonlinearities are realized by the Kerr nonlinearity. Linear coherent reservoirs can solve difficult tasks but are aided by nonlinear components in their input or output layer. Here, we compare the impact of nonlinear transformations of information in the reservoir input layer, its bulk - the fiber-ring cavity - and its readout layer. For the injection of data into the reservoir, we compare a linear input mapping to the nonlinear transfer function of a Mach Zehnder modulator. For the reservoir bulk, we quantify the impact of the optical Kerr effect. For the readout layer we compare a linear output to a quadratic output implemented by a photodiode. We find that optical nonlinearities in the reservoir itself, such as the optical Kerr nonlinearity studied in the present work, enhance the task solving capability of the reservoir. This suggests that such nonlinearities will play a key role in future coherent all-optical reservoir computers.Comment: preprin

A Quantum Optical Recurrent Neural Network for Online Processing of Quantum Times Series

Over the last decade, researchers have studied the synergy between quantum computing (QC) and classical machine learning (ML) algorithms. However, measurements in QC often disturb or destroy quantum states, requiring multiple repetitions of data processing to estimate observable values. In particular, this prevents online (i.e., real-time, single-shot) processing of temporal data as measurements are commonly performed during intermediate stages. Recently, it was proposed to sidestep this issue by focusing on tasks with quantum output, thereby removing the need for detectors. Inspired by reservoir computers, a model was proposed where only a subset of the internal parameters are optimized while keeping the others fixed at random values. Here, we also process quantum time series, but we do so using a quantum optical recurrent neural network (QORNN) of which all internal interactions can be trained. As expected, this approach yields higher performance, as long as training the QORNN is feasible. We further show that our model can enhance the transmission rate of quantum channels that experience certain memory effects. Moreover, it can counteract similar memory effects if they are unwanted, a task that could previously only be solved when redundantly encoded input signals were available. Finally, we run a small-scale version of this last task on the photonic processor Borealis, demonstrating that our QORNN can be constructed using currently existing hardware

Demonstrating Delay-based Reservoir Computing Using a Compact Photonic Integrated Chip

Photonic delay-based reservoir computing (RC) has gained considerable attention lately, as it allows for simple technological implementations of the RC concept that can operate at high speed. In this paper, we discuss a practical, compact and robust implementation of photonic delay-based RC, by integrating a laser and a 5.4cm delay line on an InP photonic integrated circuit. We demonstrate the operation of this chip with 23 nodes at a speed of 0.87GSa/s, showing performances that are similar to previous non-integrated delay-based setups. We also investigate two other post-processing methods to obtain more nodes in the output layer. We show that these methods improve the performance drastically, without compromising the computation speed

Nonlocality-induced front interaction enhancement

We demonstrate that nonlocal coupling strongly influences the dynamics of fronts connecting two equivalent states. In two prototype models we observe a large amplification in the interaction strength between two opposite fronts increasing front velocities several orders of magnitude. By analyzing the spatial dynamics we prove that way beyond quantitative effects, nonlocal terms can also change the overall qualitative picture by inducing oscillations in the front profile. This leads to a mechanism for the formation of localized structures not present for local interactions. Finally, nonlocal coupling can induce a steep broadening of localized structures, eventually annihilating them.Comment: 4 pages, 6 figure

Solitary and Coupled Semiconductor Ring Lasers as Optical Spiking Neurons

We theoretically investigate the possibility of generating pulses in an excitable (asymmetric) semiconductor ring laser (SRL) using optical trigger pulses. We show that the phase difference between the injected field and the electric field inside the SRL determines the direction of the perturbation in phase space. Due to the folded shape of the excitability threshold, this has an important influence on the ability to cross it. A mechanism for exciting multiple consecutive pulses using a single trigger pulse (i.e. multi pulse excitability) is revealed. We furthermore investigate the possibility of using asymmetric SRLs in a coupled configuration, which is a first step toward an all-optical neural network using SRLs as building blocks.Comment: 9 pages, 7 figure

Reservoir computing using a delayed feedback system: towards photonic implementations

Delayed feedback systems are known to exhibit a rich dynamical behavior, showing a wide variety of dynamical regimes. We use this richness to implement reservoir computing, a processing concept in machine learning. In this paper we demonstrate the proof of principle on an electronic system, however the approach is readily transferable to photonics, promising fast and computationally efficient all-optical processing. Using only one single node with delayed feedback instead of an entire network of nodes, we succeed in obtaining state-of-the-art results on benchmarks such as spoken digit recognition and system identification

Excitability in optical systems close to Z2-symmetry

We report theoretically and experimentally on excitability in semiconductor ring lasers in order to reveal a mechanism of excitability, general for systems close to Z2-symmetry. The global shapes of the invariant manifolds of a saddle in the vicinity of a homoclinic loop determine the origin of excitability and the fea- tures of the excitable pulses. We show how to experimentally make a semiconductor ring laser excitable by breaking the Z2-symmetry in a controlled way. The experiments confirm the theoretical predictions.Comment: 4 pages, 4 figure

Numerical investigation of semiconductor ring lasers with two external cavities

4 pages, 4 figures.-- In Proceedings Symposium IEEE/LEOS Benelux Chapter, 2008, Twente.-- PDF pre-print.We report results on the numerical analysis of the behaviour of a semiconductor ring laser under the influence of feedback from two external cavities. Double feedback arises naturally in a semiconductor ring laser, e.g. at the end facets of an outcoupling waveguide. We find that, under certain conditions, the system displays quasi-periodic and chaotic behavior.This work has been partially funded by the European Community under project IST-2005-34743 (IOLOS). This work was supported by the Belgian Science Policy Office under grant No. IAP-VI10, by the Spanish Ministry of Education (MEC) and FEDER under grants No. FIS2004-00953 (CONOCE2). GV, LG and IVE acknowledge grant and project support of the Research Foundation Flanders (FWO). IVE acknowledges advice by V. Z. Tronciu. AS acknowledges the Ramon y Cajal program by MEC.Peer reviewe