Simulation Framework for Thermal Quasi-Particle Microwave Loss in Multimaterial Superconducting Quantum Circuit Elements

Abstract

Superconducting quantum circuits constitute one of the most advanced and promising platforms for building fault-tolerant quantum computers. However, the associated relatively short coherence times remain a major challenge. Therefore quantifying the various responsible loss mechanisms is key, which can be achieved effectively by refined loss modeling. An important source of dissipation is thermal quasi-particles, for which many simulation tools exist. Here, we improve on these by integrating two of them in a self-consistent manner into an automated workflow for a circuit composed of two materials. Namely, the workflow consists of a numerical simulation of the Mattis–Bardeen surface impedance and electromagnetic finite-element simulation using Ansys HFSS to predict temperature-dependent quasi-particle loss from normal state material properties. As a test, we use it to simulate the quality factors as a function of the temperature of superconducting resonators composed of tantalum. Tantalum resonators are often found to be dominated by quasi-particle loss at a significantly lower temperature (less than 1 K) than what would be expected from the bulk critical temperature (4.4 K) observed to good approximation in dc transport measurements. A likely cause is a defect phase with a low critical temperature, potentially associated with the tantalum beta phase. By fitting the temperature-dependent loss data to the workflow results, we estimate the concentration of the defect phase. This is an important step forward in correlating material design and microwave loss.