Maxwell-Schrödinger Hybrid Simulation for Analyzing Control and Readout of Transmon Qubits

The control and readout of a transmon qubit through applied microwave pulses is a key capability in operating many quantum technologies. Currently, the design of microwave pulses for these purposes is done through simple theoretical or numerical models that do not account for how the transmon modifies the applied microwave field. In this work, we present the formulation and discretization of a self-consistent semiclassical model that solves the Schrödinger equation describing qubit dynamics in tandem with a one-dimensional wave equation describing transmission line dynamics. Numerical results are presented using this Maxwell-Schrödinger method to characterize the control and readout of a transmon qubit. We show that our method matches simple theoretical predictions in relevant operating regimes and also look at situations where simplified models break down. In the future, our method can be used to explore these broader operating regimes to search for more effective control and readout protocols.