# Towards understanding two-level-systems in amorphous solids -- Insights from quantum circuits

## TL;DR

This paper reviews recent experimental and theoretical advances in understanding two-level defects in amorphous solids, crucial for quantum circuits, by leveraging superconducting circuits to probe defect dynamics at the quantum level.

## Contribution

It synthesizes recent experimental findings and theoretical models, highlighting how superconducting circuits enable detailed study of two-level defects in amorphous materials.

## Key findings

- Superconducting circuits can probe individual two-level defects.
- Defect dynamics depend on applied field, strain, and temperature.
- Recent models explain defect behavior observed in experiments.

## Abstract

Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered -- what are these two-level defects? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to two-level defects within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects -- observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.