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

Study of wavelength switching time in tunable semiconductor micro-ring lasers: experiment and travelling wave description

We report in this paper the wavelength switching features of semiconductor ring lasers that are wavelength tunable based on filtered optical feedback. The filtered feedback provides a wavelength dependent loss mechanism in these devices with which a particular longitudinal mode, and thus a particular wavelength, can be selected by changing the filter characteristics of the feedback channel. We investigate how the wavelength switching speed depends on the amplitude of the modulation of the switching driving signal and on the different phase factors within the filtering branches of the SRL. We compare qualitatively the experimental results with numerical simulations based on a travelling wave model. We also investigate the dynamical behavior of the lasing and nonlasing longitudinal modes in the two channels of the clockwise and the counter-clockwise directions. We show the crucial importance of various phase relation factors on the wavelength switching behavior. Finally, we discuss what limits the switching speed and how we can accelerate it

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

Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation

We study experimentally and theoretically a semiconductor ring laser with four filtering channels providing filtered delayed optical feedback. To describe and analyze the wavelength selection and tuning in this device, we exploit the traveling-wave model determining the evolution of optical fields and carrier density along the ring cavity and filtering branches. The numerical results agree with the experimental observations: we can reproduce the wavelength tuning, the multiple wavelength emission, and the wavelength switching speed measured in these devices. The traveling-wave model allows us to study in detail the effect of the different laser parameters and can be useful for designing the future devices

Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation

We study experimentally and theoretically a semiconductor ring laser with four filtering channels providing filtered delayed optical feedback. To describe and analyze the wavelength selection and tuning in this device, we exploit the traveling-wave model determining the evolution of optical fields and carrier density along the ring cavity and filtering branches. The numerical results agree with the experimental observations: we can reproduce the wavelength tuning, the multiple wavelength emission, and the wavelength switching speed measured in these devices. The traveling-wave model allows us to study in detail the effect of the different laser parameters and can be useful for designing the future devices

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

Stochastic polarization switching dynamics in Vertical-Cavity Surface Emitting Lasers: Theory and Experiment

7 pages, 5 figures.We present an analytical, numerical and experimental study of the switching time and jitter of current induced polarization switching in Vertical-Cavity Surface-Emitting Lasers in the presence of spontaneous emission noise. Assuming that the switching is induced by changes in the dichroism, the problem can be reduced to the well-known first passage time problem in gain switched Class-A lasers. The theoretical results obtained in this way show excellent agreement both with numerical simulations based on the full rate equations model, and with experiments performed on oxide-confined Vertical-Cavity Surface-Emitting Lasers.This work was supported in part by the Belgian government under the Interuniversity Attraction Pole program (IAP V/18), in part by the Concerted Research Action, and in part by the Research Council of the Vrije Universiteit Brussel. The collaboration between the groups in Brussels, Palma de Mallorca, Ulm, and Florence was made possible through the European RTN network VISTA under Contract HPRN-CT-2000-00034. Additional support from, and discussions within, the framework of the European COST actions 268 and 288 are acknowledged. The work of J. Danckaert, G. Verschaffelt, and B. Nagler was supported by the Fund for Scientific Research—Flanders.Peer reviewe