A recurrent Gaussian quantum network for online processing of quantum time series.

Over the last decade, researchers have studied the interplay between quantum computing and classical machine learning algorithms. However, measurements often disturb or destroy quantum states, requiring multiple repetitions of data processing to estimate observable values. In particular, this prevents online (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, eliminating the need for detectors. Inspired by reservoir computers, a model was proposed where only a subset of the internal parameters are trained while keeping the others fixed at random values. Here, we also process quantum time series, but we do so using a Recurrent Gaussian Quantum Network (RGQN) of which all internal interactions can be trained. As expected, this increased flexibility yields higher performance in benchmark tasks. Building on this, we show that the RGQN can tackle two quantum communication tasks, while also removing some hardware restrictions of the currently available methods. First, our approach is more resource efficient to enhance the transmission rate of quantum channels that experience certain memory effects. Second, it can counteract similar memory effects if they are unwanted, a task that could previously only be solved when redundantly encoded input signals could be provided. Finally, we run a small-scale version of the last task on Xanadu's photonic processor Borealis.

Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning.

Ising machines are a promising non-von-Neumann computational concept for neural network training and combinatorial optimization. However, while various neural networks can be implemented with Ising machines, their inability to perform fast statistical sampling makes them inefficient for training neural networks compared to digital computers. Here, we introduce a universal concept to achieve ultrafast statistical sampling with analog Ising machines by injecting noise. With an opto-electronic Ising machine, we experimentally demonstrate that this can be used for accurate sampling of Boltzmann distributions and for unsupervised training of neural networks, with equal accuracy as software-based training. Through simulations, we find that Ising machines can perform statistical sampling orders-of-magnitudes faster than software-based methods. This enables the use of Ising machines beyond combinatorial optimization and makes them into efficient tools for machine learning and other applications.

Influence of the input signal's phase modulation on the performance of optical delay-based reservoir computing using semiconductor lasers.

In photonic reservoir computing, semiconductor lasers with delayed feedback have shown to be suited to efficiently solve difficult and time-consuming problems. The input data in this system is often optically injected into the reservoir. Based on numerical simulations, we show that the performance depends heavily on the way that information is encoded in this optical injection signal. In our simulations we compare different input configurations consisting of Mach-Zehnder modulators and phase modulators for injecting the signal. We observe far better performance on a one-step ahead time-series prediction task when modulating the phase of the injected signal rather than only modulating its amplitude.

Photonic Reservoir Computer with Output Expansion for Unsupervized Parameter Drift Compensation.

We present a method to improve the performance of a reservoir computer by keeping the reservoir fixed and increasing the number of output neurons. The additional neurons are nonlinear functions, typically chosen randomly, of the reservoir neurons. We demonstrate the interest of this expanded output layer on an experimental opto-electronic system subject to slow parameter drift which results in loss of performance. We can partially recover the lost performance by using the output layer expansion. The proposed scheme allows for a trade-off between performance gains and system complexity.

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 5.4 cm delay line on an InP photonic integrated circuit. We demonstrate the operation of this chip with 23 nodes at a speed of 0.87 GSa/s, showing performances that is 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.

Space division multiplexing in standard multi-mode optical fibers based on speckle pattern classification.

In optical communications the transmission bandwidth of single mode optical fibers is almost fully exploited. To further increase the capacity of a telecommunication link, multiplexing techniques can be applied across 5 physical dimensions: amplitude, quadrature, polarization, frequency and space, with all but the latter being nearly exhausted. We experimentally demonstrate the feasibility of an original space division multiplexing technique based on the classification of speckle patterns measured at the fiber's output. By coupling multiple optical signals into a standard multimode optical fiber, speckle patterns arise at the fiber's end facet. This is due to quasi-random interference between the excited modes of propagation. We show how these patterns depend on the parameters of the optical signal beams and the fiber length. Classification of the speckle patterns allows the detection of the independent signals: we can detect the state (i.e. on or off ) of different beams that are multiplexed in the fiber. Our results show that the proposed space division multiplexing on standard multimode fibers is robust to mode-mixing and polarization scrambling effects.

A poor man's coherent Ising machine based on opto-electronic feedback systems for solving optimization problems.

Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.

Monostable multivibrators as novel artificial neurons.

Retriggerable and non-retriggerable monostable multivibrators are simple timers with a single characteristic, their period. Motivated by the fact that monostable multivibrators are implementable in large quantities as counters in digital programmable hardware, we set out to investigate their applicability as building blocks of artificial neural networks. We derive the nonlinear input-output firing rate relations for single multivibrator neurons as well as the equilibrium firing rate of large recurrent networks. We show that in rate-encoded monostable multivibrators networks the synaptic weights are tunable as the period ratio of connected units, and thus reconfigurable at run time in a counter-based digital implementation. This is illustrated with the task of handwritten digit recognition. Furthermore, we show in a task-independent manner that networks of monostable multivibrators are capable of nonlinear separation, when operating directly on pulse streams. Our research implies that pulse-coupled neural networks with excitable neurons showing a delayed response can perform computations even when working solely with suprathreshold pulses.

Random number generator based on an integrated laser with on-chip optical feedback.

We discuss the design and testing of a laser integrated with a long on-chip optical feedback section. The device and feedback section have been fabricated on a generic photonic integration platform using only standard building blocks. We have been able to integrate a 10 cm feedback length on a footprint of 5.5 mm2. By controlling the amount of feedback, we achieve chaotic dynamics in the long-cavity regime and show that the resulting dynamics is sufficiently complex in order to generate random bits based on the chaotic intensity fluctuation at a rate of 500 Mbits/s.

Prediction performance of reservoir computing systems based on a diode-pumped erbium-doped microchip laser subject to optical feedback.

Reservoir computing (RC) systems are computational tools for information processing that can be fully implemented in optics. Here, we experimentally and numerically show that an optically pumped laser subject to optical delayed feedback can yield similar results to those obtained for electrically pumped lasers. Unlike with previous implementations, the input data are injected at a time interval that is much larger than the time-delay feedback. These data are directly coupled to the feedback light beam. Our results illustrate possible new avenues for RC implementations for prediction tasks.

Encryption key distribution via chaos synchronization.

We present a novel encryption scheme, wherein an encryption key is generated by two distant complex nonlinear units, forced into synchronization by a chaotic driver. The concept is sufficiently generic to be implemented on either photonic, optoelectronic or electronic platforms. The method for generating the key bitstream from the chaotic signals is reconfigurable. Although derived from a deterministic process, the obtained bit series fulfill the randomness conditions as defined by the National Institute of Standards test suite. We demonstrate the feasibility of our concept on an electronic delay oscillator circuit and test the robustness against attacks using a state-of-the-art system identification method.

Stability of steady and periodic states through the bifurcation bridge mechanism in semiconductor ring lasers subject to optical feedback.

With the development of new applications using semiconductor ring lasers (SRLs) subject to optical feedback, the stability properties of their outputs becomes a crucial issue. We propose a systematic bifurcation analysis in order to properly identify the best parameter ranges for either steady or self-pulsating periodic regimes. Unlike conventional semiconductor lasers, we show that SRLs exhibit both types of outputs for large and well defined ranges of the feedback strength. We determine the stability domains in terms of the pump parameter and the feedback phase. We find that the feedback phase is a key parameter to achieve a stable steady output. We demonstrate that the self-pulsating regime results from a particular Hopf bifurcation mechanism referred to as bifurcation bridges. These bridges connect two distinct external cavity modes and are fully stable, a scenario that was not possible for diode lasers under the same conditions.

Analytical stability boundaries for quantum cascade lasers subject to optical feedback.

We consider nonlinear rate equations appropriate for a quantum cascade laser subject to optical feedback. We analyze the conditions for a Hopf bifurcation in the limit of large values of the delay. We obtain a simple expression for the critical feedback rate that highlights the effects of key parameters such as the linewidth enhancement factor and the pump. All our asymptotic approximations are validated numerically by using a path continuation technique that allows us to follow Hopf bifurcation points in parameter space.

Reducing the phase sensitivity of laser-based optical reservoir computing systems.

Optical implementations of reservoir computing systems are very promising because of their high processing speeds and the possibility to process several tasks in parallel. These systems can be implemented using semiconductor lasers subject to optical delayed feedback and optical injection. While the amount of the feedback/injection can be easily controlled, it is much more difficult to control the optical feedback/injection phase. We present extensive numerical investigations of the influence of the feedback/injection phases on laser-based reservoir computing systems with feedback. We show that a change in the phase can lead to a strong reduction in the reservoir computing system performance. We introduce a new readout layer design that -at least for some tasks- reduces this sensitivity to changes in the phase. It consists in optimizing the readout weights from a coherent combination of the reservoir's readout signal and its delayed version rather than only from the reservoir's readout signal as is usually done.

Simultaneous Computation of Two Independent Tasks Using Reservoir Computing Based on a Single Photonic Nonlinear Node With Optical Feedback.

In this brief, we numerically demonstrate a photonic delay-based reservoir computing system, which processes, in parallel, two independent computational tasks even when the two tasks have unrelated input streams. Our approach is based on a single-longitudinal mode semiconductor ring laser (SRL) with optical feedback. The SRL emits in two directional optical modes. Each directional mode processes one individual task to mitigate possible crosstalk. We illustrate the feasibility of our scheme by analyzing the performance on two benchmark tasks: 1) chaotic time series prediction and 2) nonlinear channel equalization. We identify some feedback configurations for which the results for simultaneous prediction/classification indicate a good performance, but with slight degradation (as compared with the performance obtained for single task processing) due to nonlinear and linear interactions between the two directional modes of the laser. In these configurations, the system performs well on both tasks for a broad range of the parameters.

Delay-based reservoir computing: noise effects in a combined analog and digital implementation.

Reservoir computing is a paradigm in machine learning whose processing capabilities rely on the dynamical behavior of recurrent neural networks. We present a mixed analog and digital implementation of this concept with a nonlinear analog electronic circuit as a main computational unit. In our approach, the reservoir network can be replaced by a single nonlinear element with delay via time-multiplexing. We analyze the influence of noise on the performance of the system for two benchmark tasks: 1) a classification problem and 2) a chaotic time-series prediction task. Special attention is given to the role of quantization noise, which is studied by varying the resolution in the conversion interface between the analog and digital worlds.

Fast phase response and chaos bandwidth enhancement in semiconductor lasers subject to optical feedback and injection.

We numerically show the quantitative relation between the chaos bandwidth enhancement and fast phase dynamics in semiconductor lasers with optical feedback and optical injection. The injection increases the coupling between the intensity and the phase leading to a competition between the relaxation oscillation (RO) frequency and the intrinsic response frequency of the phase. For large feedback strengths, it is found that the chaos bandwidth is determined by the intrinsic phase response frequency. For smaller feedback strengths, the system is not chaotic and its bandwidth is determined by the RO frequency.

Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics.

Semiconductor lasers subject to delayed optical feedback have recently shown great potential in solving computationally hard tasks. By optically implementing a neuro-inspired computational scheme, called reservoir computing, based on the transient response to optical data injection, high processing speeds have been demonstrated. While previous efforts have focused on signal bandwidths limited by the semiconductor laser's relaxation oscillation frequency, we demonstrate numerically that the much faster phase response makes significantly higher processing speeds attainable. Moreover, this also leads to shorter external cavity lengths facilitating future on-chip implementations. We numerically benchmark our system on a chaotic time-series prediction task considering two different feedback configurations. The results show that a prediction error below 4% can be obtained when the data is processed at 0.25 GSamples/s. In addition, our insight into the phase dynamics of optical injection in a semiconductor laser also provides a clear understanding of the system performance at different pump current levels, even below solitary laser threshold. Considering spontaneous emission noise and noise in the readout layer, we obtain good prediction performance at fast processing speeds for realistic values of the noise strength.

Constructing optimized binary masks for reservoir computing with delay systems.

Reservoir computing is a novel bio-inspired computing method, capable of solving complex tasks in a computationally efficient way. It has recently been successfully implemented using delayed feedback systems, allowing to reduce the hardware complexity of brain-inspired computers drastically. In this approach, the pre-processing procedure relies on the definition of a temporal mask which serves as a scaled time-mutiplexing of the input. Originally, random masks had been chosen, motivated by the random connectivity in reservoirs. This random generation can sometimes fail. Moreover, for hardware implementations random generation is not ideal due to its complexity and the requirement for trial and error. We outline a procedure to reliably construct an optimal mask pattern in terms of multipurpose performance, derived from the concept of maximum length sequences. Not only does this ensure the creation of the shortest possible mask that leads to maximum variability in the reservoir states for the given reservoir, it also allows for an interpretation of the statistical significance of the provided training samples for the task at hand.

Fast random bits generation based on a single chaotic semiconductor ring laser.

The use of the postprocessing method consisting of bitwise Exclusive-OR and least significant bits extraction to generate random bit sequences typically requires two distinct chaotic outputs. While the two signals are, in general, generated using two separated devices, e.g. two Fabry-Perot lasers, a single semiconductor ring laser can be used as an alternative due to its circular symmetry which facilitates lasing in two counterpropagating mode directions. We consider a chaotic semiconductor ring laser and investigate both numerically and experimentally its characteristics for fast random bit generation. In particular, we show that by sampling each directional mode's output signal using a 8-bit analog-digital converter and through Exclusive-OR operation applied to the two resulting signals (after throwing away 4 most significant bits), we can achieve fast random bit-streams with a bit rate 4 × 10 = 40 Gbit/s, passing the statistical randomness tests. To optimize the system performance, we also study the dependence of randomness on the main system parameters and on noise.