Quantization of inductively-shunted superconducting circuits

TL;DR

This paper introduces a numerical method for accurately calculating energy levels in complex superconducting circuits with strong coupling and anharmonicity, validated by experimental data.

Contribution

The authors develop a new approach combining normal mode analysis and numerical diagonalization for highly anharmonic, inductively-shunted circuits, surpassing existing methods.

Findings

Accurate energy level calculations for fluxonium qubits with strong coupling.

Excellent agreement between theoretical spectra and experimental measurements.

Method applicable to complex superconducting circuit designs.

Abstract

We present a method for calculating the energy levels of superconducting circuits that contain highly anharmonic, inductively-shunted modes with arbitrarily strong coupling. Our method starts by calculating the normal modes of the linearized circuit and proceeds with numerical diagonalization in this basis. As an example, we analyze the Hamiltonian of a fluxonium qubit inductively coupled to a readout resonator. While elementary, this simple example is nontrivial because it cannot be efficiently treated by the method known as "black-box quantization," numerical diagonalization in the bare harmonic oscillator basis, or perturbation theory. Calculated spectra are compared to measured spectroscopy data, demonstrating excellent quantitative agreement between theory and experiment.