Circuit quantization with time-dependent magnetic fields for realistic geometries

Abstract Quantum circuit theory has become a powerful and indispensable tool to predict the dynamics of superconducting circuits. Surprisingly however, question how properly account for time-dependent driving via external magnetic fields hardly been addressed so far. Here, we derive general recipe construct low-energy Hamiltonian, taking as input only geometry solution fields. We find that interplay field distribution leads much richer than commonly anticipated, already in devices simple quantum interference device (SQUID). These can be captured by assigning negative, or even momentarily singular capacitances Josephson junctions. Negative give rise strong enhancement qubit relaxation rates, while lead finite Berry phase.