A Hammerstein Approach for Compact Model of Non-linear Circuits with Arbitrary Terminations
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Thieme, Ethan Connor [Sandia National Laboratories↗
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Learning linear optical circuits with coherent states
We analyze the energy and training data requirements for supervised learning of an M-mode linear optical circuit by minimizing an empirical risk defined solely from the action of the circuit on coherent states. When the linear optical circuit acts non-trivially only on k < M unknown modes (i.e. a linear optical k-junta), we provide an energy-efficient, adaptive algorithm that identifies the junta set and learns the circuit. We compare two schemes for allocating a total energy, E, to the learning algorithm. In the first scheme, each of the T random training coherent states has energy E/T. In the second scheme, a single random MT-mode coherent state with energy E is partitioned into T training coherent states. The latter scheme exhibits a polynomial advantage in training data size sufficient for convergence of the empirical risk to the full risk due to concentration of measure on the $(2MT-1)$-sphere. Specifically, generalization bounds for both schemes are proven, which indicate that for ε-approximation of the full risk by the empirical risk with high probability, $O(E^{2/3}M^{2/3}/\epsilon^{2/3})$ training states are sufficient for the first scheme and $O(E^{1/3}M^{1/3}/\epsilon^{2/3})$ training states are sufficient for the second scheme.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
High Linearity RF Circuits in CMOS Platforms (CRADA Final Report)
The goal of this CRADA was to understand high linearity silicon-on-insulator (SOI) radio frequency switches. The first direction investigated was high linearity RF mixers as these components are composed of a network of switches. During the course of the investigation, it was determined that while the SOI RF switches were effective in the application in mixers and produced state of the art performance, the use of SOI for mixers is not economically feasible because the technology only worked with advanced CMOS nodes <65nm which can have an NRE cost (from lithography masks) in excess of $\$$500,000.
42 ENGINEERING↗
Non-Invasive Electrode Impedance Estimation for Optimized Charge Profile Parameterization of Lithium-Ion Batteries
This work presents a non-invasive method for parameterizing a physically motivated equivalent circuit model of lithium-ion batteries using operando electrochemical impedance spectroscopy and time-domain data. The proposed model consists exclusively of linear circuit elements, enabling computationally efficient simulation and real-time implementation on battery management system chips. By integrating frequency- and time-domain measurements, the model accurately estimates internal states such as the negative electrode potential, achieving a root mean square error of 12.3 mV during fast charging validation. Parameterization requires only rate tests with sinusoidal perturbations at three different ambient temperatures, making the approach experimentally accessible. The model reveals key insights into battery behavior, including rate-dependent overpotentials primarily governed by charge transfer kinetics at the positive electrode, and temperature-dependent impedance contributions from both charge transfer and solid-state diffusion processes. Validation using reference electrodes confirms the model’s ability to detect lithium plating onset and reproduce impedance behavior across a wide range of operating conditions. The approach enables in situ optimization of fast charging profiles and lays the foundation for future extensions incorporating aging effects and plating dynamics.
25 ENERGY STORAGE↗
A Two-Dimensional Non-Linear Magnetic Equivalent Circuit Model to Facilitate the Preliminary Design of a Normal Conducting Quadrupole
Normal conducting quadrupoles have been used to focus charged particle beams in synchrotrons, beam transfer lines, medical linacs, etc. for a long time. Optimization techniques based on analytical expressions combined with the use of a numerical field analysis tool exist in the literature for the design of an optimal pole tip shape. However, the initial shape and dimensions of the remaining yoke (including the pole itself and yoke base that act as the return path) are usually less well defined. This article discusses a design methodology for a normal conducting quadrupole based on a two-dimensional magnetic equivalent circuit. Here, this approach considers the geometry of the entire magnet and the non-linear behavior of the yoke material, thereby eliminating the initial iterations. The design outcome of this exercise serves as a competent starting point and can then be used to refine the pole tip, pole taper, yoke size, and add other geometrical features to achieve the required field quality, gradient, coil considerations, etc. by employing a finite element analysis tool. An example design study to demonstrate the proposed methodology is presented.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Beyond real: alternative unitary cluster Jastrow models for molecular electronic structure calculations on near-term quantum computers
Near-term quantum devices require wavefunction ansätze that are expressive while also of shallow circuit depth in order to both accurately and efficiently simulate molecular electronic structure. While the unitary coupled cluster ansatz (e.g., UCCSD) has become a standard, the high gate count associated with the implementation of this limits its feasibility on noisy intermediate-scale quantum (NISQ) hardware. k -Fold unitary cluster Jastrow (uCJ) ansätze mitigate this challenge by providing O( kN 2 ) circuit scaling and favorable linear depth circuit implementation. Previous work has focused on the real orbitalrotation (Re-uCJ) variant of uCJ, which allows an exact (Trotter-free) implementation. Here we extend and generalize the k -fold uCJ framework by introducing two new variants, Im-uCJ and g-uCJ, which incorporate imaginary and fully complex orbital rotation operators, respectively. Similar to Re-uCJ, both of the new variants achieve quadratic gate-count scaling. Our results focus on the simplest k = 1 model, and show that the uCJ models frequently maintain energy errors within chemical accuracy (∼1 kcal mol −1 ). Both g-uCJ and Im-uCJ are more expressive in terms of capturing electron correlation and are also more accurate than the earlier Re-uCJ ansatz. We further show that Im-uCJ and g-uCJ circuits can also be implemented exactly, without any Trotter decomposition. Numerical tests using k = 1 on H 2 , H 3 + , Be 2 , C 2 H 4 , C 2 H 6 and C 6 H 6 in various basis sets confirm the practical feasibility of these shallow Jastrow-based ansätze for applications on near-term quantum hardware.
Tkachenko, Nikolay V. [University of California, B↗
Encoding of linear kinetic plasma problems in quantum circuits via data compression
We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation Aψ = b to be solved by using the quantum signal processing algorithm. The latter requires encoding of matrix A in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode A in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A quantum eigenvalue solver based on tensor networks
Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases, enabling the characterization of strongly correlated ground states with arbitrary spatial geometry. The energy is converged via a gradient-free generalized sweep algorithm based on quantum subspace diagonalization, with a potentially exponential speedup in the off-diagonal matrix element contractions upon translation into compact quantum circuits of linear depth in the number of qubits. Chemical accuracy is attained in numerical experiments for both a stretched water molecule and an octahedral arrangement of hydrogen atoms, achieving substantially better correlation energies compared to a unitary coupled-cluster benchmark, with orders of magnitude reductions in quantum resource estimates and a surprisingly high tolerance to shot noise. This proof-of-concept study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.
chemistry↗
Scaling of energy delivered through an electrostatic discharge to a small series load
We study the energy delivered through a small-resistance series “victim” load during electrostatic discharge events in air. For gap lengths over 1 mm, the fraction of the stored energy delivered is mostly gap-length independent, with a slight decrease at larger gaps due to electrode geometry. The energy to the victim scales linearly with circuit capacitance and victim load resistance but is not strongly dependent on circuit inductance. This scaling leads to a simple approach to predicting the maximum energy that will be delivered to a series resistance for the case where the victim load resistance is lower than the spark resistance.
42 ENGINEERING↗
High-Q superconducting lumped-element resonators for low-mass axion searches
Low-frequency superconducting lumped-element resonators have recently attracted significant attention in the context of axion dark matter searches. Here, we present the design and implementation of a fixed-frequency superconducting resonator operating near 250 kHz, possessing an inductor volume of ∼1 liter and achieving an unloaded quality factor Q ≈ 2.1 × 10 6 . This resonator represents a significant improvement over the state of the art and informs the design of searches for low-mass axions.
Bosons↗
Evaluating Variable-Impedance Magnetically-Insulated Transmission Lines as a Risk-Mitigation Measure for Next-Generation Pulsed Power
This project has produced the first detailed characterizations of power flow resulting from applying the “variable-impedance MITL” concept to real-life systems in Sandia’s pulsed power program (Z and next-generation pulsed power (NGPP)). We present simulation results and analyses for constant-impedance versions of both Z and NGPP and survey the operational viability of several variable-impedance re-designs in the parameter space of linear tapers. Circuit modeling (SCREAMER/Bertha) was used to pinpoint promising candidate designs, and EM-PIC (Empire) simulations were used to evaluate these candidates more rigorously. This approach was particularly successful in the Z regime which resulted in the identification of several viable variable-impedance MITL designs for each level. The approach was more challenged in the operating space NGPP occupies, producing data points that speak to a more restrictive design space due to anode plasma turn-on. In the end, we were able to converge on one viable variable-impedance design for the highest inductance line (level “F”) and one for the highest current line (level “A”). Altogether, the body of simulation evidence presented in this report suggest there does exist flexibility in operating space for magnetically-insulated transmission lines (MITLs) having variable geometric impedance to be a potential enabling technology for safely increasing current delivery (and potentially lowering stack voltage) in pulsed-power drivers by manipulating electron losses; however, operating points for a particular design must be carefully screened. Circuit and EM-PIC modeling provided consistent verdicts in safe operating regimes for operational viability, but additional physics such as anode plasma turn-on which is included in Empire but not in SCREAMER/Bertha was found to be a critical factor affecting power flow that lead to different assessments between the codes. It is not always the case that the occurrence of anode plasma caused a design to fail (some designs turned on anode plasma yet still delivered load currents meeting design targets); the details matter such as how early in the pulse anode surfaces break down (and how large a region). However, in every case that it did fail it was found that the feedback from anode plasma was the cause (i.e., turning off the anode plasma model in Empire restored agreement with the circuit model prediction). As circuit simulations represent an efficient and practical means of surveying design space compared to more computationally-expensive approaches such as EM-PIC, it could be prudent to invest in the research and development of models to include the effects of anode plasma such as ion emission in circuit codes. The variable-impedance MITL design is a new concept that enables controlled manipulation of the initial electron losses in the outer MITL and can be tested on Z today. We encourage follow-on work to explore further optimization (including alternative variable-impedance profiles, e.g., having constant dZ/dR), and to confirm the major findings presented in this report by fielding test hardware on actual Z shots.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Exact block encoding of imaginary time evolution with universal quantum neural networks
We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.
97 MATHEMATICS AND COMPUTING↗
qsp4pde v1.0
The software program is a collection of Python implementations of quantum circuits for solving linear partial differential equations using quantum signal processing. The circuits are implemented using the qiskit SDK.
Kim, Hyeongjin [Lawrence Berkeley National Laborat↗
Method for Coupled Electromagnetic and Circuit Simulations to Evaluate Surge Arrester Performance in Protecting Equipment Against E1 HEMP
Surge arrester behavioral modeling for realistic systems embedded in an E1 high-altitude electromagnetic pulse environment inherently encompasses three interconnected complications: (1) the need to account for signal propagation across two domains, electromagnetics and electrical; (2) the need to include both linear and nonlinear circuit components in the analysis; and (3) the need to understand that the over-current and over-voltage mitigation performance is dependent not only on the properties of the surge arrester and protected load but also on the topology of the overall electrical network. This study presents a framework to address these challenges in a systematic manner to consider the effectiveness of protective measures for a common class of equipment in power generation facilities. Full-wave simulations were carried out to derive circuit-domain (i.e., lumped element–based) equivalent models for the excitation waveform and the physical components of the system. Then, these equivalent models were imported to a circuit solver and combined with a high-frequency surge arrester model to evaluate mitigation performance. The methodology outlined is general enough such that it can be applied for other electromagnetic interference problems that involve E2/E3 HEMP or microwave emissions.
42 ENGINEERING↗
Impact of K-factor on Short Circuit Program Convergence for Inverter-Based Resources during Faults
Classical short-circuit programs that linearize the power network are no longer applicable for inverter based resources (IBRs), necessitating an iterative approach. Phasor domain programs can model the IBRs using an iterative approach considering nonlinear fault responses. In phasor domain models, the IBR can be modeled as a voltage controlled current source (VCCS) in tabular form with positive, negative, and zero sequence information for balanced and unbalance short-circuit faults. In the VCCS modeling of the IBR, positive and negative incremental reactive current, also known as the k-factor, plays an important role in short circuit program convergence. In this work, a few approaches: conventional VCCS modeling with a k-factor of 2, conventional VCCS modeling with a k-factor of 2 with modified pre-fault voltages, VCCS characteristics based on the power flow solution with a k-factor of 2, and VCCS characteristics based on the power flow solution with a k-factor of 1 are investigated for short circuit program convergence under higher IBR penetration. The IEEE 39 bus New England Test System is taken as the test system, and simulations are carried out in PSS®CAPE 15.0.26 simulation software. Simulation results demonstrate that IBR penetration is higher for the VCCS model, which corresponds to the power flow solution with k-factor 1, compared to other approaches.
42 ENGINEERING↗
Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model
We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.
36 MATERIALS SCIENCE↗
Quantum Time Dynamics Mediated by the Yang–Baxter Equation and Artificial Neural Networks
Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANNs) and the Yang–Baxter equation (YBE). Unlike traditional error mitigation methods, which are computationally intensive, we investigate artificial error mitigation. We developed a novel method that combines ANNs for noise mitigation combined with the YBE to generate noisy data. This approach effectively reduces noise in quantum simulations, enhancing the accuracy of the results. The YBE rigorously preserves quantum correlations and symmetries in spin chain simulations in certain classes of integrable lattice models, enabling effective compression of quantum circuits while retaining linear scalability with the number of qubits. This compression facilitates both full and partial implementations, allowing the generation of noisy quantum data on hardware alongside noiseless simulations using classical platforms. By introducing controlled noise through the YBE, we enhance the data set for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in mitigating errors in time-evolving quantum states, providing a scalable framework to enhance quantum computation fidelity, particularly in noisy intermediate-scale quantum (NISQ) systems. We demonstrate the efficacy of this approach by performing quantum time dynamics simulations using the Heisenberg XY Hamiltonian on real quantum devices.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Adaptive Variational Quantum Computing Approaches for Green’s Functions and Nonlinear Susceptibilities
Here, we present and benchmark quantum computing approaches for calculating real-time single-particle Green’s functions and nonlinear susceptibilities of Hamiltonian systems. The approaches leverage adaptive variational quantum algorithms for state preparation and propagation. Using automatically generated compact circuits, the dynamical evolution is performed over sufficiently long times to achieve adequate frequency resolution of the response functions. We showcase accurate Green’s function calculations using a statevector simulator on classical hardware for Fermi-Hubbard chains of 4 and 6 sites, with maximal ansatz circuit depths of 65 and 424 layers, respectively, and for the molecule LiH with a maximal ansatz circuit depth of 81 layers. Additionally, we consider an antiferromagnetic quantum spin-1 model that incorporates the Dzyaloshinskii-Moriya interaction to illustrate calculations of the third-order nonlinear susceptibilities, which can be measured in two-dimensional coherent spectroscopy experiments. These results demonstrate that real-time approaches using adaptive parametrized circuits to evaluate linear and nonlinear response functions can be feasible with near-term quantum processors.
97 MATHEMATICS AND COMPUTING↗