arXiv subjects

Samuel T. Elkin

Publications and source records attributed to Samuel T. Elkin.

4 recordsLinked to original sources

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↗

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

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↗

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↗