arXiv subjects

Peter J. Ehlers

Publications and source records attributed to Peter J. Ehlers.

6 recordsLinked to original sources

arXiv2026

A Single Atom in Front of a Mirror is a Universal Reservoir Computer

Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.

quant-ph↗

arXiv2025

Minimalistic and Scalable Quantum Reservoir Computing Enhanced with Feedback

Quantum Reservoir Computing (QRC) leverages quantum systems to perform complex computational tasks with exceptional efficiency and reduced energy consumption. We introduce a minimalistic QRC framework utilizing as few as five atoms in a single-mode optical cavity, combined with continuous quantum measurement. The system is conveniently scalable, as newly added atoms naturally couple with existing ones via the shared cavity field. To achieve high computational expressivity with a minimal reservoir, we include two critical elements: reservoir feedback and polynomial regression. Reservoir feedback modifies the reservoir's dynamics without altering its internal quantum hardware, while polynomial regression nonlinearly enhances output resolution. We demonstrate significant QRC performance in memory retention and nonlinear data processing through two tasks: predicting chaotic time-series data via the Mackey-Glass task and classifying sine-square waveforms. This framework fulfills QRC's objectives to minimize hardware size and energy consumption, marking a significant advancement in integrating quantum physics with machine learning technology.

quant-ph↗

arXiv2025

Practical Few-Atom Quantum Reservoir Computing

Quantum Reservoir Computing (QRC) harnesses quantum systems to tackle intricate computational problems with exceptional efficiency and minimized energy usage. This paper presents a QRC framework that utilizes a minimalistic quantum reservoir, consisting of only a few two-level atoms within an optical cavity. The system is inherently scalable, as newly added atoms automatically couple with the existing ones through the shared cavity field. We demonstrate that the quantum reservoir outperforms traditional classical reservoir computing in both memory retention and nonlinear data processing through two tasks, namely the prediction of time-series data using the Mackey-Glass task and the classification of sine-square waveforms. Our results show significant performance improvements with an increasing number of atoms, facilitated by non-destructive, continuous quantum measurements and polynomial regression techniques. These findings confirm the potential of QRC as a practical and efficient solution to addressing complex computational challenges in quantum machine learning.

quant-ph↗

arXiv2025

Stochastic Reservoir Computers

Reservoir computing is a form of machine learning that utilizes nonlinear dynamical systems to perform complex tasks in a cost-effective manner when compared to typical neural networks. Many recent advancements in reservoir computing, in particular quantum reservoir computing, make use of reservoirs that are inherently stochastic. However, the theoretical justification for using these systems has not yet been well established. In this paper, we investigate the universality of stochastic reservoir computers, in which we use a stochastic system for reservoir computing using the probabilities of each reservoir state as the readout instead of the states themselves. In stochastic reservoir computing, the number of distinct states of the entire reservoir computer can potentially scale exponentially with the size of the reservoir hardware, offering the advantage of compact device size. We prove that classes of stochastic echo state networks, and therefore the class of all stochastic reservoir computers, are universal approximating classes. We also investigate the performance of two practical examples of stochastic reservoir computers in classification and chaotic time series prediction. While shot noise is a limiting factor in the performance of stochastic reservoir computing, we show significantly improved performance compared to a deterministic reservoir computer with similar hardware in cases where the effects of noise are small.

cs.LG↗

arXiv2025

Improving the Performance of Echo State Networks Through State Feedback

Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks (ESNs), a type of reservoir computer, mirror neural networks but simplify training. They apply fixed, random linear transformations to the internal state, followed by nonlinear changes. This process, guided by input signals and linear regression, adapts the system to match target characteristics, reducing computational demands. A potential drawback of ESNs is that the fixed reservoir may not offer the complexity needed for specific problems. While directly altering (training) the internal ESN would reintroduce the computational burden, an indirect modification can be achieved by redirecting some output as input. This feedback can influence the internal reservoir state, yielding ESNs with enhanced complexity suitable for broader challenges. In this paper, we demonstrate that by feeding some component of the reservoir state back into the network through the input, we can drastically improve upon the performance of a given ESN. We rigorously prove that, for any given ESN, feedback will almost always improve the accuracy of the output. For a set of three tasks, each representing different problem classes, we find that with feedback the average error measures are reduced by $30\%-60\%$. Remarkably, feedback provides at least an equivalent performance boost to doubling the initial number of computational nodes, a computationally expensive and technologically challenging alternative. These results demonstrate the broad applicability and substantial usefulness of this feedback scheme.

cs.LG↗

arXiv2022

Entanglement between Valence and Sea Quarks in Hadrons of 1+1 Dimensional QCD

The conceptual interpretation of valence- and sea-quark separation, which is a key aspect of the parton model and of an intuitive picture of hadron structure, becomes obscured by quantum effects in QCD. This suggests that there may be measures of entanglement between quark degrees of freedom that are present in QCD, but absent in the intuitive picture with a clear valence-sea (VS) separation. In this paper, we define the first rigorous measure of VS entanglement in QCD in an attempt to bring conceptual clarity to this issue, and, potentially, to find a measure of the applicability of the parton model to QCD bound states. This VS entanglement vanishes in the large-$N_c$ limit, and it remains low when finite-$N_c$ states resemble their large-$N_c$ counterparts. We perform a numerical study of VS entanglement in 1+1 dimensional discrete light-cone quantized QCD, and in the process develop a method for building the color-singlet basis of 1+1d QCD that is manifestly complete and orthogonal by construction. We calculate this VS entanglement entropy for the first time and find that it is relatively low for the first few excited states of both mesons and baryons compared to all other states in the spectrum, with the VS entropy of ground state hadrons providing a minimum. We also see that for ground state mesons the entropy is well described in the $1/N_c$ approximation. These results suggest that low energy hadrons may be the only QCD bound states for which the large-$N_c$ expansion, and perhaps the parton model, provide an accurate description. This work also provides the first evidence that the VS entanglement entropy of QCD in 3+1d, which would likely serve as an order parameter for the transition between quark and hadron degrees of freedom, may be perturbatively accessible through a large-$N_c$ expansion.

hep-ph↗