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  • Open Access

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

Yao Lu1,2,3,*, Tianpu Zhao4, André Vallières3,4, Kevin C. Smith1,2,5, Daniel Weiss1,2, Xinyuan You3, Yaxing Zhang1,2, Suhas Ganjam1,2, Aniket Maiti1,2 et al.

John W. O. Garmon1,2, Shantanu Mundhada6, Ziwen Huang3, Ian Mondragon-Shem7, Steven M. Girvin1,2, Jens Koch7,8, and Robert J. Schoelkopf1,2,6,†

  • *Contact author: yaolu@fnal.gov
  • †Contact author: robert.schoelkopf@yale.edu
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PRX Quantum 7, 033039 – Published 27 August, 2026

DOI: https://doi.org/10.1103/4kfd-kqdg

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 numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. 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.

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Popular Summary

We introduce a practical pathway for turning standard microwave simulations of a superconducting-circuit layout into a quantitative, time-dependent physics model that captures both the intended coherent control and the noise entering through the control lines. The framework applies to realistic, geometrically complex devices and retains the relative phases and correlations among different control pathways. It therefore allows quantum engineers to evaluate intended gate operations and port-induced error mechanisms directly from the device layout, at the design stage. The framework is broadly applicable across superconducting circuits and provides practical tools for choosing filters and wiring, testing and optimizing parametric control schemes, and reducing trial and error in the laboratory. It can also help identify the mechanisms that limit superconducting devices under strong microwave drive, which are often difficult to isolate experimentally. The methods and supporting simulation resources are openly available, providing a layout-aware toolbox for designing higher-fidelity superconducting quantum hardware for computation, sensing, and measurement.

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PRX Quantum 7, 033039– Published 27 August, 2026
  • Received 14 January 2026
  • Revised 13 June 2026
  • Accepted 14 July 2026
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