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Digest - IEEE Antennas and Propagation Society. International Symposium

Full-Wave Hamiltonian Analysis of a Coaxial-Fed 3D Microwave Cavity Resonator

Soomin Moon, Thomas E. Roth

Published Jul 23, 2023• 1 citation
Publisher

Abstract

Quantum electromagnetic effects in superconducting circuits are promising phenomena to develop revolutionary quantum information processing technologies. To design complex circuits, there is a need for the development of accurate full-wave numerical models. In this work, we study the simpler classical full-wave Hamiltonian of a coaxial-fed rectangular waveguide cavity to validate field-based parts of the corresponding quantum Hamiltonian. We present the formulation of the system Hamiltonian and derive equations of motion. We compare results from our formulation using numerical eigenmodes to traditional transmission simulations of the system to validate the approach.

DOI
10.1109/usnc-ursi52151.2023.10238006

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Quantum electromagnetic effects in superconducting circuits are promising phenomena to develop revolutionary quantum information processing technologies. To design complex circuits, there is a need for the development of accurate full-wave numerical models. In this work, we study the simpler classical full-wave Hamiltonian of a coaxial-fed rectangular waveguide cavity to validate field-based parts of the corresponding quantum Hamiltonian. We present the formulation of the system Hamiltonian and derive equations of motion. We compare results from our formulation using numerical eigenmodes to traditional transmission simulations of the system to validate the approach.
Quantum information processing technologies are gaining interest due to their potential for performance exceeding what is possible with the best classical computers. One of the most promising platforms is the circuit quantum electrodynamics (cQED) architecture that controls superconducting circuit qubits by coupling them to electromagnetic fields in microwave resonators or waveguides. As these devices become increasingly complex, existing analysis and design approaches that often rely on lumped element circuit approximations can become inadequate due to their lack of accuracy and flexibility. This is leading to a growing interest in developing quantum full-wave numerical modeling methods for the high-fidelity analysis of cQED devices. In this work, we focus on a quantum full-wave modeling approach that uses a projector-based quantization approach that allows a problem to be decomposed into distinct subdomains whose fields can be quantized more easily. This leads to a framework that can naturally incorporate microwave ports, which is not straightforward with other formulations. Here, we consider an explicit problem of a coaxial-fed rectangular waveguide cavity to validate parts of our projector-based formalism. Toward this end, we apply this approach to a classical Hamiltonian analysis of this system that can be used to more easily validate the relevant full-wave aspects of the corresponding quantum formulation. In addition to presenting the formulation of the full-wave classical Hamiltonian of the system, we derive equations of motion and discuss an analytical solution procedure with an input-output theory approach. We validate our formulation by comparing the input-output theory results to standard finite element method (FEM) scattering parameter simulations.
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 3-D 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 3-D 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 3-D devices.
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.
Superconducting quantum circuit design is reliant on accurately mapping design parameters to a quantum Hamiltonian. Designers typically rely on computationally intensive finite-element electromagnetic simulations. However, effective circuit-level models can in principle capture much of the relevant physics for these systems, reducing the need for finite-element simulations. A barrier to implementing these simpler models has been the prevalence of distributed elements such as coplanar waveguides resonators in device designs. Techniques for modeling these distributed elements have been developed, but may be difficult to scale, reduce intuition, and give inaccurate results under strong coupling. In this work we describe a simple effective circuit-level model that faithfully reproduces the scattering parameters, and subsequently can predict certain Hamiltonian parameters, for a coupled, distributed element within a broader two-port network even up to strong coupling. Our approach does not explicitly require an electromagnetic simulation. Our model, along with other common lumped models used in black box quantization, is publicly available to researchers via an open-source code package, simpleLOMs\texttt{simpleLOMs}simpleLOMs.
A promising way to scale up quantum information processing hardware is to link different devices together using propagating photons. To accurately model these quantum effects, a fully-quantum treatment is needed to look at the photon transport properties at the single- and few-photon levels. Quantum full-wave numerical modeling will be critical to successfully designing these interconnects, but such tools do not yet exist and validating their performance as they are developed remains a challenge. In this work, we continue developing analytical quantum full-wave solutions that can be used to help validate these kinds of numerical methods. Here, we analyze a system where a single transmon qubit is inserted inside a 3D rectangular cavity, and consider its coupling to two coaxial ports. We then analyze the single-photon transport properties through this system by deriving the single-photon scattering matrix in the quantum input-output theory formalism. We then compare the results of the scattering matrices in the good- and bad-cavity limits, providing a validation aid for future numerical methods.
Circuit quantum electrodynamics is one of the most promising platforms for building quantum information processors. To meet the stringent performance requirements, high-fidelity general-purpose numerical methods are increasingly needed to improve designs. Currently, there exist a limited number of methods for analyzing these systems and they suffer from problematic efficiency limitations. One challenge in developing more efficient methods is the lack of available reference data that can be generated to validate them. Here, we develop an analytical quantum full-wave solution for a transmon qubit in a 3D cavity that can validate numerical methods in the future. We start by reviewing the basics of the field-based quantization method used before showing how classical electromagnetic theories can be used to analytically evaluate all field-based parameters in our formulation. We validate our analytical solution by calculating experimentally-relevant system parameters and comparing against approaches that use numerical EM eigenmodes in their solution.