Ultrastrong coupling to parasitic modes in superconducting circuits with hyperinductors

Parasitic modes are inevitable in any real-world circuit. The hope of any practical circuit design is that these modes are sufficiently above the frequency band of interest and do not participate in the low-frequency dynamics of the circuit. A notorious example is a large-value inductor. As the value of the inductance increases with the inductor length, so does the parasitic capacitance. Even in the simplest qubit circuit, in which a Josephson junction is shunted by a hyperinductor, the distributed nature of parasitic capacitance leads to multiple parasitic modes that couple ultrastrongly to the qubit. This ultrastrong coupling of the parasitic modes prevents a perturbation theory treatment of the qubit excitation spectra, while a complete quantum description of the underlying qubit circuit is computationally prohibitive. Progress can be made using an effective multi-mode Hamiltonian that fully reproduces the experimental data both below and above the lowest parasitic modes. This method allows the extraction of the bare qubit circuit parameters that are not renormalized by the presence of parasitic modes.