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Digest - IEEE Antennas and Propagation Society. International Symposium

Full-Wave Computation of the Spontaneous Emission Rate of a Transmon Qubit

Thomas E. Roth, Weng Cho Chew

Published Dec 4, 2021• 2 citations
Publisher

Abstract

Understanding the spontaneous emission rate of transmon qubits is an important step in the design of many quantum electromagnetic devices, such as single photon sources and quantum computers. Despite its importance, the spontaneous emission rate is often determined using approximate circuit models or is inferred from measurements on a fabricated device. To improve the accuracy of predictions, it is better to use full-wave numerical methods for this problem. 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 demonstrate this process by computing the spontaneous emission rate of a single photon source and find qualitative agreement with a similar fabricated device.

DOI
10.1109/aps/ursi47566.2021.9704323

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Understanding the spontaneous emission rate of transmon qubits is an important step in the design of many quantum electromagnetic devices, such as single photon sources and quantum computers. Despite its importance, the spontaneous emission rate is often determined using approximate circuit models or is inferred from measurements on a fabricated device. To improve the accuracy of predictions, it is better to use full-wave numerical methods for this problem. 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 demonstrate this process by computing the spontaneous emission rate of a single photon source and find qualitative agreement with a similar fabricated device.
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.
Superconducting qubits are one of the most mature approaches to realize quantum computers. Unfortunately, existing design approaches use full-wave computational electro-magnetics methods to model these devices in inefficient ways that become impractical if even a few qubits are considered. This work uses a field-based formalism to derive a simple formula for the exchange coupling rate between multiple qubits, which is a key design parameter for creating large-scale quantum architectures. This approach is relevant for the common situation of transmon qubits dispersively coupled via an electromagnetic resonator or environment. Then the accuracy of this approach is validated by comparing it to existing modeling approaches on a realistic superconducting circuit topology.
Single photon sources are an important component in many quantum information processing systems. Despite their importance, current modeling methods predominantly focus on developing optimistic performance bounds, and are not conducive to performing engineering optimization studies. To enhance the capability of modeling methods, we propose a process to utilize the classical electromagnetic dyadic Green's function of a system as an integral component of determining the emitted photon states produced by a single photon source. Importantly, the Green's function can be readily computed using standard fullwave numerical methods, making it a viable analysis tool. We demonstrate this process by characterizing the emission of a microwave frequency single photon source that uses a transmon as a quantum emitter, and find qualitative agreement with a fabricated device that has similar design characteristics.
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.
Currently, circuit quantum electrodynamics architectures have emerged as one of the most popular approaches to implement practical quantum information processing hardware. Although significant progress has been made, many technical issues remain that limit the performance of fabricated devices. One approach to accelerate progress in the engineering design of these devices is to develop improved numerical modeling methods. Current modeling methods generally rely on approximate lumped element circuit models to describe the complex network of microwave transmission lines required to operate a circuit quantum electrodynamics device. This reduction in complexity in the theoretical model is valuable for gaining insight into the operation of a device, but does limit the opportunity for using these models to optimize the performance of practical devices. To develop rigorous numerical modeling methods, it is necessary to move toward theoretical descriptions of circuit quantum electrodynamics devices that retain the full details of the three-dimensional vector electromagnetic fields that exist in these systems. In this work, we present details on such a theoretical model for one of the most commonly used circuit quantum electrodynamics systems, a transmon qubit coupled to microwave transmission lines. We discuss the quantization of our new model and show that by adopting relevant approximations our model can be reduced to the same lumped element descriptions commonly used in the literature. We also discuss the derivation of quantum equations of motion for the coupled field-transmon system, which can be used as the starting point for developing full-wave numerical solvers for these circuit quantum electrodynamics systems in the future.