Power-Law Scaling of Relaxation Time Fluctuations in Transmon Qubits

Abstract

We have measured temporal fluctuations in the energy relaxation time <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> of a series of 3D transmon qubits. At 20 mK, the relaxation times of the devices have average values between 2 and 190 μs, with standard deviations as large as 20% of the averages. Over the different devices, this fluctuation magnitude roughly scales as a power law in the average <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , with an exponent near 1.5. With increasing temperature, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> decreases due to a higher density of thermally-generated quasiparticles. For an individual device measured up to 250 mK, the fluctuation magnitude appears to be proportional to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . We present a model of quasiparticle dissipation channels that reproduces both of the observed scaling relationships.