Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

TL;DR

This paper develops new numerical methods to accurately model the time-dependent Hamiltonians of microwave-driven superconducting circuits, enabling better design and control of quantum devices in complex electromagnetic environments.

Contribution

The authors introduce a generalized, non-lumped-element numerical approach using classical microwave simulations to obtain time-dependent Hamiltonians for arbitrary superconducting circuit geometries.

Findings

Successfully characterizes driven properties of realistic circuits.

Captures coherent dynamics, relaxation, and dephasing effects.

Applicable to complex electromagnetic environments.

Abstract

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce novel numerical techniques that leverage classical microwave simulations that can be efficiently executed in finite element solvers, to obtain the time-dependent Hamiltonian of a microwave-driven superconducting circuit with arbitrary geometries. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.