Efficient evaluation of decoherence rates in complex Josephson circuits

TL;DR

This paper provides a comprehensive quantitative analysis of decoherence rates in a flux-type Josephson qubit with complex circuit elements, highlighting the dominant contributions from circuit couplings and employing dimensionality reduction techniques.

Contribution

It introduces a detailed modeling approach for Josephson circuits, including stray capacitances, and develops a Born-Oppenheimer approximation to efficiently compute decoherence rates.

Findings

Decoherence rates vary significantly along the optimal flux line.

Coupling to the large loop dominates decoherence contributions.

Dimensionality reduction simplifies complex quantum circuit analysis.

Abstract

A complete analysis of the decoherence properties of a Josephson junction qubit is presented. The qubit is of the flux type and consists of two large loops forming a gradiometer and one small loop, and three Josephson junctions. The contributions to relaxation (T_1) and dephasing (T_\phi) arising from two different control circuits, one coupled to the small loop and one coupled to a large loop, is computed. We use a complete, quantitative description of the inductances and capacitances of the circuit. Including two stray capacitances makes the quantum mechanical modeling of the system five dimensional. We develop a general Born-Oppenheimer approximation to reduce the effective dimensionality in the calculation to one. We explore T_1 and T_\phi along an optimal line in the space of applied fluxes; along this "S line" we see significant and rapidly varying contributions to the decoherence parameters, primarily from the circuit coupling to the large loop.