arXiv subjects

Frank Barrows

Publications and source records attributed to Frank Barrows.

16 recordsLinked to original sources

arXiv2026

Generating quantum error correcting codes from topological pre-thermal scars

Quantum many-body scars are rare nonthermal states embedded within otherwise thermalizing spectra, making them promising candidates for storing and manipulating quantum information. However, a general framework that can both identify such states without prior knowledge of their microscopic scarring mechanism and determine when they enable a quantum error correcting code has remained elusive. Here, we develop an end-to-end framework connecting nonthermal-state discovery to certifiable quantum error correction using a many-body spectral localizer. By searching for states jointly localized in energy and a diagnostic observable in systems with a many-body grading symmetry, the spectral localizer identifies candidate scars within dense many-body spectra in tandem with a topological index whose shifts determine their graded subspace. For suitable pairs of same-graded scars, the grading renders grading-odd errors exactly detectable, while their localization can suppress the logical action of sufficiently local grading-even error products, yielding an approximate Knill--Laflamme condition and an operator-algebra quantum error-correction structure. We demonstrate the scar-identification framework in one- and two-dimensional density-difference-dependent bosonic models and in the PXP model, and explicitly construct the resulting approximate quantum code in the one-dimensional bosonic system. Our results establish a systematic route from identifying nonthermal many-body states to exploiting them for protecting quantum information, and position pseudospectral methods as a broadly applicable tool for discovering useful behaviors in interacting quantum systems.

cond-mat.quant-gas↗

arXiv2026

Resistive Switching and Neuromorphic Computing in Metal/Nb:SrTiO$_3$: Mechanisms, Interface Physics, and Charge Transport

Resistive switching (RS) in Nb-doped SrTiO$_3$ (Nb:STO) based memristive devices has attracted sustained interest in information processing and novel computing because of its forming-free operation, large on/off ratio, and gradual conductance modulation. Metal/Nb:STO Schottky junctions have emerged as a prototypical system for understanding RS mechanisms. Despite more than two decades of research, the physical origin of RS remains controversial, with proposed mechanisms including charge trapping and detrapping, oxygen vacancy migration, tunneling, interfacial redox reactions, and conductive filament formation. In this review, we examine these seemingly competing mechanisms and show that many experimental observations can be understood within a unified framework centered on the formation and evolution of an extrinsic interfacial layer at the metal/Nb:STO interface. We discuss how interface quality and defect-mediated processes, including proton incorporation, oxygen vacancy dynamics, and tunneling, govern Schottky barrier modulation and RS behavior. We further summarize how fabrication conditions, measurement protocols, and aging influence the interface formation and switching characteristics. This review establishes an integrated picture of M/Nb:STO heterojunctions and provides design principles for reliable oxide memristive devices through interface and defect engineering in M/Nb:STO and M/oxide/Nb:STO systems.

cond-mat.mtrl-sci↗

arXiv2026

Geometry-Induced Domain-Wall Pinning and $\mathbb{Z}_2$ Asymmetry in Nominally One-Dimensional Rydberg Arrays

We perform experiments on QuEra's neutral-Rydberg-atom Aquila quantum computer, using quasi-adiabatic evolution on 1-dimensional models. We use hardware fine-tuning to balance the measurement statistics close to zero net magnetization, in two different geometric outlines: one closed triangular model with 33 atoms, and one 47-atom square with an engineered atom vacancy. The nature of this processor restricts the geometry of the atoms that can be programmed to a 2D plane. We report effects not predicted by the pure 1D Ising model, such as pinning of domain walls and $\mathbb{Z}_2$ symmetry breaking due to the interplay between van der Waals interactions and the Rydberg blockade. In particular, atoms around the atom vacancy and at the vertices of the 1-dimensional square-outline model strongly prefer the Rydberg state, leading to the effective model having a ferromagnetic bond across the vacancy.

quant-ph↗

arXiv2026

Self-Organized Learning in Oscillatory Neural Networks with Memristive Signed Couplings

Oscillatory neural networks (ONNs) have emerged as a promising neuromorphic architecture, leveraging coupled dynamical systems to perform computation and represent information through phase relationships. Their interactions can be designed to support intrinsic energy-minimizing dynamics, enabling tasks such as associative memory and optimization, and positioning them as a candidate architecture for continuous learning and inference. We present a neuromorphic primitive implemented using memristive edges with inhibitory couplings as a potential design for autonomous learning, and provide circuit simulation validation that the system is capable of denoising noisy inputs on an auto-associative task. While numerical Hopfield/Ising models routinely assume signed weights, neuromorphic implementations of ONNs often fail to realize negative weights due to device and circuit constraints. A practically implementable route to inhibitory (negative) weights is particularly valuable: it expands the class of attractor structures accessible to oscillator networks beyond purely synchronous couplings, and supports phase-coded memories where anti-phase constraints are not merely transiently enforced during training but can persist autonomously after release. We provide circuit simulations and theoretical analyses demonstrating that signed effective weights are necessary for anti-phase attractors to persist autonomously.

cs.NE↗

arXiv2026

How to Train Your Resistive Network: Generalized Equilibrium Propagation and Analytical Learning

Machine learning is a powerful method of extracting meaning from data; unfortunately, current digital hardware is extremely energy-intensive. There is interest in an alternative analog computing implementation that could match the performance of traditional machine learning while being significantly more energy-efficient. However, it remains unclear how to train such analog computing systems while adhering to locality constraints imposed by the physical (as opposed to digital) nature of these systems. Local learning algorithms such as Equilibrium Propagation and Coupled Learning have been proposed to address this issue. In this paper, we develop an algorithm to exactly calculate gradients using a graph theoretic and analytical framework for Kirchhoff's laws. We also introduce Generalized Equilibrium Propagation, a framework encompassing a broad class of Hebbian learning algorithms, including Coupled Learning and Equilibrium Propagation, and show how our algorithm compares. We demonstrate our algorithm using numerical simulations and show that we can train resistor networks without the need for a replica or readout over all resistors, only at the output layer. We also show that under the analytical gradient approach, it is possible to update only a subset of the resistance values without a strong degradation in performance.

cs.LG↗

arXiv2025

Autonomous Learning of Attractors for Neuromorphic Computing with Wien Bridge Oscillator Networks

We present an oscillatory neuromorphic primitive implemented with networks of coupled Wien bridge oscillators and tunable resistive couplings. Phase relationships between oscillators encode patterns, and a local Hebbian learning rule continuously adapts the couplings, allowing learning and recall to emerge from the same ongoing analog dynamics rather than from separate training and inference phases. Using a Kuramoto-style phase model with an effective energy function, we show that learned phase patterns form attractor states and validate this behavior in simulation and hardware. We further realize a 2-4-2 architecture with a hidden layer of oscillators, whose bipartite visible-hidden coupling allows multiple internal configurations to produce the same visible phase states. When inputs are switched, transient spikes in energy followed by relaxation indicate how the network can reduce surprise by reshaping its energy landscape. These results support coupled oscillator circuits as a hardware platform for energy-based neuromorphic computing with autonomous, continuous learning.

cs.NE↗

arXiv2025

Probing Antiferromagnetic Hysteresis on Programmable Quantum Annealers

Using programmable analog quantum annealing processors, we implement a sampling-based magnetic hysteresis protocol to probe the counterintuitive notion of magnetic memory in antiferromagnetic models. A key component of this protocol responsible for the hysteresis is a transverse field, which enables state transitions, while the longitudinal magnetic field sweep is done via a longitudinal control field. We observe intriguing non-monotonic magnetization, alongside full saturation and reversal of the hysteresis curve, Barkhausen-like noise, as well as emergent magnetic domains mediated by quantum fluctuations that give rise to the magnetic memory effect in antiferromagnets.

quant-ph↗

arXiv2025

Direct Visualization of the Magnetic Monopole Field in a 3D Artificial Spin Ice

Magnetic monopoles, long hypothesised as fundamental particles carrying isolated magnetic charge, emerge in spin-ice systems as fractionalised excitations governed by the ice rule. Yet their three-dimensional field structure has never been directly visualised. Here, we use two-photon lithography and processing to fabricate a fully three-dimensional artificial spin-ice lattice with diamond-bond geometry. We then use scanning nitrogen-vacancy magnetometry to directly measure the stray magnetic fields of both charge-neutral and monopole vertices. We find that ice-rule vertices produce antivortex textures directly above their vertices, stabilised by the local frustrated two-in/two out ordering principle. Direct imaging of the monopole stray field shows a highly divergent profile. By correlating experiment with micromagnetic simulations and performing a multipole expansion of the reconstructed magnetisation, we reveal that monopoles in 3DASI are non-trivial micromagnetic entities, carrying both magnetic charge and an intrinsic moment, giving rise to anisotropic interactions that are dependent upon the quasiparticles position on the lattice. Results suggest that as monopoles separate under an applied field, the dipolar contribution to their interaction reorients relative to the underlying Coulombic field, revealing that monopole coupling is tunable through geometry, being set by the local vertex topology. These findings establish 3DASI as a programmable magnetic metamaterial in which nanoscale geometry governs the energetics and dynamics of emergent magnetic charges.

cond-mat.mes-hall↗

arXiv2025

Magnetic Memory and Hysteresis from Quantum Transitions: Theory and Experiments on Quantum Annealers

Quantum annealing leverages quantum tunneling for non-local searches, thereby minimizing memory effects that typically arise from metastabilities. Nonetheless, recent work has demonstrated robust hysteresis in large-scale transverse-field Ising systems implemented on D-Wave's analog quantum hardware. The quantum nature of these intriguing results remains to be understood at a deeper level. Here, we present a conceptual framework that explains the observed behavior by combining two-level Landau-Zener transitions via a first-order piecewise-constant propagator with semiclassical domain-wall kinetics. We test this approach experimentally on a quantum annealer, where we observe clear coercivity even in one-dimensional rings with periodic boundary conditions comprising up to 4,906 qubits-regimes where classical hysteresis is forbidden, but quantum hysteresis is not. Our framework reproduces the measured kink densities, hysteresis loop shapes, and longitudinal sweep-rate scaling trends observed in data from three different D-Wave quantum annealers. In particular, it captures striking non-monotonic features and transiently negative susceptibilities, identifying them as genuine quantum memory effects. These results establish programmable quantum annealers as powerful testbeds for exploring memory-endowed non-equilibrium dynamics in quantum many-body systems.

quant-ph↗

arXiv2025

A unifying approach to self-organizing systems interacting via conservation laws

We present a unified framework for embedding and analyzing dynamical systems using generalized projection operators rooted in local conservation laws. By representing physical, biological, and engineered systems as graphs with incidence and cycle matrices, we derive dual projection operators that decompose network fluxes and potentials. This formalism aligns with principles of non-equilibrium thermodynamics and captures a broad class of systems governed by flux-forcing relationships and local constraints. We extend this approach to collective dynamics through the PRojective Embedding of Dynamical Systems (PrEDS), which lifts low-dimensional dynamics into a high-dimensional space, enabling both replication and recovery of the original dynamics. When systems fall within the PrEDS class, their collective behavior can be effectively approximated through projection onto a mean-field space. We demonstrate the versatility of PrEDS across diverse domains, including resistive and memristive circuits, adaptive flow networks (e.g., slime molds), elastic string networks, and particle swarms. Notably, we establish a direct correspondence between PrEDS and swarm dynamics, revealing new insights into optimization and self-organization. Our results offer a general theoretical foundation for analyzing complex networked systems and for designing systems that self-organize through local interactions.

cond-mat.soft↗

arXiv2025

Magnetic Hysteresis Experiments Performed on Quantum Annealers

While quantum annealers have emerged as versatile and controllable platforms for experimenting on correlated spin systems, the important phenomenology of magnetic memory and hysteresis remain unexplored on hardware designed to escape metastable states via quantum tunneling. Here, we present the first general protocol to experiment on magnetic hysteresis on programmable quantum annealers, and implement it on three D-Wave superconducting qubit quantum annealers, using up to thousands of spins, for both ferromagnetic and disordered Ising models, and across different graph topologies. We observe hysteresis loops whose area depends non-monotonically on quantum fluctuations, exhibiting both expected and unexpected features, such as disorder-induced steps and non-monotonicities. Our work establishes quantum annealers as a platform for probing non-equilibrium emergent magnetic phenomena, thereby broadening the role of analog quantum computers into foundational questions in condensed matter physics.

quant-ph↗

arXiv2025

Voltage-Controlled Oscillator and Memristor-Based Analog Computing for Solving Systems of Linear Equations

Matrix computations have become increasingly significant in many data-driven applications. However, Moores law for digital computers has been gradually approaching its limit in recent years. Moreover, digital computers encounter substantial complexity when performing matrix computations and need a long time to finish the computations, and existing analog matrix computation schemes require a large chip area and power consumption. This paper proposes a linear algebra system of equations based on integrators, which features low power consumption, compact area, and fast computation time. Due to the simple structure of the ring oscillator, the ring oscillator-based integrator exhibits a compact area and low power consumption. Therefore, ring oscillator-based integrators are introduced into the linear algebra system of equations, and this system can be used to compute the linear algebra equations of the matrix with either positive or negative values. This paper provides a detailed analysis and verification of the proposed circuit structure. Compared to similar circuits, this work has significant advantages in terms of area, power consumption, and computation speed.

eess.SY↗

arXiv2024

R-Ising: Effective resistance in random magnetic nanowires networks

Random assemblies of magnetic nanowires represent a unique class of materials with promising applications in spintronics and information storage. These assemblies exhibit complex behavior due to the combination of magnetic dipolar interactions between the nanowires and electronic transport properties governed by tunneling barriers at magnetic tunnel junctions (MTJs). The intricate interplay of these phenomena makes the study of magnetic nanowire networks a rich area of research. In this study, we develop a theoretical framework to analyze the resistive behavior of random magnetic nanowire networks. By employing a combination of graph theoretical approaches and mean-field theory, we derive an effective resistance model that encapsulates the contributions of magnetic interactions between the nanowires. Our findings show the importance of considering both the magnetic and electrical properties of nanowire networks in the design and optimization of amorphous resistive devices.

cond-mat.stat-mech↗

arXiv2024

Uncontrolled learning: co-design of neuromorphic hardware topology for neuromorphic algorithms

Hardware-based neuromorphic computing remains an elusive goal with the potential to profoundly impact future technologies and deepen our understanding of emergent intelligence. The learning-from-mistakes algorithm is one of the few training algorithms inspired by the brain's simple learning rules, utilizing inhibition and pruning to demonstrate self-organized learning. Here we implement this algorithm in purely neuromorphic memristive hardware through a co-design process. This implementation requires evaluating hardware trade-offs and constraints. It has been shown that learning-from-mistakes successfully trains small networks to function as binary classifiers and perceptrons. However, without tailoring the hardware to the algorithm, performance decreases exponentially as the network size increases. When implementing neuromorphic algorithms on neuromorphic hardware, we investigate the trade-offs between depth, controllability, and capacity, the latter being the number of learnable patterns. We emphasize the significance of topology and the use of governing equations, demonstrating theoretical tools to aid in the co-design of neuromorphic hardware and algorithms. We provide quantitative techniques to evaluate the computational capacity of a neuromorphic device based on the measurements performed and the underlying circuit structure. This approach shows that breaking the symmetry of a neural network can increase both the controllability and average network capacity. By pruning the circuit, neuromorphic algorithms in all-memristive device circuits leverage stochastic resources to drive local contrast in network weights. Our combined experimental and simulation efforts explore the parameters that make a network suited for displaying emergent intelligence from simple rules.

cond-mat.dis-nn↗

arXiv2024

Memristive Linear Algebra

The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the potential of memristive crossbars in implementing matrix inversion algorithms. We explore both static and dynamic approaches, emphasizing the advantages of analog and in-memory computing for matrix operations beyond multiplication. Our results demonstrate that memristive arrays can significantly reduce computational complexity and power consumption compared to traditional digital methods for certain matrix tasks. Furthermore, we address the challenges of device variability, precision, and scalability, providing insights into the practical implementation of these algorithms.

cond-mat.mes-hall↗

arXiv2024

Network analysis of memristive device circuits: dynamics, stability and correlations

Networks with memristive devices are a potential basis for the next generation of computing devices. They are also an important model system for basic science, from modeling nanoscale conductivity to providing insight into the information-processing of neurons. The resistance in a memristive device depends on the history of the applied bias and thus displays a type of memory. The interplay of this memory with the dynamic properties of the network can give rise to new behavior, offering many fascinating theoretical challenges. But methods to analyze general memristive circuits are not well described in the literature. In this paper we develop a general circuit analysis for networks that combine memristive devices alongside resistors, capacitors and inductors and under various types of control. We derive equations of motion for the memory parameters of these circuits and describe the conditions for which a network should display properties characteristic of a resonator system. For the case of a purely memresistive network, we derive Lyapunov functions, which can be used to study the stability of the network dynamics. Surprisingly, analysis of the Lyapunov functions show that these circuits do not always have a stable equilibrium in the case of nonlinear resistance and window functions. The Lyapunov function allows us to study circuit invariances, wherein different circuits give rise to similar equations of motion, which manifest through a gauge freedom and node permutations. Finally, we identify the relation between the graph Laplacian and the operators governing the dynamics of memristor networks operators, and we use these tools to study the correlations between distant memristive devices through the effective resistance.

cond-mat.dis-nn↗