Circuit quantization with time-dependent magnetic fields for realistic geometries

Understand

Quantum circuit theory has become a powerful and indispensable tool to predict the dynamics of superconducting circuits.

• Surprisingly however, the question of how to properly account for a time-dependent driving via external magnetic fields has hardly been addressed so far.
• Here, we derive a general recipe to construct a low-energy Hamiltonian, taking as input only the circuit geometry and the solution of the external magnetic fields.
• A gauge fixing procedure for the scalar and vector potentials is given which assures that time-varying magnetic fluxes make contributions only to the potential function in the Schr\"odinger equation.