Limits and Extensions of the Impedance Formulae for the Design of Superconducting Quantum Processors

Blackbox quantization methods and in particular impedance formulae became indispensable tools for the streamlined design of the quantum processors connecting microwave simulations to the quantum Hamiltonian parameters such as the exchange coupling rates between qubits. We will start by reviewing lumped circuit quantization methods and introduce the blackbox quantization approach. We will then study the accuracy of the impedance formulae in the large anharmonicity limit and when they might break down. Recent extensions of these methods to the non-reciprocal interactions and admittance networks will also be reviewed.