Exact quantization of superconducting circuits

TL;DR

This paper provides a theoretical framework for exactly quantizing superconducting circuits with weakly anharmonic qubits coupled to multimode cavities, deriving formulas for dressed frequencies and nonlinearities.

Contribution

It introduces a unitary transformation that diagonalizes the harmonic part of the circuit, enabling exact analysis of energy levels and nonlinearities in complex superconducting circuits.

Findings

Derived closed-form formulas for dressed frequencies and Kerr nonlinearities.

Applicable to arbitrary detuning and coupling regimes, including beyond dispersive.

Validated the approach with examples involving transmons and resonators.

Abstract

We present a theoretical description for circuits consisting of weak anharmonic qubits coupled to cavity multimodes. We obtain a unitary transformation that diagonalizes harmonic sector of the circuit. Weak anharmonicity does not alter the normal mode basis, however it can modify energy levels. We study two examples of a transmon and two transmons coupled to bus resonator, and we determine dressed frequencies and Kerr nonlinearities in closed form formulas. Our results are valid for arbitrary frequency detuning and coupling within and beyond dispersive regime.