Energy-participation quantization of Josephson circuits

TL;DR

This paper introduces an energy-participation ratio method for efficiently quantizing complex superconducting Josephson circuits, enabling accurate modeling of their quantum properties and dissipation.

Contribution

The paper presents a universal, efficient electromagnetic eigenmode simulation-based method to calculate energy participation ratios for nonlinear circuit elements, improving quantum Hamiltonian determination.

Findings

Accurately predicts nonlinear couplings within a few percent.

Works across a wide energy range and various circuit types.

Validated on multiple Josephson circuits with experimental agreement.

Abstract

Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are one of the leading platforms for emerging quantum technologies. Increasing circuit complexity further requires efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here, we present a method based on the energy-participation ratio (EPR) of a dissipative or nonlinear element in an electromagnetic mode. The EPR, a number between zero and one, quantifies how much of the energy of a mode is stored in each element. It obeys universal constraints--valid regardless of the circuit topology and nature of the nonlinear elements. The EPR of the elements are calculated from a unique, efficient electromagnetic eigenmode simulation of the linearized circuit, including lossy elements. Their set is the key input to the determination of the quantum Hamiltonian of the system. The method provides an intuitive and simple-to-use tool to quantize multi-junction circuits. It is especially well-suited for finding the Hamiltonian and dissipative parameters of weakly anharmonic systems, such as transmon qubits coupled to resonators, or Josephson transmission lines. We experimentally tested this method on a variety of Josephson circuits, and demonstrated agreement within several percents for nonlinear couplings and modal Hamiltonian parameters, spanning five-orders of magnitude in energy, across a dozen samples.