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United States National Committee of URSI National Radio Science Meeting

Analytical Quantum Full-Wave Solution of Single-Photon Transport Through a 3D Transmon

Soomin Moon, Thomas E. Roth

Published Jan 6, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.23919/nrsm68586.2026.11551104

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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.
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.
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.
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.
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.
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.
Superconducting qubits are one of the most mature platforms for achieving practical quantum computers, but significant performance improvements are still needed. To improve the engineering of these systems, three-dimensional (3D) full-wave computational electromagnetics analyses are increasingly being turned to. 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 modeling framework that we illustrate in the context of evaluating the qubit-qubit exchange coupling rate between transmon qubits. This quantity is a key design parameter that determines the entanglement rate for fast multiqubit 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 needed quantity involving the dyadic Green's function can be related to the impedance response of the system that can be easily and efficiently computed with classical computational electromagnetics tools. We demonstrate the validity and efficacy of this approach by simulating four practical multiqubit 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 multicoupler device and identifying operating points where the qubit crosstalk becomes zero.