arXiv subjects

Kathy Lüdge

Publications and source records attributed to Kathy Lüdge.

At least 19 recordsLinked to original sources

arXiv2026

Optically Writable Atomic Vapor Memory as a Substrate for Optical Reservoir Computing

We present an optical random access memory (ORAM) based on warm cesium (Cs) atomic vapor and demonstrate its operation as the physical substrate of a reservoir computer. Information is stored in the hyperfine population distribution of a Cs ensemble via optical pumping and retrieved through differential probe absorption. Spatial multiplexing via acousto-optic deflection provides eight addressable memory rails able to store up to 3.8 bits of information per rail. Employing this platform as a temporally multiplexed reservoir, we achieve a kernel rank ($\mathrm{KR}= 8.8 \pm 0.4$), and a minimum bit error rate of $0.02 \pm 0.01$ on the Exclusive-or (XOR) benchmark. We find the limited memory lifetime constrains the achievable temporal depth, encouraging further research into fast addressable memories. This constitutes the first demonstration of a free-space, optically writable atomic RAM as a substrate in an optical reservoir computing system.

physics.atom-ph↗

arXiv2026

Multistability and state-switching in series-coupled resonant tunneling diodes

Resonant tunneling diodes (RTDs) embedded in an electrical circuit are known for their neuron-like response characteristics, which makes them promising candidates for neuromorphic applications. This paper investigates the dynamical response of series-coupled RTDs and systematically analyzes the impact of coupling and inhomogeneities on the solution structure. We further propose a scheme for controlled switching between coexisting stable states which allows to realize tunable memory elements in these circuits. The coupled RTD system exhibits a rich bifurcation structure, showing different degrees of multistability between symmetric and antisymmetric solutions. Limit-cycle branches and their dependence on the system parameters are analyzed using numerical continuation methods. A central focus is placed on the role of symmetry. For two identical RTDs, the system possesses a $\mathbb{Z}_2$ exchange symmetry, which governs the emergence of symmetry-breaking bifurcations and multistable states. The analysis is further generalized to $N$ coupled RTDs, revealing the underlying $S_N$ symmetry structure and its influence on the organization of equilibrium branches, paving the way for neuromorphic network operation.

physics.comp-ph↗

arXiv2026

Reservoir Computing with a single Josephson junction

Physical reservoir computing exploits the nonlinear dynamics of a physical system to perform information processing tasks. Josephson junctions (JJs), as nonlinear superconducting devices with rich dynamical behavior, represent promising yet relatively unexplored candidates for reservoir computing. In this work, we demonstrate for the first time that a single Josephson junction can be employed as a reservoir computing substrate without the use of an explicit delay loop. Using numerical simulations, we analyze the reservoir performance in different dynamical regimes and show that optimal performance is achieved when the JJ operates in a stable yet responsive regime. Despite the absence of delayed feedback, the JJ exhibits sufficient memory through its intrinsic dynamics to achieve good performance on a chaotic time series prediction task. In addition, we explore an alternative input masking approach based on continuous modulation, highlighting its compatibility with practical implementations. These results establish Josephson junctions as a viable and efficient platform for reservoir computing and open the way to ultrafast, low-dissipation hardware realizations.

nlin.CD↗

arXiv2026

Distributed Coherent Optical Computing via Injection-Locked Photonic Networks

Coherent photonic computing uses both the phase and amplitude of light to implement linear operations such as dot products and matrix multiplication but requires phase stability between the interfering paths. This poses a challenge for such strategies when optical data is generated at a remote source due to environmental phase variations in fiber. Conventional approaches to distributed computing rely on optical-to-electrical conversion and buffering, limiting truly real-time and distributed computation. Here, we propose a new strategy via optical injection locking to enable distributed, real-time coherent optical processing without unnecessary conversions in the optical-to-electrical or analog-to-digital domains. Using a semiconductor laser rate-equation model, we explore the conditions required for stable operation by sweeping the power injection ratio, frequency detuning, and modulation conditions of the remote and injected lasers. Our results indicate that higher injection powers broaden the locking margin but more readily exhibit frequency-selective features associated with relaxation oscillations and increased amplitude-phase mixing, whereas lower injection powers yield a narrower, but more predictable operating window which remains stable under large modulation depth. End-to-end symbol-sequence simulations with balanced detection and temporal integration further confirm that reducing the injection ratio suppresses residual remote-modulation components in the injected laser output and improves computational accuracy. Overall, our study provides guidance and design trade-offs for remote coherent detection and distributed coherent photonic computing enabled by injection locking.

physics.optics↗

arXiv2026

Memory-Nonlinearity Trade-off across Quantum Reservoir Computing Frameworks

Quantum reservoir computing (QRC) harnesses driven quantum dynamics for time-series processing, yet the mechanisms behind the differing performance levels across its many implementations remain unclear. We show that apparently unrelated approaches-including memory restriction, weak measurements, operation near the edge of quantum chaos, and dissipative dynamics-are in fact governed by the same underlying principle, namely a tunable balance between memory retention and nonlinear response. Using the information processing capacity, a dynamical measure from nonlinear systems theory, we place these behaviors in a unified framework and identify the regimes in which quantum reservoirs surpass the standard protocol. Our results reveal a fundamental connection between memory and nonlinear response. This provides a general design principle for enhanced information processing and enables systematic analysis and optimization inspired by classical dynamical quantifiers.

quant-ph↗

arXiv2026

On Minimizing Krylov Complexity Using Higher-Order Generators

Krylov complexity provides a powerful framework for characterizing the dynamical evolution of quantum systems through the spreading of states in Krylov space. The motivation for this is rooted in the optimality of the Krylov basis for the analyzed cost function. In this work, we reinterpret the motivation for the Krylov basis from a dynamical perspective and show that it corresponds to a first-order approximation of the time-evolution operator. We extend this framework to higher-order generators and analytically disprove the optimality assumption by showing that an infinite-order generator can be constructed to exhibit smaller spread for arbitrary times. We propose a natural time scale for the construction of these higher-order generators and discuss results for matrices sampled from Gaussian Unitary Ensembles, demonstrating smaller Krylov complexity at all higher orders. These results extend the framework of Krylov complexity beyond the conventional Krylov basis by disproving the widely held assumption of optimality, extending the construction to higher-order generators, and introducing a physically motivated method for their construction. Our findings therefore suggest that previous statements and results concerning Krylov complexity may need to be reconsidered.

quant-ph↗

arXiv2025

Engineering Quantum Reservoirs through Krylov Complexity, Expressivity and Observability

This study employs Krylov-based information measures to understand task performance in quantum reservoir computing, a sub-field of quantum machine learning. In our study we show that fidelity and spread complexity can only explain the task performance for short time evolutions of the quantum systems. We then discuss two measures, Krylov expressivity and Krylov observability, and compare them to task performance and the information processing capacity. Our results show that Krylov observability exhibits almost identical behavior to information processing capacity, while being three orders of times faster to compute. In the case when the system is undersampled Krylov observability best captures the behavior of the task performance.

quant-ph↗

arXiv2025

From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing

We demonstrate that time-evolved operators can construct a Krylov space to compute Operator complexity and introduce Krylov observability as a measure of effective phase space dimension in quantum systems. We test Krylov observability in the framework of quantum reservoir computing and show that it closely mirrors information processing capacity, a data-driven expressivity metric, while achieving computation times that are orders of magnitude faster. Our results validate Operator complexity and give the interpretation that data in a quantum reservoir is mapped onto the Krylov space.

quant-ph↗

arXiv2025

Data-Driven Performance Measures using Global Properties of Attractors for Black-Box Surrogate Models of Chaotic Systems

In climate systems, physiological models, optics, and many more, surrogate models are developed to reconstruct chaotic dynamical systems. We introduce four data-driven measures using global attractor properties to evaluate the quality of the reconstruction of a given surrogate time series. The measures are robust against the initial position of the chaotic system as they are based on empirical approximations of the correlation integral and the probability density function, both of which are global properties of the attractor. In contrast to previous methods, we do not need a manual fitting procedure, making the measures straightforward to evaluate. Using a hypothesis testing framework, we can systematically find and reject surrogate models whose reconstructions significantly differ from the true system. Further, we show that the measures can be used as a statistical ranking metric, which in practice allows for hyperparameter optimization. Applying our measures to reservoir computing with a low number of nodes, we demonstrate how the measures can be used to reject poor reconstructions and use them as a tool to find an optimal spectral radius for which considerably fewer solutions are rejected and the overall quality of the solution improves.

physics.comp-ph↗

arXiv2025

Influence of noise-induced modulations on the timing stability of passively mode-locked semiconductor laser subject to optical feedback

We show that passively mode-locked lasers subject to feedback from a single external cavity can exhibit large timing fluctuations on short time scales despite having a relatively small long-term timing jitter, meaning that the commonly used von Linde and Kéfélian techniques of experimentally estimating the timing jitter can lead to large errors in the estimation of the arrival time of pulses. We also show that adding a second feedback cavity of the appropriate length can significantly suppress noise-induced modulations that are present in the single feedback system. This reduces the short time scale fluctuations of the interspike interval time and at the same time improves the variance of the fluctuation of the pulse arrival times on long time scales.

physics.optics↗

arXiv2025

Utilizing rate-independent hysteresis for analog computing

Physical systems exhibiting hysteresis are increasingly being used in neuromorphic and in-memory computing research. Generally, the resistance switching of devices with rate-independent hysteresis are being investigated for their use as trainable weights in neural networks, whereas the dynamics of devices showing rate-dependent hysteresis are being investigate for their potential as nodes in, for example in reservoir computing systems. In our work we instead show the computing potential of a simple rate-independent hysteresis system. We show that by driving a system of only two linear branches with time-multiplexed inputs it is possible to generate nonlinear transforms and perform timeseries prediction tasks.

physics.comp-ph↗

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

High-Speed Time Series Prediction with a GHz-rate Photonic Spiking Neural Network built with a single VCSEL

Photonic technologies hold significant potential for creating innovative, high-speed, efficient and hardware-friendly neuromorphic computing platforms. Neuromorphic photonic methods leveraging ubiquitous, technologically mature and cost-effective Vertical-Cavity Surface Emitting Lasers (VCSELs) are of notable interest. VCSELs have demonstrated the capability to replicate neuronal optical spiking responses at ultrafast rates. These characteristics have triggered research into applying these key-enabling devices in spike-based photonic computing. Here, a GHz-rate photonic Spiking Neural Network (p-SNN) using a single VCSEL is reported, and its application to a complex time-series prediction task is demonstrated for the first time. The VCSEL p-SNN combined with a technique to induce network memory, is applied to perform multi-step-ahead predictions of a chaotic time-series. By providing the feedforward p-SNN with only two temporally separated inputs excellent accuracy is experimentally demonstrated over a range of prediction horizons. VCSEL-based p-SNNs therefore offer ultrafast, efficient operation in complex predictive tasks whilst enabling hardware implementations. The inherent attributes and performance of VCSEL p-SNNs hold great promise for use in future light-enabled neuromorphic computing hardware.

physics.comp-ph↗

arXiv2024

Time-multiplexed Reservoir Computing with Quantum-Dot Lasers: Does more complexity lead to better performance?

Reservoir computing with optical devices offers an energy-efficient approach for time-series forecasting. Quantum dot lasers with feedback are modelled in this paper to explore the extent to which increased complexity in the charge carrier dynamics within the nanostructured semiconductor can enhance the prediction performance. By tuning the scattering interactions, the laser's dynamics and response time can be finely adjusted, allowing for a systematic investigation. It is found that both system response time and task requirements need to be considered to find optimal operation conditions. Further, lasers with pronounced relaxation oscillations outperform those with strongly damped dynamics, even if the underlying charge carrier dynamics is more complex. This demonstrates that optimal reservoir computing performance relies not only on internal complexity but also on the effective utilization of these dynamics through the output sampling process.

physics.comp-ph↗

arXiv2024

Canard cascading in networks with adaptive mean-field coupling

Canard cascading (CC) is observed in dynamical networks with global adaptive coupling. It is a fast-slow phenomenon characterized by a recurrent sequence of fast transitions between distinct and slowly evolving quasi-stationary states. In this letter, we uncover the dynamical mechanisms behind CC, using an illustrative example of globally and adaptively coupled semiconductor lasers, where CC represents sequential switching on and off the lasers. Firstly, we show that CC is a robust and truly adaptive network effect that is scalable with network size and does not occur without adaptation. Secondly, we uncover multiple saddle slow manifolds (unstable quasi-stationary states) linked by heteroclinic orbits (fast transitions) in the phase space of the system. This allows us to identify CC with a novel heteroclinic canard orbit that organises different unstable quasi-stationary states into an intricate fast-slow limit cycle. Although individual quasi-stationary states are unstable (saddles), the CC cycle as a whole is attractive and robust to parameter changes.

nlin.AO↗

arXiv2024

Measurable Krylov Spaces and Eigenenergy Count in Quantum State Dynamics

In this work, we propose a quantum-mechanically measurable basis for the computation of spread complexity. Current literature focuses on computing different powers of the Hamiltonian to construct a basis for the Krylov state space and the computation of the spread complexity. We show, through a series of proofs, that time-evolved states with different evolution times can be used to construct an equivalent space to the Krylov state space used in the computation of the spread complexity. Afterwards, we introduce the effective dimension, which is upper-bounded by the number of pairwise distinct eigenvalues of the Hamiltonian. The computation of the spread complexity requires knowledge of the Hamiltonian and a classical computation of the different powers of the Hamiltonian. The computation of large powers of the Hamiltonian becomes increasingly difficult for large systems. The first part of our work addresses these issues by defining an equivalent space, where the original basis consists of quantum-mechanically measurable states. We demonstrate that a set of different time-evolved states can be used to construct a basis. We subsequently verify the results through numerical analysis, demonstrating that every time-evolved state can be reconstructed using the defined vector space. Based on this new space, we define an upper-bounded effective dimension and analyze its influence on finite-dimensional systems. We further show that the Krylov space dimension is equal to the number of pairwise distinct eigenvalues of the Hamiltonian, enabling a method to determine the number of eigenenergies the system has experimentally. Lastly, we compute the spread complexities of both basis representations and observe almost identical behavior, thus enabling the computation of spread complexities through measurements.

quant-ph↗

arXiv2024

Data-Driven Acceleration of Multi-Physics Simulations

Multi-physics simulations play a crucial role in understanding complex systems. However, their computational demands are often prohibitive due to high dimensionality and complex interactions, such that actual calculations often rely on approximations. To address this, we introduce a data-driven approach to approximate interactions among degrees of freedom of no direct interest and thus significantly reduce computational costs. Focusing on a semiconductor laser as a case study, we demonstrate the superiority of this method over traditional analytical approximations in both accuracy and efficiency. Our approach streamlines simulations, offering promise for complex multi-physics systems, especially for scenarios requiring a large number of individual simulations.

physics.comp-ph↗

arXiv2024

Stability of Optically Injected Two-State Quantum-Dot Lasers

Simultaneous two-state lasing is a unique property of semiconductor quantum-dot (QD) lasers. This not only changes steady-state characteristics of the laser device but also its dynamic response to perturbations. In this paper we investigate the dynamic stability of QD lasers in an external optical injection setup. Compared to conventional single-state laser devices, we find a strong suppression of dynamical instabilities in two-state lasers. Furthermore, depending on the frequency and intensity of the injected light, pronounced areas of bistability between both lasing frequencies appear, which can be employed for fast optical switching in all-optical photonic computing applications. These results emphasize the suitability of QD semiconductor lasers in future integrated optoelectronic systems where a high level of stability is required.

physics.optics↗