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

Superconducting quantum circuits constitute one of the most advanced and promising platforms for building faulttolerant 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 materials design and microwave loss.