Figure 1. Models of two-level systems (TLSs) in the Josephson junction of a superconducting qubit.

(a) Schematic of the phase qubit circuit used in this work and illustration of proposed TLS mechanisms: tunnelling atoms, trapped electrons, dangling bonds, and hydroxide defects. (b) Sketch of the TLS eigenfunctions in a double-well potential that is characterized by the strain-dependent asymmetry energy ε and the tunnel coupling Δ. (c) Potential energy and indication of the two lowest eigenstates of the phase qubit.