Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits, Part 1: Modeling Coherent Modulation Induced by Electric and Magnetic Fields

Time‑dependent microwave drives are fundamental in superconducting circuits, enabling coherent control while inadvertently introducing unwanted noise. Accurately modeling the corresponding time‑dependent Hamiltonians of driven Josephson devices, however, goes beyond the scope of standard static methods such as black‑box quantization (BBQ) or energy‑participation‑ratio (EPR) analysis. One notable challenge is the ambiguity in time‑dependent flux allocation, which can yield inconsistent dynamical predictions, a problem examined in previous studies [1,2]. In this work, we introduce three complementary numerical techniques, all based on classical microwave simulations, that enable efficient construction of the time‑dependent Hamiltonian of a microwave-driven superconducting circuit with arbitrary geometries. We apply these methods on realistic device layouts in arbitrary electromagnetic environments, demonstrating their generality over previous approaches. Together, these methods establish a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

 

[1] You et al., Phys. Rev. B 99, 174512 (2019)

[2] Riwar and DiVincenzo, npj Quantum Inf 8, 36 (2022)