arXiv subjects

Thomas E. Roth

Publications and source records attributed to Thomas E. Roth.

14 recordsLinked to original sources

arXiv2026

Parasitic MIMO Beamforming for Multi-Active Multi-Parasitic Antenna Arrays with Binary Control

In 6G, MIMO dimensions continue to scale, yet the increased cost, power consumption, and hardware complexity associated with growing RF chains limit practical deployment. Parasitic antennas offer a promising alternative that can add spatial degrees of freedom and array gain without a proportional increase in RF chains. From a communication perspective, prior work on parasitic antennas has primarily focused on adjusting continuous reactance values using varactors, but such varactor-based tuning has increased cost and complexity in the analog control and practical RF circuit design. This paper proposes a multi-active multi-parasitic antenna (MAMP) architecture with binary controllers, where each parasitic element operates in one of two discrete reactance states. To validate the practicality of the system, we experimentally identify array geometries that best match the actual radiation patterns with those of the mathematical model through HFSS simulations. We express the induced current vector as a quadratic function of the binary state vector, and propose a pair of discrete reactance values that minimize the relative error of the proposed model while being implementable with off-the-shelf RF components. With these results, we develop two transmit beamforming codebook designs based on the generalized Lloyd algorithm. The first design exhaustively searches for all possible binary combinations to find the optimal solution, representing the theoretical upper limits of our framework. The second design leverages eigenvalue perturbation to significantly reduce computational complexity, making it suitable for online adaptation. Extensive simulations under various channel scenarios demonstrate that the proposed codebook designs enable MAMP with only few active antennas to achieve beamforming performance comparable to fully active antenna arrays with significantly more active antennas.

eess.SP↗

arXiv2026

Singular Vector Finite Element Basis Functions for Tetrahedra in Complex Electromagnetic Geometries

Electromagnetic finite element method (FEM) implementations using traditional basis functions struggle to accurately represent field behavior near singular features such as conducting wedges. To combat this, specialized singular basis functions have been introduced to directly model the singular fields in these regions, leading to substantially improved performance. While these efforts have been pursued extensively in 2D, few functions have been developed for 3D elements. In this work, we develop basis functions for this in tetrahedra. Unlike prior functions, these basis functions are additive, meaning they are included alongside the standard vector basis functions to achieve more robust performance. Further, these functions are designed to be adaptable to tetrahedra touching several unique singular features by using combinations of basis functions singular with respect to each node and edge in the element, making them applicable to highly complex geometries. Higher-order interpolatory versions of the basis functions for modeling singular behavior with greater accuracy are also provided. These basis functions lead to substantial improvements in accuracy relative to the standard basis functions, and allow otherwise expensive simulations to be performed at far lower costs. As an application example, we perform simulations to extract critical quantities for designing superconducting qubits that significantly depend on the behavior of singular fields. In Ansys HFSS, this took 21.27 hours and a peak memory usage of 6.23 TB with 800 processors available, while using our singular basis functions achieved comparable results in 196 seconds while using 27.24 GB of memory and only 16 processors. Due to these benefits, our singular basis functions could be applied to enable design optimization of electromagnetic geometries with dominantly singular behavior, such as superconducting qubits.

physics.comp-ph↗

arXiv2026

Dissipative Channels Determine Open Electromagnetic Quantization

We formulate a quantization scheme for open electromagnetic systems with arbitrary passive boundary conditions. Rather than specifying reservoirs phenomenologically, the method identifies them from the dissipation geometry of the Maxwell operator. Factoring the imaginary part of the Maxwell operator gives a bosonic realization of the field operator and separates the fluctuation channels into medium-assisted reservoirs from material absorption and boundary-assisted reservoirs from exchange through the open boundary. Depending on the boundary condition, the latter become free-space radiation modes, impedance-load channels, guided port modes, or more general boundary channels. Green-function input-output relations then follow as an application, yielding frequency-dependent scattering and noise kernels without Markov or single-mode assumptions. To illustrate the practical application, we consider a lossy structure with mixed impedance and outgoing boundaries, and photonic integrated circuit configurations with waveguide port boundaries.

quant-ph↗

arXiv2026

Analytical Quantum Full-Wave Analysis of Few-Photon Transport Through a Superconducting Cavity Qubit

A promising way to scale up superconducting quantum computers is to link different devices together using propagating photons. Correspondingly, accurately modeling the quantum information transfer in such quantum interconnects is critical to advancing this emerging technology. To accomplish this, a full-wave quantum numerical model is essential for describing the few-photon transport characteristics of various components. Unfortunately, validating the accuracy of such numerical models remains a difficult challenge due to the lack of appropriate analytical solutions for standard component types. Recently, progress has been made on creating the first-ever analytical quantum full-wave solutions for a superconducting circuit quantum device. These efforts considered the case of two-photon transport through an empty rectangular waveguide cavity and the interactions of photons inside a closed rectangular waveguide cavity with a transmon qubit formed by a Josephson junction connected across the terminals of a small wire dipole antenna. Here, we advance these efforts by considering the one- and two-photon transport properties through a rectangular waveguide cavity containing a qubit in this form when the cavity is interfaced with via two coaxial ports. Such devices can be used in various ways for quantum interconnects, such as to form parts of a quantum memory or a photon source. We perform this analysis leveraging a quantum input-output theory formalism to derive the relevant single- and two-photon transport characteristics of interest. We then examine the signatures of the nonlinear quantum scattering effects in the good and bad cavity regimes of cavity quantum electrodynamics. In the future, these analytical results can be used to validate numerical full-wave quantum solvers for modeling quantum interconnects.

quant-ph↗

arXiv2025

Incorporating multi-qubit exchange coupling effects between transmon qubits in Maxwell-Schr\"{o}dinger numerical methods

Superconducting qubits have emerged as a leading platform for realizing quantum computers. Accurate modeling of these devices is essential for predicting performance, improving design, and optimizing control. Many modeling approaches currently rely on lumped circuit approximations or other simplified treatments that can be limited in resolving the interplay between the qubit dynamics and the electromagnetic circuitry, leading to significant experimental deviations from numerical predictions at times. To address many of these limitations, methods that self-consistently solve the Schr\"{o}dinger equation for qubit dynamics with the classical Maxwell's equations have been developed and shown to accurately predict a wide range of effects related to superconducting qubit control and readout. Despite these successes, these methods have not been able to consider multi-qubit effects that give rise to qubit-qubit entanglement. Here, we address this by rigorously deriving how multi-qubit coupling effects between transmon qubits can be embedded into Maxwell-Schr\"{o}dinger methods. To support this, we build on earlier first-principles derivations of Maxwell-Schr\"{o}dinger methods for the specific case of two transmon qubits coupled together through a common electromagnetic system in the dispersive regime. To aid in validating aspects of the Maxwell-Schr\"{o}dinger framework, we also provide a new interpretation of Maxwell-Schr\"{o}dinger methods as an efficient simulation strategy to capture the class of non-Markovian open quantum system dynamics. Our results demonstrate that these effects can give rise to strong classical crosstalk that can significantly alter multi-qubit dynamics, which we demonstrate for the cross-resonance gate. These classical crosstalk effects have been noted in cross-resonance experiments, but previous quantum theory and device analysis could not explain their origin.

quant-ph↗

arXiv2025

Opportunities and Challenges of Computational Electromagnetics Methods for Superconducting Circuit Quantum Device Modeling: A Practical Review

High-fidelity numerical methods that model the physical layout of a device are essential for the design of many technologies. For methods that characterize electromagnetic effects, these numerical methods are referred to as computational electromagnetics (CEM) methods. Although the CEM research field is mature, emerging applications can still stress the capabilities of the techniques in use today. The design of superconducting circuit quantum devices falls in this category due to the unconventional material properties and important features of the devices covering nanometer to centimeter scales. Such multiscale devices can stress the fundamental properties of CEM tools which can lead to an increase in simulation times, a loss in accuracy, or even cause no solution to be reliably found. While these challenges are being investigated by CEM researchers, knowledge about them is limited in the broader community of users of these CEM tools. This review is meant to serve as a practical introduction to the fundamental aspects of the major CEM techniques that a researcher may need to choose between to model a device, as well as provide insight into what steps they may take to alleviate some of their challenges. Our focus is on highlighting the main concepts without rigorously deriving all the details, which can be found in many textbooks and articles. After covering the fundamentals, we discuss more advanced topics related to the challenges of modeling multiscale devices with specific examples from superconducting circuit quantum devices. We conclude with a discussion on future research directions that will be valuable for improving the ability to successfully design increasingly more sophisticated superconducting circuit quantum devices. Although our focus and examples are taken from this area, researchers from other fields will still benefit from the details discussed here.

quant-ph↗

arXiv2024

Field-Based Formalism for Calculating Multi-Qubit Exchange Coupling Rates for Transmon Qubits

Superconducting qubits are one of the most mature platforms for quantum computing, but significant performance improvements are still needed. To improve the engineering of these systems, 3D full-wave computational electromagnetics analyses are increasingly being used. Unfortunately, existing analysis approaches often rely on full-wave simulations using eigenmode solvers that are typically cumbersome, not robust, and computationally prohibitive if devices with more than a few qubits are to be analyzed. To improve the characterization of superconducting circuits while circumventing these drawbacks, this work begins the development of an alternative framework that we illustrate in the context of evaluating the qubit-qubit exchange coupling rate between transmon qubits. This is a key design parameter that determines the entanglement rate for fast multi-qubit gate performance and also affects decoherence sources like qubit crosstalk. Our modeling framework uses a field-based formalism in the context of macroscopic quantum electrodynamics, which we use to show that the qubit-qubit exchange coupling rate can be related to the electromagnetic dyadic Green's function linking the qubits together. We further show how the quantity involving the dyadic Green's function can be related to the impedance response of the system that can be efficiently computed with classical computational electromagnetics tools. We demonstrate the validity and efficacy of this approach by simulating four practical multi-qubit superconducting circuits and evaluating their qubit-qubit exchange coupling rates. We validate our results against a 3D numerical diagonalization method and against experimental data where available. We also demonstrate the impact of the qubit-qubit exchange coupling rate on qubit crosstalk by simulating a multi-coupler device and identifying operating points where the qubit crosstalk becomes zero.

quant-ph↗

arXiv2024

Multiphysics Numerical Method for Modeling Josephson Traveling-Wave Parametric Amplifiers

Josephson traveling-wave parametric amplifiers (JTWPAs) are wideband, ultralow-noise amplifiers used to enable the readout of superconducting qubits. While individual JTWPAs have achieved high performance, behavior between devices is inconsistent due to wide manufacturing tolerances. Amplifier designs could be modified to improve resilience towards variations in amplifier components; however, existing device models often rely on analytical techniques that typically fail to incorporate component variations. To begin addressing this issue, a 1D numerical method for modeling JTWPAs is introduced in this work. The method treats the Josephson junctions and transmission lines in an amplifier as coupled subsystems and can easily incorporate arbitrary parameter variations. We discretize the transmission line subsystem with a finite element time domain method and the Josephson junction subsystem with a finite difference method, with leapfrog time marching used to evolve the system in time. We validate our method by comparing the computed gain to an analytical model for a traditional JTWPA architecture and one with resonant phase matching. We then use our method to demonstrate the impact of variations in Josephson junctions and phase-matching resonators on amplification. In future work, the method will be adjusted to incorporate additional amplifier architectures and extended to a 3D full-wave approach.

physics.comp-ph↗

arXiv2024

Analytical Quantum Full-Wave Solutions for a 3D Circuit Quantum Electrodynamics System

High-fidelity general-purpose numerical methods are increasingly needed to improve superconducting circuit quantum information processor performance. One challenge in developing such numerical methods is the lack of reference data to validate them. To address this, we have designed a 3D system where all electromagnetic properties needed in a quantum analysis can be evaluated using analytical techniques from classical electromagnetic theory. Here, we review the basics of our field-based quantization method and then use these techniques to create the first-ever analytical quantum full-wave solution for a superconducting circuit quantum device. Specifically, we analyze a coaxial-fed 3D waveguide cavity with and without transmon quantum bits inside the cavity. We validate our analytical solutions by comparing them to numerical methods in evaluating single photon interference and computing key system parameters related to controlling quantum bits. In the future, our analytical solutions can be used to validate numerical methods, as well as build intuition about important quantum effects in realistic 3D devices.

quant-ph↗

arXiv2023

Maxwell-Schrödinger Modeling of Superconducting Qubits Coupled to Transmission Line Networks

In superconducting circuit quantum information technologies, classical microwave pulses are applied to control and measure the qubit states. Currently, the design of these microwave pulses use simple theoretical or numerical models that do not account for the self-consistent interactions of how the qubit state modifies the applied microwave pulse. In this work, we present the formulation and finite element time domain discretization of a semiclassical Maxwell-Schrödinger method for describing these self-consistent dynamics for the case of a superconducting qubit capacitively coupled to a general transmission line network. We validate the proposed method by characterizing key effects related to common control and measurement approaches for transmon and fluxonium qubits in systems that are amenable to theoretical analysis. Our numerical results also highlight scenarios where including the self-consistent interactions are essential. By treating the microwaves classically, our method is substantially more efficient than fully-quantum methods for the many situations where the quantum statistics of the microwaves are not needed. Further, our approach does not require any reformulations when the transmission line system is modified. In the future, our method can be used to rapidly explore broader design spaces to search for more effective control and measurement protocols for superconducting qubits.

quant-ph↗

arXiv2023

Generalized Helmholtz Decomposition for Modal Analysis of Electromagnetic Problems in Inhomogeneous Media

Potential-based formulation with generalized Lorenz gauge can be used in the quantization of electromagnetic fields in inhomogeneous media. However, one often faces the redundancy of modes when finding eigenmodes from potential-based formulation. In free space, this can be explained by the connection to the well-known Helmholtz decomposition. In this work, we generalize the Helmholtz decomposition to its generalized form, echoing the use of generalized Lorenz gauge in inhomogeneous media. We formulate electromagnetics eigenvalue problems using vector potential formulation which is often used in numerical quantization. The properties of the differential operators are mathematically analyzed. Orthogonality relations between the two classes of modes are proved in both continuous and discrete space. Completeness of two sets of modes and the orthogonality relations are numerically validated in inhomogeneous anisotropic media. This work serves as a foundation for numerical quantization of electromagnetic fields in inhomogeneous media with potential-based formulation.

physics.optics↗

arXiv2022

Full-Wave Methodology to Compute the Spontaneous Emission Rate of a Transmon Qubit

The spontaneous emission rate (SER) is an important figure of merit for any quantum bit (qubit), as it can play a significant role in the control and decoherence of the qubit. As a result, accurately characterizing the SER for practical devices is an important step in the design of quantum information processing devices. Here, we specifically focus on the experimentally popular platform of a transmon qubit, which is a kind of superconducting circuit qubit. Despite the importance of understanding the SER of these qubits, it is often determined using approximate circuit models or is inferred from measurements on a fabricated device. To improve the accuracy of predictions in the design process, it is better to use full-wave numerical methods that can make a minimal number of approximations in the description of practical systems. In this work, we show how this can be done with a recently developed field-based description of transmon qubits coupled to an electromagnetic environment. We validate our model by computing the SER for devices similar to those found in the literature that have been well-characterized experimentally. We further cross-validate our results by comparing them to simplified lumped element circuit and transmission line models as appropriate.

quant-ph↗

arXiv2021

An Introduction to the Transmon Qubit for Electromagnetic Engineers

One of the most popular approaches being pursued to achieve a quantum advantage with practical hardware are superconducting circuit devices. Although significant progress has been made over the previous two decades, substantial engineering efforts are required to scale these devices so they can be used to solve many problems of interest. Unfortunately, much of this exciting field is described using technical jargon and concepts from physics that are unfamiliar to a classically trained electromagnetic engineer. As a result, this work is often difficult for engineers to become engaged in. We hope to lower the barrier to this field by providing an accessible review of one of the most prevalently used quantum bits (qubits) in superconducting circuit systems, the transmon qubit. Most of the physics of these systems can be understood intuitively with only some background in quantum mechanics. As a result, we avoid invoking quantum mechanical concepts except where it is necessary to ease the transition between details in this work and those that would be encountered in the literature. We believe this leads to a gentler introduction to this fascinating field, and hope that more researchers from the classical electromagnetic community become engaged in this area in the future.

quant-ph↗

arXiv2021

Circuit quantum electrodynamics: A new look toward developing full-wave numerical models

Devices built using circuit quantum electrodynamics architectures are one of the most popular approaches currently being pursued to develop quantum information processing hardware. Although significant progress has been made over the previous two decades, there remain many technical issues limiting the performance of fabricated systems. Addressing these issues is made difficult by the absence of rigorous numerical modeling approaches. This work begins to address this issue by providing a new mathematical description of one of the most commonly used circuit quantum electrodynamics systems, a transmon qubit coupled to microwave transmission lines. Expressed in terms of three-dimensional vector fields, our new model is better suited to developing numerical solvers than the circuit element descriptions commonly used in the literature. We present details on the quantization of our new model, and derive quantum equations of motion for the coupled field-transmon system. These results can be used in developing full-wave numerical solvers in the future. To make this work more accessible to the engineering community, we assume only a limited amount of training in quantum physics and provide many background details throughout derivations.

quant-ph↗