arXiv subjects

Peter Bienstman

Publications and source records attributed to Peter Bienstman.

At least 19 recordsLinked to original sources

arXiv2026

Comparative Study of Potts Machine Dynamics and Performance for Max-k-Cut

Combinatorial optimization problems in logistics, finance, energy, and scheduling routinely involve multi-state decision variables. Ising machines (IMs) require binary expansions (e.g., one-hot encoding) to encode such variables, whereas Potts machines (PMs) represent them natively. By doing so, PMs are expected to outperform IMs on multi-state problems. To the best of our knowledge, no systematic study of PM models has yet assessed whether this expectation holds. We therefore benchmark five representative PMs against a reference IM on Max-3-Cut and Max-4-Cut, using 800-vertex GSet graphs and random graphs of up to 50 vertices. Surprisingly, the reference IM still outperforms every PM, and the IM supremacy increases significantly in going from Max-3-Cut to Max-4-Cut. These results provide clear evidence that current PM dynamics underperform relative to binary approaches, even in regimes where they are presumed advantageous. We provide a way forward by quantifying the underperformance of current PMs, as well as by identifying three dynamical properties that correlate strongly with their performance ranking. Our work stresses the need for more systematic assessments of algorithmic performance in order to guide the design of more effective Potts machines.

cond-mat.stat-mech↗

arXiv2026

Baudrate- and Reach-Flexible All-Optical Equalization with a Co-Packaged Photonic Reservoir and Receiver

Intensity-modulation direct-detection links must support increasing baudrates and transmission distances while operating under stringent power and cost constraints. However, as data rates and reaches increase, chromatic dispersion induces stronger inter-symbol interference and, after direct detection, frequency-selective fading, thus requiring increasingly powerful equalization. In conventional receivers, this translates into digital equalization whose complexity scales unfavorably with data rate. Photonic-domain equalization offers a hardware-based alternative that operates naturally at line rate and mitigates frequency fading. However, prior demonstrations were not readily adaptable for different rate and/or reach operation. In this paper, we experimentally demonstrate all-optical equalization across 10-46 Gbaud and 10-250 km SSMF in the C-band enabled solely through retraining of the readout layer, achieving up to four orders of magnitude BER improvement over standard DSP equalization. The demonstrator comprises a 16-node spatially multiplexed reservoir, programmable on-chip readout, and co-packaged receiver front-end. To our knowledge, this is the first co-packaged photonic reservoir receiver and the first demonstration of simultaneous baudrate- and reach-flexible equalization using a fixed-topology integrated photonic circuit.

physics.optics↗

arXiv2026

Node-reduction through Joint Optimization of Input and Readout Layers in Photonic Reservoir Equalization

Photonic reservoir computing is a machine learning paradigm in which a recurrent neural network remains fixed while only the output weights are trained. This makes it a well-suited approach for high-speed signal equalisation in optical communication systems, offering a trainable, low-power, and low-complexity solution. However, achieving strong performance typically requires relatively large network sizes, as learning is confined to the output layer. To address this, we investigate the role of trainable input mappings alongside conventional output weight optimisation. Across a range of short- and mid-reach IM/DD transmission scenarios, reaching up to 200 km for a 28 GBd NRZ signal, improvements of over two orders of magnitude in BER are achieved. This enables halving the network size while maintaining comparable performance. Furthermore, we show that this approach effectively extends the memory of the reservoir, resulting in over three orders of magnitude improvement in memory-intensive tasks. These results also show that starting at 16 nodes a performance of at least one to two magnitudes better than both a complexity matched FFE and a Volterra filter of second order are reached.

physics.optics↗

arXiv2025

LuxIA: A Lightweight Unitary matriX-based Framework Built on an Iterative Algorithm for Photonic Neural Network Training

PNNs present promising opportunities for accelerating machine learning by leveraging the unique benefits of photonic circuits. However, current state of the art PNN simulation tools face significant scalability challenges when training large-scale PNNs, due to the computational demands of transfer matrix calculations, resulting in high memory and time consumption. To overcome these limitations, we introduce the Slicing method, an efficient transfer matrix computation approach compatible with back-propagation. We integrate this method into LuxIA, a unified simulation and training framework. The Slicing method substantially reduces memory usage and execution time, enabling scalable simulation and training of large PNNs. Experimental evaluations across various photonic architectures and standard datasets, including MNIST, Digits, and Olivetti Faces, show that LuxIA consistently surpasses existing tools in speed and scalability. Our results advance the state of the art in PNN simulation, making it feasible to explore and optimize larger, more complex architectures. By addressing key computational bottlenecks, LuxIA facilitates broader adoption and accelerates innovation in AI hardware through photonic technologies. This work paves the way for more efficient and scalable photonic neural network research and development.

cs.LG↗

arXiv2025

Experimental Investigation of Time Series Classification using a Self-Pulsing Microring Resonator Network

Photonic neuromorphic computing offers compelling advantages in power efficiency and parallel processing, but often falls short in realizing scalable nonlinearity and long-term memory. These limitations can be overcome by silicon microring resonator (MRR) networks. These integrated photonic circuits enable compact, high-throughput neuromorphic computing by simultaneously exploiting spatial, temporal, and wavelength dimensions. This work provides an in-depth study of of MRR networks for photonics-based machine learning (ML). We investigate the system's effectiveness on two widely used image classification benchmarks, MNIST and Fashion-MNIST, by encoding images directly into time sequences. In particular, we enhance the computational performance of a linear readout classifier within the reservoir computing paradigm through the strategic use of multiple physical output ports, diverse laser wavelengths, and varied input power levels. Moreover, we explore a single-pixel classification setting, where inference does not require digital memory, thanks to the inherent memory and parallelism of our MRR network.

physics.optics↗

arXiv2025

A More Convex Ising Formulation of Max-3-Cut Using Higher-Order Spin Interactions

Many combinatorial optimization problems (COPs) are naturally expressed using variables that take on more than two discrete values. To solve such problems using Ising machines (IMs) - specialized analog or digital devices designed to solve COPs efficiently - these multi-valued integers must be encoded using binary spin variables. A common approach is one-hot encoding, where each variable is represented by a group of spins constrained so that exactly one spin is in the "up" state. However, this encoding introduces energy barriers: changing an integer's value requires flipping two spins and passing through an invalid intermediate state. This creates rugged energy landscapes that may hinder optimization. We propose a higher-order Ising formulation for Max-3-Cut, which is the smallest fundamental COP with multi-valued integer variables. Our formulation preserves valid configurations under single-spin updates. The resulting energy landscapes are smoother, and we show that this remains true even when the binary variables are relaxed to continuous values, making it well-suited for analog IMs as well. Benchmarking on such an IM, we find that the higher-order formulation leads to significantly faster solutions than the Ising baseline. Interestingly, we find that an empirical rescaling of some terms in the Ising formulation - a heuristic proposed in prior work - approaches the performance of the higher-order Ising formulation, underscoring the importance of empirical parameter tuning in COP encodings.

cond-mat.stat-mech↗

arXiv2025

How to Incorporate Higher-order Interactions in Analog Ising Machines

Ising machines (IMs) are specialized devices designed to efficiently solve combinatorial optimization problems. Among such problems, Boolean Satisfiability (SAT) is particularly relevant in industrial applications. To solve SAT problems using IMs, it is crucial to incorporate higher-order interactions. However, in analog IMs, interactions of different orders scale unevenly with the continuous spin amplitudes, introducing imbalances that can significantly degrade performance. We present a numerical comparison of methods to mitigate these imbalances, evaluating time-to-solution and success rate on Uniform Random 3-SAT instances from the SATLIB benchmark set. Our results show that the most effective approach employs spin interactions that are proportional to the signs of spins, rather than their continuous amplitudes. This generalizes our previous work, which showed that such interactions best mitigate imbalances induced by external fields in quadratic analog IMs. In this work, its advantage becomes substantially more pronounced, as it naturally mitigates imbalances across all interaction orders. We further demonstrate that smooth approximations of this method make it compatible with analog hardware. Our findings underscore the central role of spin-sign-based interactions in enabling robust and scalable analog IM dynamics.

cond-mat.stat-mech↗

arXiv2025

How to Incorporate External Fields in Analog Ising Machines

Ising machines (IMs) are specialized devices designed to efficiently solve combinatorial optimization problems (COPs). They consist of artificial spins that evolve towards a low-energy configuration representing a problem's solution. Most realistic COPs require both spin-spin couplings and external fields. In IMs with analog spins, these interactions scale differently with the continuous spin amplitudes, leading to imbalances that affect performance. Various techniques have been proposed to mitigate this issue, but their performance has not been benchmarked. We address this gap through a numerical analysis. We evaluate the time-to-solution of these methods across three distinct problem classes with up to 500 spins. Our results show that the most effective way to incorporate external fields is through an approach where the spin interactions are proportional to the spin signs, rather than their continuous amplitudes.

cond-mat.stat-mech↗

arXiv2025

Real-time all-optical signal equalisation with silicon photonic recurrent neural networks

Communication through optical fibres experiences limitations due to chromatic dispersion and nonlinear Kerr effects that degrade the signal. Mitigating these impairments is typically done using complex digital signal processing algorithms. However, these equalisation methods require significant power consumption and introduce high latencies. Photonic reservoir computing (a subfield of neural networks) offers an alternative solution, processing signals in the analog optical Domain. In this work, we present to our knowledge the very first experimental demonstration of real-time online equalisation of fibre distortions using a silicon photonics chip that combines the recurrent reservoir and the programmable readout layer. We successfully equalize a 28 Gbps on-off keying signal across varying power levels and fibre lengths, even in the highly nonlinear regime. We obtain bit error rates orders of magnitude below previously reported optical equalisation methods, reaching as low as 4e-7 , far below the generic forward error correction limit of 5.8e-5 used in commercial Ethernet interfaces. Also, simulations show that simply by removing delay lines, the system becomes compatible with line rates of 896 Gpbs. Using wavelength multiplexing, this can result in a throughput in excess of 89.6 Tbps. Finally, incorporating non-volatile phase shifters, the power consumption can be less than 6 fJ/bit.

physics.optics↗

arXiv2025

Roadmap on Neuromorphic Photonics

This roadmap consolidates recent advances while exploring emerging applications, reflecting the remarkable diversity of hardware platforms, neuromorphic concepts, and implementation philosophies reported in the field. It emphasizes the critical role of cross-disciplinary collaboration in this rapidly evolving field.

cs.ET↗

arXiv2024

Reservoir computing with all-optical non-fading memory in a self-pulsing microresonator network

Photonic neuromorphic computing may offer promising applications for a broad range of photonic sensors, including optical fiber sensors, to enhance their functionality while avoiding loss of information, energy consumption, and latency due to optical-electrical conversion. However, time-dependent sensor signals usually exhibit much slower timescales than photonic processors, which also generally lack energy-efficient long-term memory. To address this, we experimentally demonstrate a first implementation of physical reservoir computing with non-fading memory for multi-timescale signal processing. This is based on a fully passive network of 64 coupled silicon microring resonators. Our compact photonic reservoir is capable of hosting energy-efficient nonlinear dynamics and multistability. It can process and retain input signal information for an extended duration, at least tens of microseconds. Our reservoir computing system can learn to infer the timing of a single input pulse and the spike rate of an input spike train, even after a relatively long period following the end of the input excitation. We demonstrate this operation at two different timescales, with approximately a factor of 5 difference. This work presents a novel approach to extending the memory of photonic reservoir computing and its timescale of application.

physics.optics↗

arXiv2024

Braided interferometer mesh for robust photonic matrix-vector multiplications with non-ideal components

Matrix-vector multiplications (MVMs) are essential for a wide range of applications, particularly in modern machine learning and quantum computing. In photonics, there is growing interest in developing architectures capable of performing linear operations with high speed, low latency, and minimal loss. Traditional interferometric photonic architectures, such as the Clements design, have been extensively used for MVM operations. However, as these architectures scale, improving stability and robustness becomes critical. In this paper, we introduce a novel photonic braid interferometer architecture that outperforms both the Clements and Fldzhyan designs in these aspects. Using numerical simulations, we evaluate the performance of these architectures under ideal conditions and systematically introduce non-idealities such as insertion losses, beam splitter imbalances, and crosstalk. The results demonstrate that the braid architecture offers superior robustness due to its symmetrical design and reduced layer count. Further analysis shows that the braid architecture is particularly advantageous in large-scale implementations, delivering better performance as the size of the interferometer increases. We also assess the footprint and total insertion losses of each architecture. Although waveguide crossings in the braid architecture slightly increase the footprint and insertion loss, recent advances in crossing technology significantly minimize these effects. Our study suggests that the braid architecture is a robust solution for photonic neuromorphic computing, maintaining high fidelity in realistic conditions where imperfections are inevitable.

physics.optics↗

arXiv2024

The Taiji microresonator as an unidirectional spiking neuron

While biological neurons ensure unidirectional signalling, scalable integrated photonic neurons, such as silicon microresonators, respond the same way regardless of excitation direction due to the Lorentz reciprocity principle. Here, we show that a non-linear Taiji microresonator is a proper optical analogous of a biological neuron showing both a spiking response as well as a direction dependence response.

physics.optics↗

arXiv2024

Invited: Neuromorphic architectures based on augmented silicon photonics platforms

In this work, we discuss our vision for neuromorphic accelerators based on integrated photonics within the framework of the Horizon Europe NEUROPULS project. Augmented integrated photonic architectures that leverage phase-change and III-V materials for optical computing will be presented. A CMOS-compatible platform will be discussed that integrates these materials to fabricate photonic neuromorphic architectures, along with a gem5-based simulation platform to model accelerator operation once it is interfaced with a RISC-V processor. This simulation platform enables accurate system-level accelerator modeling and benchmarking in terms of key metrics such as speed, energy consumption, and footprint.

cs.ET↗

arXiv2023

Emergent self-adaptation in an integrated photonic neural network for backpropagation-free learning

Plastic self-adaptation, nonlinear recurrent dynamics and multi-scale memory are desired features in hardware implementations of neural networks, because they enable them to learn, adapt and process information similarly to the way biological brains do. In this work, we experimentally demonstrate these properties occurring in arrays of photonic neurons. Importantly, this is realised autonomously in an emergent fashion, without the need for an external controller setting weights and without explicit feedback of a global reward signal. Using a hierarchy of such arrays coupled to a backpropagation-free training algorithm based on simple logistic regression, we are able to achieve a performance of 98.2% on the MNIST task, a popular benchmark task looking at classification of written digits. The plastic nodes consist of silicon photonics microring resonators covered by a patch of phase-change material that implements nonvolatile memory. The system is compact, robust, and straightforward to scale up through the use of multiple wavelengths. Moreover, it constitutes a unique platform to test and efficiently implement biologically plausible learning schemes at a high processing speed.

physics.optics↗

arXiv2023

Integrated Photonic Reservoir Computing with All-Optical Readout

Integrated photonic reservoir computing has been demonstrated to be able to tackle different problems because of its neural network nature. A key advantage of photonic reservoir computing over other neuromorphic paradigms is its straightforward readout system, which facilitates both rapid training and robust, fabrication variation-insensitive photonic integrated hardware implementation for real-time processing. We present our recent development of a fully-optical, coherent photonic reservoir chip integrated with an optical readout system, capitalizing on these benefits. Alongside the integrated system, we also demonstrate a weight update strategy that is suitable for the integrated optical readout hardware. Using this online training scheme, we successfully solved 3-bit header recognition and delayed XOR tasks at 20 Gbps in real-time, all within the optical domain without excess delays.

physics.optics↗

arXiv2023

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.

quant-ph↗

arXiv2023

NEUROPULS: NEUROmorphic energy-efficient secure accelerators based on Phase change materials aUgmented siLicon photonicS

This special session paper introduces the Horizon Europe NEUROPULS project, which targets the development of secure and energy-efficient RISC-V interfaced neuromorphic accelerators using augmented silicon photonics technology. Our approach aims to develop an augmented silicon photonics platform, an FPGA-powered RISC-V-connected computing platform, and a complete simulation platform to demonstrate the neuromorphic accelerator capabilities. In particular, their main advantages and limitations will be addressed concerning the underpinning technology for each platform. Then, we will discuss three targeted use cases for edge-computing applications: Global National Satellite System (GNSS) anti-jamming, autonomous driving, and anomaly detection in edge devices. Finally, we will address the reliability and security aspects of the stand-alone accelerator implementation and the project use cases.

cs.AR↗