Maxwell-Schr\"{o}dinger Modeling of Superconducting Qubits Coupled to Transmission Line Networks

TL;DR

This paper introduces a Maxwell-Schrödinger modeling approach for superconducting qubits coupled to transmission lines, enabling efficient, self-consistent simulations of microwave control and measurement effects without full quantum complexity.

Contribution

The work develops a semiclassical Maxwell-Schrödinger method that accounts for self-consistent interactions in superconducting qubit systems, improving modeling efficiency and flexibility.

Findings

Validated the method with transmon and fluxonium qubits

Identified scenarios where self-consistent interactions are crucial

Demonstrated efficiency over fully quantum models

Abstract

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 use 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-Schr\"{o}dinger 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 are 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.