Direct prediction of quantum circuit outcome probabilities using physics-aware graph neural networks
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Hothem, Daniel George [Sandia National Laboratorie↗
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A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits
Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit’s generators.
97 MATHEMATICS AND COMPUTING↗
Introduction: Neuromorphic Materials
The explosive growth in data collection and the need to process it efficiently, as well as the desire to automate increasingly complex tasks in transportation, medical care, manufacturing, security and many other fields have motivated a growing interest in neuromorphic computing. Unlike the binary, transistorbased ON/OFF logic gates and separate logic and memory functionalities employed in digital computing, neuromorphic computing is inspired by animal brains that use interconnected synapses and neurons to perform processing, storage and transmission of information at the same location, while only consuming ~20 W or less of power. Motivated by the brain’s efficiency, adaptability, self-learning and resiliency qualities, neuromorphic computing can be broadly defined as an approach to processing and storing information using hardware and algorithms inspired by models of biological neural systems. Present research in neuromorphic computing encompasses approaches that vary significantly in their degree of neuro-inspiration, from systems that only incorporate features such as asynchronous, event-driven operation or use crossbar arrays of non-volatile memory (NVM) elements to accelerate deep neural networks (DNNs), to designs that embrace the extreme parallelism, sparsity, reconfigurability, adaptability, complexity and stochasticity observed in nervous systems. The term ‘neuromorphic’ computing is often credited to Carver Mead, who in the 1980s investigated Si-based analog electronics to replicate functions of the animal retina. Earlier important advances in this field include the work of Frank Rosenblatt, who proposed the concept of the perceptron, Bernard Widrow, who used this concept to build one of the first analog neural networks, the Adaline and many other researchers (see ref. 6 for an historical perspective on neuromorphic computing). With the recent increase in the use of artificial intelligence and large language models, and rising concerns over the associated energy costs, interest in neuromorphic hardware has expanded rapidly. According to some estimates, driven largely by the drastic growth in the training use of artificial intelligence (AI) models using the current computing architectures, the energy cost of computing is projected to reach the energy supply worldwide by 2045. Furthermore, while this is not a realistic outcome, it means that, if more efficient computing technologies are not developed -- soon -- the world will soon become one where demand for energy and market constraints limit the continued increase of societal access to AI and cloud services from data centers. Data centers used for training and use of these models consume hundreds of terawatt hours of electricity, already past 4% of the US electricity demand.
Circuits↗
Uncontrolled Learning: Codesign of Neuromorphic Hardware Topology for Neuromorphic Algorithms
Neuromorphic computing has the potential to revolutionize future technologies and our understanding of intelligence, yet it remains challenging to realize in practice. The learning-from-mistakes algorithm, inspired by the brain's simple learning rules of inhibition and pruning, is one of the few brain-like training methods. This algorithm is implemented in neuromorphic memristive hardware through a codesign process that evaluates essential hardware trade-offs. While the algorithm effectively trains small networks as binary classifiers and perceptrons, performance declines significantly with increasing network size unless the hardware is tailored to the algorithm. This work investigates the trade-offs between depth, controllability, and capacity—the number of learnable patterns—in neuromorphic hardware. This highlights the importance of topology and governing equations, providing theoretical tools to evaluate a device's computational capacity based on its measurements and circuit structure. The findings show that breaking neural network symmetry enhances both controllability and capacity. Additionally, by pruning the circuit, neuromorphic algorithms in all-memristive circuits can utilize stochastic resources to create local contrasts in network weights. Through combined experimental and simulation efforts, the parameters are identified that enable networks to exhibit emergent intelligence from simple rules, advancing the potential of neuromorphic computing.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A Neural Network-Based Power Mismatch Elimination Strategy for Integrated Solar and ESS AC/DC Systems (MARS)
The multiport autonomous reconfigurable solar power plant (MARS) is a promising concept for the integration of photovoltaic (PV) and energy storage system (ESS) to the transmission ac grid and a high-voltage direct current (HVdc) link. The presence of PV and ESS in each arm of the MARS results in uneven distribution of active power among different submodules (SMs), thereby leading to unbalanced SM capacitor voltages and potentially compromising the system stability. Moreover, in the case of partial shadings, shaded PV SMs will suffer from decreased power injections causing power mismatch in the MARS system. To address this issue, a neural-network-based power mismatch elimination (NNPME) strategy is proposed in this article. The proposed NNPME strategy optimizes ESS usage and leverages both dc and ac circulating currents to facilitate power transfer among the SMs, arms, and phases of the MARS system. Simulation and control hardware-in-the-loop (cHIL) experiments demonstrate the effectiveness of the proposed NNPME strategy. Compared with the traditional approaches, the proposed NNPME strategy can significantly enhance system efficiency and ensure stable and continuous operation, even in the presence of uneven power distribution within the MARS system.
14 SOLAR ENERGY↗
On the universality of S n -equivariant k -body gates
The importance of symmetries has recently been recognized in quantum machine learning from the simple motto: if a task exhibits a symmetry (given by a group $\mathfrak{G}$), the learning model should respect said symmetry. This can be instantiated via $\mathfrak{G}$-equivariant quantum neural networks (QNNs), i.e. parametrized quantum circuits whose gates are generated by operators commuting with a given representation of $\mathfrak{G}$. In practice, however, there might be additional restrictions to the types of gates one can use, such as being able to act on at most k qubits. In this work we study how the interplay between symmetry and k-bodyness in the QNN generators affect its expressiveness for the special case of $\mathfrak{G}=S_n$, the symmetric group. Our results show that if the QNN is generated by one- and two-body Sn-equivariant gates, the QNN is semi-universal but not universal. That is, the QNN can generate any arbitrary special unitary matrix in the invariant subspaces, but has no control over the relative phases between them. Then, we show that in order to reach universality one needs to include n-body generators (if n is even) or ($n-1$)-body generators (if n is odd). As such, our results brings us a step closer to better understanding the capabilities and limitations of equivariant QNNs.
97 MATHEMATICS AND COMPUTING↗
Absence of Barren Plateaus and Scaling of Gradients in the Energy Optimization of Isometric Tensor Network States
Abstract Vanishing gradients can pose substantial obstacles for high-dimensional optimization problems. Here we consider energy minimization problems for quantum many-body systems with extensive Hamiltonians and finite-range interactions, which can be studied on classical computers or in the form of variational quantum eigensolvers on quantum computers. Barren plateaus correspond to scenarios where the average amplitude of the energy gradient decreases exponentially with increasing system size. This occurs, for example, for quantum neural networks and for brickwall quantum circuits when the depth increases polynomially in the system size. Here we prove that the variational optimization problems for matrix product states, tree tensor networks, and the multiscale entanglement renormalization ansatz are free of barren plateaus. The derived scaling properties for the gradient variance provide an analytical guarantee for the trainability of randomly initialized tensor network states (TNS) and motivate certain initialization schemes. In a suitable representation, unitary tensors that parametrize the TNS are sampled according to the uniform Haar measure. We employ a Riemannian formulation of the gradient based optimizations which simplifies the analytical evaluation.
Barthel, Thomas↗
AI-Powered Knowledge Graphs for Neuromorphic and Energy-Efficient Computing
The surge in scientific literature obscures breakthroughs and hinders the discovery of new research paths. We propose an artificial intelligence (AI) powered framework using large language models (LLMs) and knowledge graphs (KGs) to automate parts of scientific discovery, focusing on energy-efficient AI circuits. Our hybrid approach combines LLMs, structured data, and ontology-based reasoning to construct a comprehensive knowledge graph that integrates insights across computational neuroscience, spiking neuron models, learning rules, architectural motifs, and neuromorphic device technologies. This multi-domain representation enables the generation of hypotheses that connect biological function with implementable, energy-efficient hardware architectures. Using KG embeddings and graph neural networks, the framework generates hypotheses for novel circuits, validates them through optimization on exascale HPC systems, and with tools like SuperNeuro and Fugu, the most promising designs will be prototyped in hardware. This open-source system aims to accelerate discoveries and bridging neuroscience with hardware innovation, drive collaboration, and unlock new opportunities in low-power AI computing.
Gautam, Ashish [ORNL]↗
Component-Level Inverse Design of Transmon Qubits Using Neural Networks
Designing a superconducting qubit to realize specific Hamiltonian parameters typically requires iterating through a time and compute-intensive forward loop in which the designer chooses a layout geometry, simulates it, extracts circuit parameters such as capacitances, and refines the geometry. We study the inverse version of this task using a neural-network workflow that maps target Hamiltonian parameters directly to component-level layout parameters, which we subsequently demonstrate on a planar transmon layout. During training, we pair the inverse model with a frozen forward surrogate model and evaluate the loss in Hamiltonian space rather than in layout-parameter space. In validation against a conventional EM solver, 97% of generated designs produce usable geometries, and the inverse-plus-surrogate pipeline reaches mean percent errors of 0.73% for qubit frequency and 1.58% for anharmonicity, comparable to or below the fabrication and simulation-to-measurement uncertainty expected for academic-process transmon devices of this type. A single pipeline query takes ~60 ms on CPU, versus ~2 min for a conventional EM capacitance extraction on the same hardware, a speedup of approximately 2,000x. Batching minimizes the AI model inference overhead, reducing the runtime to 3.1 microseconds per sample on CPU and 2.6 microseconds per sample on GPU at a batch size of 2048, resulting in speedups of 3.9 x 10^7 and 4.6 x 10^7, respectively, relative to a single conventional CPU EM extraction. Our results indicate that component-level inverse design usefully extends and complements conventional EM simulation, including for small datasets on the order of 1,000 samples.
Seidel, Olivia [Fermilab; Texas U., Arlington]↗
Leveraging dendritic complexity for neuromorphic computing
Abstract Beyond-von Neumann computing approaches are necessary to sustain the growth of microelectronics and the increasing appetite for artificial intelligence/machine learning algorithms. Neuromorphic computing is an emerging paradigm that takes inspiration from the brain to provide a path forward to improve the computational efficiency and computational density of next-generation computing architectures. In nature, we observe brains performing complex computations with a much smaller energy footprint than conventional computing approaches. Current neuromorphic systems are focused primarily on scalability, namely, increasing the number of computational units (neurons) and connections between units (synapses). However, for brain-like cognition and efficiency in next-generation computing hardware, we need increased complexity in function, as well as improved connection density for scalability. Here, we present our work that aims to incorporate dendrites for ‘compute-on-wire’ in neuromorphic architectures to increase the computational complexity (e.g. number of programmable parameters, nonlinear dynamics) as well as computational efficiency (energy/compute) of artificial neural networks (ANNs). We do this by showcasing neuromorphic dendrite elements that can be leveraged for various applications. We will present examples of neuroscience-inspired direction-selective circuits and an ANN with active dendrites leveraging shunting inhibition. We also demonstrate the benefits of using dendrites in deep neural networks. To conclude, we discuss how we can utilize emerging hardware devices in these systems and design next-generation neuromorphic architectures with dendrites.
Cardwell, Suma G. (ORCID:0000000226575545)↗
Towards Generalizable and Efficient Circuit Topology Design: A Graph-Transformer-based Surrogate Model with Curriculum Learning
Unlike circuit parameter and sizing optimizations, the automated design of analog circuit topologies poses significant challenges for learning-based approaches. One challenge arises from the combinatorial growth of the topology space with circuit size, which limits the topology optimization efficiency. Moreover, traditional circuit evaluation methods are time-consuming, while the presence of data discontinuity in the topology space makes the accurate prediction of circuit performance exceptionally difficult for unseen topologies. To tackle these challenges, we design a novel Graph-Transformer-based Network (GTN) as the surrogate model for circuit evaluation, offering a substantial acceleration in the speed of circuit topology optimization without sacrificing performance. Our GTN model architecture is designed to embed voltage changes in circuit loops and current flows in connected devices, enabling accurate performance predictions for circuits with unseen topologies. To address the cold start problem when scaling GTN to large-scale circuits, we further introduce a curriculum learning strategy that progressively trains GTN from small-scale to large-scale circuits. This approach enables the model to first learn fundamental physical principles from simpler topologies and gradually adapt to complex configurations, effectively bridging the circuit complexity gap and improving prediction accuracy. Taking the power converter circuit design as an experimental task, our GTN model significantly outperforms an analytical approach and baseline methods directly utilizing graph neural networks. Furthermore, GTN achieves less than 5% relative error and 196× speed-up compared with high-fidelity simulation. Notably, our GTN surrogate model empowers an automatic circuit design framework to discover circuits of comparable quality to those identified through high-fidelity simulation while reducing the time required by up to 98.2%. With curriculum learning, the enhanced GTN achieves a 51% improvement for performance prediction of large-scale circuits compared to the GTN model without this strategy. These advancements establish GTN as a scalable framework for automated analog circuit design across varying circuit complexity levels.
Lu, Haoshu [New Jersey Institute of Technology (NJ↗
Certifying almost all quantum states with few single-qubit measurements
Certifying that an n -qubit state synthesized in the laboratory is close to a given target state is a fundamental task in quantum information science. However, existing rigorous protocols applicable to general target states have potentially prohibitive resource requirements in the form of either deep quantum circuits or exponentially many single-qubit measurements. Here we prove that almost all n -qubit target states, including those with exponential circuit complexity, can be certified from only O ( n 2 ) single-qubit measurements. Given access to the target state’s amplitudes, our protocol requires only O ( n 3 ) classical computation. This result is established by a technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state and for learning and verifying neural networks, tensor networks and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties of a synthesized state that would otherwise require an exponential number of measurements on the state. We demonstrate these applications in numerical experiments with up to 120 qubits and observe an advantage over existing methods such as cross-entropy benchmarking.
information theory and computation↗
Quantum graph learning and algorithms applied in quantum computer sciences and image classification
Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On-chip probabilistic inference for charged-particle tracking at the sensor edge
Modern scientific instruments operate under increasingly extreme constraints on bandwidth, latency, and power. Inference at the sensor edge determines experimental data collection efficiency by deciding which information to save for further analysis. Particle tracking detectors at the Large Hadron Collider exemplify this challenge: pixelated silicon sensors generate rich spatiotemporal ionization patterns, yet most of this information is discarded due to data-rate limitations. Concurrently, advancements in co-design tools provide rapid turn-around for incorporating machine learning into application-specific integrated circuits, motivating designs for particle detectors with new integrated technologies. We demonstrate that neural networks embedded in the front-end electronics can infer charged-particle kinematic parameters from a single silicon layer. We regress hit positions and incident angles with calibrated uncertainties, while satisfying stringent constraints on numerical precision, latency, and silicon area. Our results establish a path toward probabilistic inference directly at the edge, opening new opportunities for intelligent sensing in high-rate scientific instruments.
Das, Arghya Ranjan [Purdue U.] (ORCID:000000018451↗
Evaluating pulse-shaping capabilities of next-generation pulsed power architectures
This project evaluated the pulse shaping capabilities of next-generation pulsed power (NGPP) architectures. NGPP architectures share several common attributes including multiple independent pulse-generation lines, a radial water-insulated impedance transformer, and a central vacuum insulated load region. A multi-module circuit model was developed, incorporating independent pulse-generation lines and a 2-D transmission line mesh of the radial impedance transformer to assess the effects of azimuthal asymmetry in pulse-shaped experiments. Circuit model simulations demonstrated that NGPP architectures are able to produce the the desired current pulse shapes for exemplar NGPP experiments. Additionally, the project explored automated methods for experiment design, including derivative -ree optimization and machine learning. Pulse-shaped experiments require designers to determine machine parameters that reliably produce the desired current pulse at the load, a process that typically relies on expert knowledge and iterative adjustments using the Z circuit model. Given the increased complexity of NGPP systems, this manual approach may be impractical. While the evaluated methods do not eliminate the need for manual iteration, they can reduce the time required for experiment design. Derivative-free optimization automates much of the trial-and-error process, providing a close starting point for manual adjustments or making small modifications to near-final designs. Meanwhile, deep neural network methods can generate a good qualitative match to the desired current pulse in under one second without requiring circuit model simulations.
42 ENGINEERING↗
Accelerating computing for the future electric grid (CRADA Final Report)
As a participant in the Cyclotron Road Lab-Embedded Entrepreneurship Program (LEEP), Vellex Computing, Inc. has successfully validated the "Vellex Computing Stack," a breakthrough Analog Neural Computer (ANC) specifically designed for high-performance edge optimization. This project achieved critical milestones in mixed-signal circuit stability and software-hardware co-design, directly addressing national priorities in semiconductor resiliency. The success of this work is deeply rooted in the support from the Cyclotron Road LEEP, which provided the essential "hard tech" runway—funding, mentorship, and access to Lawrence Berkeley National Laboratory’s world-class characterization facilities—allowing Vellex to overcome the "Valley of Death" often faced by deep-tech hardware startups. By leveraging LBNL’s advanced testing infrastructure, Vellex was able to rigorously benchmark the ANC architecture against state-of-the-art digital solutions, a feat that would have been resource-prohibitive independently. This collaboration has not only advanced American leadership in analog computing but has also matured Vellex’s technology to a stage ripe for private sector commercialization.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Using Explainable Artificial Intelligence to Predict Perovskite Solar Cell Electrical Metastability from Operando Photoluminescence Images in Accelerated Stress Testing
Metal halide perovskite (MHP) solar cells exhibit a metastable response to bias governed by coupled ionic–electronic processes, complicating the conventional reciprocity relation between luminescence intensity and device open-circuit voltage (V oc ). This limits the use of luminescence as a diagnostic for device screening or accelerated stress testing, motivating new approaches that can interpret photoluminescence (PL) signals under nonequilibrium conditions. From the artificial intelligence perspective, we develop an explainable deep learning framework that integrates convolutional neural networks (CNN), long short-term memory (LSTM) layers, and an attention mechanism to learn spatiotemporal features from operando photoluminescence PL image sequences. The model achieves a mean absolute error of ±0.027 V in predicting open-circuit voltage transients and reduces extreme-tail errors by up to 78% compared to physics-based reciprocity calculations. Gradient-weighted Class Activation Mapping (Grad-CAM) provides interpretability by highlighting physically meaningful regions such as electrode edges and emergent defect features. From the engineering application perspective, this framework enables accurate, contactless prediction of device V oc and identification of degradation-relevant features during accelerated aging of perovskite solar cells. This approach demonstrates how explainable AI can enhance operando diagnostics and reliability analysis in photovoltaic devices under nonequilibrium conditions.
14 SOLAR ENERGY↗
Nonlinear thermodynamic computing out of equilibrium
We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times.
Whitelam, Stephen [Lawrence Berkeley National Labo↗