Memorial for Dr. Erik Bollt
In this paper, we give a memorial tribute to Prof. Erik M. Bollt (1967--2025).
math.HO↗
arXiv subjects
Daniel J. Gauthier
Publications and source records attributed to Daniel J. Gauthier.
Accurate Data-Based State Estimation from Power Loads Inference in Electric Power Grids
Accurate state estimation is a crucial requirement for the reliable operation and control of electric power systems. Here, we construct a data-driven, numerical method to infer missing power load values in large-scale power grids. Given partial observations of power demands, the method estimates the operational state using a linear regression algorithm, exploiting statistical correlations within synthetic training datasets. We evaluate the performance of the method on three synthetic transmission grid test systems. Numerical experiments demonstrate the high accuracy achieved by the method in reconstructing missing demand values under various operating conditions. We further apply the method to real data for the transmission power grid of Switzerland. Despite the restricted number of observations in this dataset, the method infers missing power loads rather accurately. Furthermore, Newton-Raphson power flow solutions show that deviations between true and inferred values for power loads result in smaller deviations between true and inferred values for flows on power lines. This ensures that the estimated operational state correctly captures potential line contingencies. Overall, our results indicate that simple data-based regression techniques can provide an efficient and reliable alternative for state estimation in modern power grids.
eess.SY↗
An improved update rule for probabilistic computers
Many hard combinatorial problems can be mapped onto Ising models, which replicate the behavior of classical spins. Recent advances in probabilistic computers are characterized by parallelization and the introduction of novel hardware platforms. An interesting application of probabilistic computers is to operate them in `reverse' mode, where the network self-organizes its behavior to find the input bits that result in an output state. This can be used, for example, as a factorizer of semiprimes. One issue with simulating probabilistic computers on standard logic devices, such as field-programmable gate arrays, is that the update rules for each spin involve many multiplications, evaluation of a hyperbolic tangent, and a high-resolution numerical comparison. We simplify these rules, which improves the spatial and temporal circuit complexity when simulating a probabilistic computer on a field-programmable gate array. Applying our method to factorizing semiprimes, we achieve at least an order-of-magnitude reduction in the on-chip resources and the time-to-solution compared to recently reported methods. For a 32-bit semiprime, we achieve an average factorization in $\sim$100 s. Our approach will inspire new physical realizations of probabilistic computers because we relax some of their update-rule requirements.
physics.comp-ph↗
Superconducting Qubit Readout Using Next-Generation Reservoir Computing
Quantum processors require rapid and high-fidelity simultaneous measurements of many qubits. While superconducting qubits are among the leading modalities toward a useful quantum processor, their readout remains a bottleneck. Traditional approaches to processing measurement data often struggle to account for crosstalk present in frequency-multiplexed readout, the preferred method to reduce the resource overhead. Recent approaches to address this challenge use neural networks to improve the state-discrimination fidelity. However, they are computationally expensive to train and evaluate, resulting in increased latency and poor scalability as the number of qubits increases. We present an alternative machine learning approach based on next-generation reservoir computing that constructs polynomial features from the measurement signals and maps them to the corresponding qubit states. This method is highly parallelizable, avoids the costly nonlinear activation functions common in neural networks, and supports real-time training, enabling fast evaluation, adaptability, and scalability. Despite its lower computational complexity, our reservoir approach is able to maintain high qubit-state-discrimination fidelity. Relative to traditional methods, our approach achieves error reductions of up to 50% and 11% on single- and five-qubit datasets, respectively, and delivers up to 2.5x crosstalk reduction on the five-qubit dataset. Compared with recent machine-learning methods, evaluating our model requires 100x fewer multiplications for single-qubit and 2.5x fewer for five-qubit models. This work demonstrates that reservoir computing can enhance qubit-state discrimination while maintaining scalability for future quantum processors.
quant-ph↗
Drone- and Vehicle-Based Quantum Key Distribution
Quantum key distribution is a point-to-point communication protocol that leverages quantum mechanics to enable secure information exchange. Commonly, the transmitter and receiver stations are at fixed locations, and the single-photon quantum states are transmitted over fiber or free space. Here, we describe a modular, platform-agnostic, quantum key distribution transmitter and receiver with reduced size, weight, and power consumption to realize a mobile quantum communication system. We deploy the system on different moving platforms, demonstrating drone-to-drone, drone-to-vehicle, and vehicle-to-vehicle quantum communication, achieving secure key rates in the finite-key regime in the range of 1.6 - 20 kbps. To prove the security of the system, we develop advanced physics models of the devices that account for non-ideal behaviors that are of greater importance in mobile platforms. The modular system can be easily upgraded to include sources of entangled photonic quantum states, which will find application in future quantum networks.
quant-ph↗
Efficient measurement of neutral-atom qubits with matched filters
Quantum computers require high-fidelity measurement of many qubits to achieve a quantum advantage. Traditional approaches suffer from readout crosstalk for a neutral-atom quantum processor with a tightly spaced array. Although classical machine learning algorithms based on convolutional neural networks can improve fidelity, they are computationally expensive, making it difficult to scale them to large qubit counts. We present two simpler and scalable machine learning algorithms that realize matched filters for the readout problem. One is a local model that focuses on a single qubit, and the other uses information from neighboring qubits in the array to prevent crosstalk among the qubits. We demonstrate error reductions of up to 32% and 43% for the site and array models, respectively, compared to a conventional Gaussian threshold approach. Additionally, our array model uses two orders of magnitude fewer trainable parameters and four orders of magnitude fewer multiplications and nonlinear function evaluations than a recent convolutional neural network approach, with only a minor (3.5%) increase in error across different readout times. Another strength of our approach is its physical interpretability: the learned filter can be visualized to provide insights into experimental imperfections. We also show that a convolutional neural network model for improved can be pruned to have 70x and 4000x fewer parameters, respectively, while maintaining similar errors. Our work shows that simple machine learning approaches can achieve high-fidelity qubit measurements while remaining scalable to systems with larger qubit counts.
quant-ph↗
Locality Blended Next Generation Reservoir Computing For Attention Accuracy
We extend an advanced variation of a machine learning algorithm, next-generation reservoir Computing (NGRC), to forecast the dynamics of the Ikeda map of a chaotic laser. The machine learning model is created by observing time-series data generated by the Ikeda map, and the trained model is used to forecast the behavior without any input from the map. The Ikeda map is a particularly challenging problem to learn because of the complicated map functions. We overcome the challenge by a novel improvement of the NGRC concept by emphasizing simpler polynomial models localized to well-designed regions of phase space and then blending these models between regions, a method that we call locality blended next-generation reservoir computing (LB-NGRC). This approach allows for better performance with relatively smaller data sets, and gives a new level of interpretability. We achieve forecasting horizons exceeding five Lyapunov times, and we demonstrate that the `climate' of the model is learned over long times.
nlin.CD↗
A Quantum Key Distribution System for Mobile Platforms with Highly Indistinguishable States
Quantum key distribution (QKD) allows two users to exchange a provably secure key for cryptographic applications. In prepare-and-measure QKD protocols, the states must be indistinguishable to prevent information leakage to an eavesdropper performing a side-channel attack. Here, we measure the indistinguishability of quantum states in a prepare-and-measure three-state BB84 polarization-based decoy state protocol using resonant-cavity light-emitting diodes (RC-LEDs) as the source in the transmitter. We make the spatial, spectral, and temporal DOF of the generated quantum states nearly indistinguishable using a spatial filter single-mode fiber, a narrow-band spectral filter, and adjustable timing of the electrical pulses driving the RC-LEDs, respectively. The sources have fully indistinguishable transverse spatial modes. The measured fractional mutual information between an assumed eavesdropper and the legitimate receiver is $2.39\times10^{-5}$ due to the spectral distinguishability and $4.31\times10^{-5}$ for the temporal distinguishability. The source is integrated into a full QKD system operating in a laboratory environment, where we achieve a raw key rate of 532 Kbits/s with an average quantum bit error rate of 1.83\%. The low system size, weight, and power make it suitable for mobile platforms such as uncrewed aerial vehicles (drones) or automobiles.
quant-ph↗
Controlling Chaos Using Edge Computing Hardware
Machine learning provides a data-driven approach for creating a digital twin of a system - a digital model used to predict the system behavior. Having an accurate digital twin can drive many applications, such as controlling autonomous systems. Often the size, weight, and power consumption of the digital twin or related controller must be minimized, ideally realized on embedded computing hardware that can operate without a cloud-computing connection. Here, we show that a nonlinear controller based on next-generation reservoir computing can tackle a difficult control problem: controlling a chaotic system to an arbitrary time-dependent state. The model is accurate, yet it is small enough to be evaluated on a field-programmable gate array typically found in embedded devices. Furthermore, the model only requires 25.0 $\pm$ 7.0 nJ per evaluation, well below other algorithms, even without systematic power optimization. Our work represents the first step in deploying efficient machine learning algorithms to the computing "edge."
cs.LG↗
Controlling Chaotic Maps using Next-Generation Reservoir Computing
In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic Hénon map, including controlling the system between unstable fixed-points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only 10 data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error.
cs.LG↗
Perspectives on adaptive dynamical systems
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges, and give perspectives on future research directions, looking to inspire interdisciplinary approaches.
nlin.AO↗
Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing
Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture that, when combined with a next-generation reservoir computer, displays state-of-the-art performance with a computational time $10^3-10^4$ times faster for training process and training data set $\sim 10^2$ times smaller than other machine learning algorithms. We also take advantage of the translational symmetry of the model to further reduce the computational cost and training data, each by a factor of $\sim$10.
cs.LG↗
Learning unseen coexisting attractors
Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing approaches. Recently, a simpler formulation, known as next-generation reservoir computing, removes many algorithm metaparameters and identifies a well-performing traditional reservoir computer, thus simplifying training even further. Here, we study a particularly challenging problem of learning a dynamical system that has both disparate time scales and multiple co-existing dynamical states (attractors). We compare the next-generation and traditional reservoir computer using metrics quantifying the geometry of the ground-truth and forecasted attractors. For the studied four-dimensional system, the next-generation reservoir computing approach uses $\sim 1.7 \times$ less training data, requires $10^3 \times$ shorter `warm up' time, has fewer metaparameters, and has an $\sim 100\times$ higher accuracy in predicting the co-existing attractor characteristics in comparison to a traditional reservoir computer. Furthermore, we demonstrate that it predicts the basin of attraction with high accuracy. This work lends further support to the superior learning ability of this new machine learning algorithm for dynamical systems.
cs.LG↗
Mathematical Model of Strong Physically Unclonable Functions Based on Hybrid Boolean Networks
We introduce a mathematical framework for simulating Hybrid Boolean Network (HBN) Physically Unclonable Functions (PUFs, HBN-PUFs). We verify that the model is able to reproduce the experimentally observed PUF statistics for uniqueness $μ_{inter}$ and reliability $μ_{intra}$ obtained from experiments of HBN-PUFs on Cyclone V FPGAs. Our results suggest that the HBN-PUF is a true `strong' PUF in the sense that its security properties depend exponentially on both the manufacturing variation and the challenge-response space. Our Python simulation methods are open-source and available at https://github.com/Noeloikeau/networkm.
cs.CR↗
Sensitivity of a Chaotic Logic Gate
Chaotic logic gates or `chaogates' are a promising mixed-signal approach to designing universal computers. However, chaotic systems are exponentially sensitive to small perturbations, and the effects of noise can cause chaotic computers to fail. Here, we examine the sensitivity of a simulated chaogate to noise and other parameter variations (such as differences in supply voltage). We find that the regions in parameter space corresponding to chaotic dynamics coincide with the regions of maximum error in the computation. Further, this error grows exponentially within 4-10 iterations of the chaotic map. As such, we discuss the fundamental limitations of chaotic computing, and suggest potential improvements. Our Python simulation methods are open-source and available at https://github.com/Noeloikeau/chaogate.
nlin.CD↗
Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing
Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy, as well as reconstruct the general properties of a chaotic attractor without requiring a model. In this work, we show that the ability to learn the dynamics of a complex system can be extended to systems with co-existing attractors, here a 4-dimensional extension of the well-known Lorenz chaotic system. We demonstrate that a reservoir computer can infer entirely unexplored parts of the phase space: a properly trained reservoir computer can predict the existence of attractors that were never approached during training and therefore are labelled as unseen. We provide examples where attractor inference is achieved after training solely on a single noisy trajectory.
cs.LG↗
Symmetry-Aware Reservoir Computing
We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increases its processing power. We apply our method to the parity task, a challenging benchmark problem that highlights inversion and permutation symmetries, and to a chaotic system inference task that presents an inversion symmetry rule. For the parity task, our symmetry-aware RC obtains zero error using an exponentially reduced neural network and training data, greatly speeding up the time to result and outperforming hand crafted artificial neural networks. When both symmetries are respected, we find that the network size $N$ necessary to obtain zero error for 50 different RC instances scales linearly with the parity-order $n$. Moreover, some symmetry-aware RC instances perform a zero error classification with only $N=1$ for $n\leq7$. Furthermore, we show that a symmetry-aware RC only needs a training data set with size on the order of $(n+n/2)$ to obtain such performance, an exponential reduction in comparison to a regular RC which requires a training data set with size on the order of $n2^n$ to contain all $2^n$ possible $n-$bit-long sequences. For the inference task, we show that a symmetry-aware RC presents a normalized root-mean-square error three orders-of-magnitude smaller than regular RCs. For both tasks, our RC approach respects the symmetries by adjusting only the input and the output layers, and not by problem-based modifications to the neural network. We anticipate that generalizations of our procedure can be applied in information processing for problems with known symmetries.
cs.NE↗
High-Resolution Waveform Capture Device on a Cyclone-V FPGA
We introduce the waveform capture device (WCD), a flexible measurement system capable of recording complex digital signals on trillionth-of-a-second (ps) time scales. The WCD is implemented via modular code on an off-the-shelf field-programmable gate-array (FPGA, Intel/Altera Cyclone V), and incorporates both time-to-digital converter (TDC) and digital storage oscilloscope (DSO) functionality. The device captures a waveform by taking snapshots of a signal as it propagates down an ultra-fast transmission line known as a carry chain (CC). It is calibrated via a novel dynamic phase-shifting (DPS) method that requires substantially less data and resources than the state-of-the-art. Using DPS, we find the measurement resolution - or mean propagation delay from one CC element to the next - to be 4.91 +/- 0.04 ps (4.54 +/- 0.02 ps) for a pulse of logic high (low). Similarly, we find the single-shot precision - or mean error on the timing of the waveform - to be 29.52 ps (27.14 ps) for pulses of logic high (low). We verify these findings by reproducing commercial oscilloscope measurements of asynchronous ring-oscillators on FPGAs, finding the mean pulse width to be 0.240 +/- 0.002 ns per inverter gate. Finally, we present a careful analysis of design constraints, introduce a novel error correction algorithm, and sketch a simple extension to the analog domain. We also provide the Verilog code instantiating the our design on an FPGA in an Appendix, and make our methods available as an open-source Python library at https://github.com/Noeloikeau/fpyga.
cs.AR↗