Systematic construction of time-dependent Hamiltonians for microwave-driven Josephson circuits

Modeling circuits and numerically obtaining their time-dependent Hamiltonians are essential for predicting device dynamics and designing high-fidelity quantum operations. Well-established methods, including black-box quantization [1] and the energy participation ratio method [2], primarily focus on modeling static circuits. Recent studies [3, 4] address circuit quantization in the presence of time-dependent magnetic fields. However, modeling realistic circuits with multiple modes subject to charge and flux drives, based on the geometric details of the circuit layout and drive characteristics, remains an open challenge. In this talk, we introduce three complementary methods for constructing the time-dependent Hamiltonian for a given circuit layout, leveraging well-established microwave simulation techniques. Our methods capture incoherent dynamics caused by noisy drive ports, including drive-induced relaxation and dephasing. We present concrete examples illustrating the application of these methods in the optimization of circuit designs.

[1] Nigg et al., PRL 108, 240502 (2012)

[2] Minev et al., npj QI 7, 131 (2021)

[3] You et al., PRB 99, 174512 (2019)

[4] Riwar and DiVincenzo, npj QI 8, 36 (2022)