Maxwell-Schrödinger Modeling of a Superconducting Qubit Coupled to a Transmission Line Network

• Published in: IEEE journal on multiscale and multiphysics computational techniques Vol. 9; pp. 61 - 74
• Main Authors: Roth, Thomas E., Elkin, Samuel T.
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: circuit quantum electrodynamics; Circuits; Computational electromagnetics; Electrodynamics; Hybrid modeling; Mathematical models; Microwave circuits; Microwave measurement; Microwaves; Numerical models; Power transmission lines; Quantum phenomena; Quantum statistics; Qubit; Qubits (quantum computing); Superconducting microwave devices; superconducting qubits; Superconducting transmission lines; Superconductivity; Transmission line measurements; Transmission lines
• ISSN: 2379-8815; 2379-8815
• DOI: 10.1109/JMMCT.2024.3349433

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 uses 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 is 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.