Black-box superconducting circuit quantization

TL;DR

This paper introduces a semi-classical approach to derive the effective quantum Hamiltonian for complex superconducting circuits, enabling accurate modeling of multi-mode systems like 3D-transmons with experimental validation.

Contribution

It presents a novel semi-classical method that uses classical linear response to determine the quantum Hamiltonian of weakly anharmonic superconducting circuits with arbitrary environments.

Findings

Accurately computes low-energy spectra of 3D-transmon systems

Achieves quantitative agreement with experimental measurements

Provides a versatile framework for complex circuit quantization

Abstract

We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with measurements is found.