Analytical Quantum Full-Wave Solution of a Circuit Quantum Electrodynamic Device

The circuit quantum electrodynamics (cQED) architecture is one of the most promising approaches currently being explored, but substantial design improvements are still needed for these technologies to reach their full potential for practical applications. Current modeling of cQED systems typically relies on lumped element approximations to the complex microwave networks involved to greatly simplify the analysis. However, these simplified solutions lack the level of details that are usually required for accurate predictions in real-world physical implementations. As a result, there is growing interest in developing robust and highly-accurate numerical modeling methods to help accelerate the development of this burgeoning quantum information processing technology. In the context of cQED, this requires moving toward quantum full-wave numerical models that rigorously incorporate all relevant electromagnetic effects into the model.

One common challenge with developing numerical methods is the need to validate that the method produces accurate results. Often, it is not practical to rely soley on measurements to perform this validation because measurements are both expensive and subject to many external factors that may corrupt the measured result. The typical solution to this problem is to develop an analytical solution that can provide enough accuracy so that the general-purpose numerical method can be expected to converge to the analytical result. In the case of quantum full-wave numerical modeling, no analytical solution currently exists, which hinders the development of this numerical modeling field. To address this, we are developing an analytical quantum full-wave solution of a transmon qubit in a 3D microwave cavity. To do this, we are utilizing our recently-developed full-wave projector-based quantization approach for cQED systems to mathematically describe the system. Through careful design of our geometry, we can determine all the quantities in our system Hamiltonian using mature analytical full-wave techniques from classical electromagnetics. 

Once this analytical quantum full-wave solution is developed, it will be possible to perform in-depth analyses of many quantum effects in cQED devices ranging from simple single qubit operations to more complex multiple qubit interactions. These solutions will have an important impact on the development of future quantum full-wave numerical methods by serving as a reliable validation method, which is a key piece currently missing in this nascent field.