Systematic Characterization of Transmon Qubit Stability with Thermal Cycling

TL;DR

The paper addresses the problem of long-term stability in superconducting qubits under repeated thermal cycling. It analyzes a longitudinal dataset of 27 transmon qubits over four thermal cycles spanning roughly nine months and introduces the $T_1$ Spectral Topography Fidelity ($T_1$-STF) to quantify changes in the TLS defect landscape via time-frequency relaxation maps. The results establish a clear stability hierarchy: intrinsic parameters like $f_{01}$ and the baseline $T_1$ are robust to thermal stress, while the TLS environment and flux offsets undergo strong cycle-to-cycle reconfiguration, with a single cycle effectively resetting the spectral landscape as if thousands of hours of cryogenic diffusion occurred. These findings highlight the need for automated recalibration in scalable quantum processors and point to controlled thermal cycling as a potential, probabilistic reset strategy for problematic defect configurations.

Abstract

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 ($T_1$) 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 $T_1$ 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.

Figures (4)

• Figure 1: Systematic characterization of parameter stability across four thermal cycles for 11 transmon qubits (Q1--Q11). (a) Evolution of the maximum qubit frequency deviation, $\Delta f_{01}^{\max}$. Values are relative to the thermal cycle-1 baseline. (b) Evolution of the absolute sweet-spot flux bias offset, $\Delta I_{b}^{\max}$. The colored dashed lines track individual qubits, revealing stochastic fluctuations.
• Figure 2: Statistical characterization of energy relaxation time ($T_1$) stability. (a) Inter-cycle $T_1$ stability. For each qubit, the bar height represents the mean $T_1$ value calculated from multiple measurement sessions conducted within a single thermal cycle. The star marker ($*$) indicates the maximum $T_1$ value observed among those sessions in the same cycle. (b) Intra-cycle $T_1$ stability. For each qubit, the multiple bars represent individual measurement sessions taken sequentially within one thermal cycle. For each session (bar), its height corresponds to the mean $T_1$, and the associated star marker denotes the maximum $T_1$ measured within that specific session.
• Figure 3: Comparison of frequency-dependent energy relaxation ($T_1$) landscapes. (a) Raw time-frequency spectrograms of the excited state probability $p_1$ comparing data from thermal cycle-4 (left panel) and thermal cycle-3 (right panel). The vertical axis represents the qubit frequency $f_{01}$, and the horizontal axis represents the delay time $\tau$. (b) Raw time-frequency spectrograms of $p_1$ from two independent measurements within thermal cycle-3. (c) Z-score normalized $p_1$ maps corresponding to (a). (d) Z-score normalized $p_1$ maps corresponding to (b).
• Figure 4: Quantitative analysis of spectral stability using the $T_1$ STF, $\rho$. (a) Intra-thermal cycle temporal evolution of $\rho$. $\Delta t$ represents the time interval between two measurement sessions within the same thermal cycle. The markers distinguish the datasets from thermal cycle-2 (stars), thermal cycle-3 (triangles), and thermal cycle-4 (circles), while colors correspond to different qubits. The horizontal dashed gray line marks the mean fidelity level of the inter-thermal cycle data (from panel b), representing the baseline of a randomized environment. (b) Inter-thermal cycle reproducibility. The scatter plot displays the $T_1$-STF calculated between maps of the same qubit taken from adjacent thermal cycles (thermal cycle-2 vs. 3, and thermal cycle-3 vs. 4). The consistently low values ($\rho \sim 0.3$) indicate that the microscopic defect landscape is effectively uncorrelated after a thermal cycle.