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IEEE Transactions on Applied Superconductivity

Power-Law Scaling of Relaxation Time Fluctuations in Transmon Qubits

Kungang Li, S. K. Dutta, Zach Steffen, B. S. Palmer, Christopher J. Lobb, F. C. Wellstood

Published Feb 8, 2023• 3 citations
Publisher

Abstract

We have measured temporal fluctuations in the energy relaxation timeT1of 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 averageT1, with an exponent near 1.5. With increasing temperature,T1decreases 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 toT1. We present a model of quasiparticle dissipation channels that reproduces both of the observed scaling relationships.

DOI
10.1109/tasc.2023.3243198

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We have measured temporal fluctuations in the energy relaxation timeT1of 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 averageT1, with an exponent near 1.5. With increasing temperature,T1decreases 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 toT1. We present a model of quasiparticle dissipation channels that reproduces both of the observed scaling relationships.
Abstract We benchmark the decoherence of superconducting transmon qubits to examine the temporal stability of energy relaxation, dephasing, and qubit transition frequency. By collecting statistics during measurements spanning multiple days, we find the mean parameters T1‾\overline {T_1}T1​​ T 1 ¯ = 49 μs and T2∗‾\overline {T_2^ \ast }T2∗​​ T 2 * ¯ = 95 μs; however, both of these quantities fluctuate, explaining the need for frequent re-calibration in qubit setups. Our main finding is that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems (TLS). Through statistical analysis, we determine sub-millihertz switching rates of these TLS and observe the coherent coupling between an individual TLS and a transmon qubit. Finally, we find evidence that the qubit’s frequency stability produces a 0.8 ms limit on the pure dephasing which we also observe. These findings raise the need for performing qubit metrology to examine the reproducibility of qubit parameters, where these fluctuations could affect qubit gate fidelity.
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The temporal stability and reproducibility of qubit parameters are critical for the long-term operation and maintenance of superconducting quantum processors. In this work, we present a comprehensive longitudinal characterization of 27 frequency-tunable transmon qubits spanning over one year across four thermal cycles. Our results establish a distinct hierarchy of stability for superconducting hardware. We find that the intrinsic device parameters determining the qubit frequency and the baseline energy relaxation times (T1T_1T1​) exhibit high robustness against thermal stress, characterized by frequency deviations typically confined within 0.5\% and non-degraded coherence baselines. In stark contrast, the environmental variables, specifically the background magnetic flux offsets and the microscopic landscape of two-level system (TLS) defects, undergo a significant stochastic reconfiguration after each cycle. By employing frequency-dependent relaxation spectroscopy and a quantitative metric, the T1T_1T1​ Spectral Topography Fidelity, we demonstrate that thermal cycling acts as a ``hard reset'' for the local defect environment. This process introduces a level of spectral randomization equivalent to thousands of hours of continuous low-temperature evolution. These findings confirm that while the fabrication quality is preserved, the specific noise realization is statistically distinct for each thermal cycle, necessitating automated recalibration strategies for large-scale quantum systems.
We report the measurement of the fluctuations of a transmon qubit through the noise spectrum of the microwave signal that measures its state. The amplitude of the Lorentzian noise power spectrum allows us to determine the average qubit excitation, in agreement with the estimated thermal radiation reaching the sample. Its width yields the qubit energy relaxation rate that decreases with temperature, contrary to the predictions for a two-level system solely coupled to thermal radiation. This indicates the existence of another non-radiative energy relaxation channel for the qubit.
Materials improvements in transmon qubits have yielded remarkable advances in qubit lifetimes (T1)and coherence times (T2). However, state-of-the-art superconducting qubits experience temporal fluctuations in their performance, which limit gate fidelities and quantum processor performance. We observe correlated increases in qubit relaxation and dephasing rates that last for minutes to hours, which we call T1 and T2 excursions. Using interleaved lifetime and coherence time measurements, noise spectroscopy, and two-level-system (TLS) spectroscopy, we find that these excursions are caused by single or few strongly-coupled TLS defects that spectrally diffuse into resonance with the qubit frequency. Our measurement protocol provides a powerful tool for understanding the noise sources that cause temporal fluctuations in superconducting qubit performance.
The quasiparticle density observed in low-temperature superconducting circuits is several orders of magnitude larger than the value expected at thermal equilibrium. The tunneling of this excess of quasiparticles across Josephson junctions is recognized as one of the main loss and decoherence mechanisms in superconducting qubits. Here we present a unified impedance theory that accounts for quasiparticle energy loss in circuit regions both far from and near to (across) junctions. Our theory leverages the recent experimental demonstration that the excess quasiparticles are in quasiequilibrium [Connolly et al., Phys. Rev. Lett. 132, 217001 (2024)] and uses a generalized fluctuation-dissipation theorem to predict the amount of charge and flux noise generated by them. We compute the resulting energy relaxation time T1{T}_{1}T1​ in transmon qubits with and without junction asymmetric gap engineering, and show that quasiparticles residing away from junctions can play a dominant role in the former case. They also may provide an upper limit for resonator quality factors if the density of amorphous two-level systems is reduced. In addition, we show that charge noise from quasiparticles leads to flux noise that is logarithmic in frequency, giving rise to a ``nearly white'' contribution that is comparable to the flux noise observed in flux qubits. This contrasts with amorphous two-level systems, whose associated flux noise is shown to be super-Ohmic. We discuss how this quasiparticle flux noise can limit ${T}_{2}^{\ensuremath{\ast}}$ coherence times in flux-tunable qubits. The final conclusion is that asymmetric gap engineering can greatly reduce noise and increase coherence times in superconducting qubits.