arXiv subjects

Serge Massar

Publications and source records attributed to Serge Massar.

At least 37 records · Page 2Linked to original sources

arXiv2022

Photonic reservoir computer based on frequency multiplexing

Reservoir computing is a brain inspired approach for information processing, well suited to analogue implementations. We report a photonic implementation of a reservoir computer that exploits frequency domain multiplexing to encode neuron states. The system processes 25 comb lines simultaneously (i.e. 25 neurons), at a rate of 20 MHz. We illustrate performances on two standard benchmark tasks: channel equalization and time series forecasting. We also demonstrate that frequency multiplexing allows output weights to be implemented in the optical domain, through optical attenuation. We discuss the perspectives for high speed high performance low footprint implementations.

physics.optics↗

arXiv2021

Characterizing the intersection of QMA and coQMA

We show that the functional analogue of QMA$\cap$coQMA, denoted F(QMA$\cap$coQMA), equals the complexity class Total Functional QMA (TFQMA). To prove this we need to introduce alternative definitions of QMA$\cap$coQMA in terms of a single quantum verification procedure. We show that if TFQMA equals the functional analogue of BQP (FBQP), then QMA$\cap$coQMA = BQP. We show that if there is a QMA complete problem that (robustly) reduces to a problem in TFQMA, then QMA$\cap$coQMA = QMA. These results provide strong evidence that the inclusions FBQP$\subseteq$TFQMA$\subseteq$FQMA are strict, since otherwise the corresponding inclusions in BQP$\subseteq$QMA$\cap$coQMA$\subseteq$QMA would become equalities.

quant-ph↗

arXiv2021

Photonic Extreme Learning Machine based on frequency multiplexing

The optical domain is a promising field for physical implementation of neural networks, due to the speed and parallelism of optics. Extreme Learning Machines (ELMs) are feed-forward neural networks in which only output weights are trained, while internal connections are randomly selected and left untrained. Here we report on a photonic ELM based on a frequency-multiplexed fiber setup. Multiplication by output weights can be performed either offline on a computer, or optically by a programmable spectral filter. We present both numerical simulations and experimental results on classification tasks and a nonlinear channel equalization task.

cs.ET↗

arXiv2021

Resource efficient single photon source based on active frequency multiplexing

We propose a new single photon source based on the principle of active multiplexing of heralded single photons which, unlike previously reported architecture, requires a limited amount of physical resources. We discuss both its feasibility and the purity and indistinguishability of single photons as function of the key parameters of a possible implementation.

quant-ph↗

arXiv2020

Random pattern and frequency generation using a photonic reservoir computer with output feedback

Reservoir computing is a bio-inspired computing paradigm for processing time dependent signals. The performance of its analogue implementations matches other digital algorithms on a series of benchmark tasks. Their potential can be further increased by feeding the output signal back into the reservoir, which would allow to apply the algorithm to time series generation. This requires, in principle, implementing a sufficiently fast readout layer for real-time output computation. Here we achieve this with a digital output layer driven by a FPGA chip. We demonstrate the first opto-electronic reservoir computer with output feedback and test it on two examples of time series generation tasks: frequency and random pattern generation. We obtain very good results on the first task, similar to idealised numerical simulations. The performance on the second one, however, suffers from the experimental noise. We illustrate this point with a detailed investigation of the consequences of noise on the performance of a physical reservoir computer with output feedback. Our work thus opens new possible applications for analogue reservoir computing and brings new insights on the impact of noise on the output feedback.

cs.NE↗

arXiv2020

Online training for high-performance analogue readout layers in photonic reservoir computers

Introduction. Reservoir Computing is a bio-inspired computing paradigm for processing time-dependent signals. The performance of its hardware implementation is comparable to state-of-the-art digital algorithms on a series of benchmark tasks. The major bottleneck of these implementation is the readout layer, based on slow offline post-processing. Few analogue solutions have been proposed, but all suffered from notice able decrease in performance due to added complexity of the setup. Methods. Here we propose the use of online training to solve these issues. We study the applicability of this method using numerical simulations of an experimentally feasible reservoir computer with an analogue readout layer. We also consider a nonlinear output layer, which would be very difficult to train with traditional methods. Results. We show numerically that online learning allows to circumvent the added complexity of the analogue layer and obtain the same level of performance as with a digital layer. Conclusion. This work paves the way to high-performance fully-analogue reservoir computers through the use of online training of the output layers.

cs.NE↗

arXiv2020

Total Functions in QMA

The complexity class QMA is the quantum analog of the classical complexity class NP. The functional analogs of NP and QMA, called functional NP (FNP) and functional QMA (FQMA), consist in either outputting a (classical or quantum) witness, or outputting NO if there does not exist a witness.The classical complexity class Total Functional NP (TFNP) is the subset of FNP for which it can be shown that the NO outcome never occurs. TFNP includes many natural and important problems. In the present work we introduce the complexity class of Total Functional QMA (TFQMA), the quantum analog of TFNP. We show that FQMA and TFQMA can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. In so doing we introduce new notions such as the eigenbasis and spectrum of a quantum verification procedure which are of interest by themselves. We then provide examples of problems that lie in TFQMA, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that Group Non-Membership, which was known to belong to QMA, in fact belongs to TFQMA. We also provide a simple oracle with respect to which we have a separation between FBQP and TFQMA. In the conclusion we discuss the relation between TFQMA, public key quantum money, and the complexity of quantum states.

quant-ph↗

arXiv2019

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.

physics.app-ph↗

arXiv2019

Four-wave mixing and enhanced analogue Hawking effect in a nonlinear optical waveguide

We study in detail the scattering of light on a soliton propagating in a waveguide which has been proposed as an experimental system in which one could observe the analogue Hawking effect. When not applying the rotating wave approximation, we show that the linearized wave equation governing perturbations has the same structure as that governing phonon propagation in an atomic Bose condensate. By taking into account the full dispersion relation, we then show that the scattering coefficients encoding the production of photon pairs are amplified by a resonance effect related to the modulation instability occurring in the presence of a continuous wave. When using a realistic example of a silicon nitride waveguide on a silica substrate, we find that a soliton of duration 10 fs would spontaneously emit about one photon pair for every cm it travels, which makes the effect readily observable. This result is confirmed by numerically solving the equation encoding the Kerr nonlinearity and governing the evolution of the full field (soliton plus perturbations). We discuss the link with previous works devoted to the analogue Hawking effect where the pair creation rates were about six orders of magnitude smaller.

physics.optics↗

arXiv2018

Using a reservoir computer to learn chaotic attractors, with applications to chaos synchronisation and cryptography

Using the machine learning approach known as reservoir computing, it is possible to train one dynamical system to emulate another. We show that such trained reservoir computers reproduce the properties of the attractor of the chaotic system sufficiently well to exhibit chaos synchronisation. That is, the trained reservoir computer, weakly driven by the chaotic system, will synchronise with the chaotic system. Conversely, the chaotic system, weakly driven by a trained reservoir computer, will synchronise with the reservoir computer. We illustrate this behaviour on the Mackey-Glass and Lorenz systems. We then show that trained reservoir computers can be used to crack chaos based cryptography and illustrate this on a chaos cryptosystem based on the Mackey-Glass system. We conclude by discussing why reservoir computers are so good at emulating chaotic systems.

cs.NE↗

arXiv2018

Device-independent randomness generation with sublinear shared quantum resources

In quantum cryptography, device-independent (DI) protocols can be certified secure without requiring assumptions about the inner workings of the devices used to perform the protocol. In order to display nonlocality, which is an essential feature in DI protocols, the device must consist of at least two separate components sharing entanglement. This raises a fundamental question: how much entanglement is needed to run such DI protocols? We present a two-device protocol for DI random number generation (DIRNG) which produces approximately $n$ bits of randomness starting from $n$ pairs of arbitrarily weakly entangled qubits. We also consider a variant of the protocol where $m$ singlet states are diluted into $n$ partially entangled states before performing the first protocol, and show that the number $m$ of singlet states need only scale sublinearly with the number $n$ of random bits produced. Operationally, this leads to a DIRNG protocol between distant laboratories that requires only a sublinear amount of quantum communication to prepare the devices.

quant-ph↗

arXiv2018

Brain-inspired photonic signal processor for periodic pattern generation and chaotic system emulation

Reservoir computing is a bio-inspired computing paradigm for processing time-dependent signals. Its hardware implementations have received much attention because of their simplicity and remarkable performance on a series of benchmark tasks. In previous experiments the output was uncoupled from the system and in most cases simply computed offline on a post-processing computer. However, numerical investigations have shown that feeding the output back into the reservoir would open the possibility of long-horizon time series forecasting. Here we present a photonic reservoir computer with output feedback, and demonstrate its capacity to generate periodic time series and to emulate chaotic systems. We study in detail the effect of experimental noise on system performance. In the case of chaotic systems, this leads us to introduce several metrics, based on standard signal processing techniques, to evaluate the quality of the emulation. Our work significantly enlarges the range of tasks that can be solved by hardware reservoir computers, and therefore the range of applications they could potentially tackle. It also raises novel questions in nonlinear dynamics and chaos theory.

cs.NE↗

arXiv2016

Parallel photonic reservoir computing using frequency multiplexing of neurons

Today's unrelenting increase in demand for information processing creates the need for novel computing concepts. Reservoir computing is such a concept that lends itself particularly well to photonic hardware implementations. Over recent years, these hardware implementations have gained maturity and now achieve state-of-the-art performance on several benchmark tasks. However, implementations so far are essentially all based on sequential data processing, leaving the inherent parallelism of photonics unexploited. Parallel implementations process all neurons simultaneously, and therefore have the potential of reducing computation time by a factor equal to the number of neurons, compared to sequential architectures. Here, we report a parallel reservoir computer that uses frequency domain multiplexing of neuron states. We illustrate its performance on standard benchmark tasks such as nonlinear channel equalization, the reproduction of a nonlinear 10th-order system, and speech recognition, obtaining error rates similar to previous optical experiments. The present experiment is thus an important step towards high speed, low footprint, all optical photonic information processing.

cs.ET↗

arXiv2016

Embodiment of Learning in Electro-Optical Signal Processors

Delay-coupled electro-optical systems have received much attention for their dynamical properties and their potential use in signal processing. In particular it has recently been demonstrated, using the artificial intelligence algorithm known as reservoir computing, that photonic implementations of such systems solve complex tasks such as speech recognition. Here we show how the backpropagation algorithm can be physically implemented on the same electro-optical delay-coupled architecture used for computation with only minor changes to the original design. We find that, compared when the backpropagation algorithm is not used, the error rate of the resulting computing device, evaluated on three benchmark tasks, decreases considerably. This demonstrates that electro-optical analog computers can embody a large part of their own training process, allowing them to be applied to new, more difficult tasks.

cs.ET↗

arXiv2016

Online Training of an Opto-Electronic Reservoir Computer Applied to Real-Time Channel Equalisation

Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals. The performance of its analogue implementation are comparable to other state of the art algorithms for tasks such as speech recognition or chaotic time series prediction, but these are often constrained by the offline training methods commonly employed. Here we investigated the online learning approach by training an opto-electronic reservoir computer using a simple gradient descent algorithm, programmed on an FPGA chip. Our system was applied to wireless communications, a quickly growing domain with an increasing demand for fast analogue devices to equalise the nonlinear distorted channels. We report error rates up to two orders of magnitude lower than previous implementations on this task. We show that our system is particularly well-suited for realistic channel equalisation by testing it on a drifting and a switching channels and obtaining good performances

cs.ET↗

arXiv2016

Measuring the Nonlinear Refractive Index of Graphene using the Optical Kerr Effect Method

By means of the ultrafast optical Kerr effect method coupled to optical heterodyne detection (OHD-OKE), we characterize the third order nonlinear response of graphene at telecom wavelength, and compare it to experimental values obtained by the Z-scan method on the same samples. From these measurements, we estimate a negative nonlinear refractive index for monolayer graphene, $n_2 = - 1.1\times 10^{-13} m^2/W$. This is in contradiction to previously reported values, which leads us to compare our experimental measurements obtained by the OHD-OKE and the Z-scan method with theoretical and experimental values found in the literature, and to discuss the discrepancies, taking into account parameters such as doping.

physics.optics↗

arXiv2015

Device-Independent Bit Commitment based on the CHSH Inequality

Bit commitment and coin flipping occupy a unique place in the device-independent landscape, as the only device-independent protocols thus far suggested for these tasks are reliant on tripartite GHZ correlations. Indeed, we know of no other bipartite tasks, which admit a device-independent formulation, but which are not known to be implementable using only bipartite nonlocality. Another interesting feature of these protocols is that the pseudo-telepathic nature of GHZ correlations -- in contrast to the generally statistical character of nonlocal correlations, such as those arising in the violation of the CHSH inequality -- is essential to their formulation and analysis. In this work, we present a device-independent bit commitment protocol based on CHSH testing, which achieves the same security as the optimal GHZ-based protocol. The protocol is analyzed in the most general settings, where the devices are used repeatedly and may have long-term quantum memory. We also recast the protocol in a post-quantum setting where both honest and dishonest parties are restricted only by the impossibility of signaling, and find that overall the supra-quantum structure allows for greater security.

quant-ph↗

arXiv2015

Hyperdense coding and superadditivity of classical capacities in hypersphere theories

In quantum superdense coding, two parties previously sharing entanglement can communicate a two bit message by sending a single qubit. We study this feature in the broader framework of general probabilistic theories. We consider a particular class of theories in which the local state space of the communicating parties corresponds to Euclidean hyperballs of dimension n (the case n = 3 corresponds to the Bloch ball of quantum theory). We show that a single n-ball can encode at most one bit of information, independently of n. We introduce a bipartite extension of such theories for which there exist dense coding protocols such that log_2 (n+1) bits are communicated if entanglement is previously shared by the communicating parties. For n > 3, these protocols are more powerful than the quantum one, because more than two bits are communicated by transmission of a system that locally encodes at most one bit. We call this phenomenon hyperdense coding. Our hyperdense coding protocols imply superadditive classical capacities: two entangled systems can encode log_2 (n+1) > 2 bits, even though each system individually encodes at most one bit. In our examples, hyperdense coding and superadditivity of classical capacities come at the expense of violating tomographic locality or dynamical continuous reversibility.

quant-ph↗