Systematic Characterization of Transmon Qubit Stability with Thermal Cycling

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.

💡 Research Summary

This paper presents a systematic, year‑long study of the stability of 27 frequency‑tunable transmon qubits subjected to four complete thermal cycles (warm‑up to room temperature and cooldown to ~20 mK). The authors first examine static device parameters: the maximum transition frequency (f_max) and the sweet‑spot flux bias (I_max). Across all cycles, f_max varies by less than ±20 MHz (≈0.5 % of a typical 4.5 GHz transmon), indicating that the Josephson junctions, capacitors, and overall chip geometry remain structurally intact despite repeated thermal expansion and contraction. In contrast, I_max shows stochastic shifts up to 0.12 Φ₀ between cycles, reflecting reconfiguration of trapped magnetic flux and flux‑trapping sites induced by thermal cycling.

Energy‑relaxation times (T₁) are then measured. While the baseline T₁ (the average over many measurements) stays roughly constant across cycles—high‑coherence qubits maintain ~30–35 µs—the intra‑cycle spread between mean and maximum T₁ can be large (e.g., Q8 reaches ~80 µs in a “clean” moment). This spread is attributed to the interaction of the qubit with a dense bath of weakly coupled two‑level system (TLS) defects that drift in frequency over time, occasionally resonating with the qubit and increasing loss.

To move beyond single‑point T₁ data, the authors acquire frequency‑dependent relaxation spectrograms: two‑dimensional maps of excited‑state population p₁(τ, ω) as a function of delay time τ and qubit frequency ω. Each spectrogram is treated as a matrix Φ, Z‑score normalized, and compared using Euclidean distance δ. An empirical scaling factor α converts δ into the T₁ Spectral Topography Fidelity (STF), ρ = α δ. High ρ (≈0.8–0.9) indicates that two spectrograms share the same TLS configuration, while low ρ (≈0.3) signals a substantial reconfiguration.

The analysis reveals that spectrograms taken within the same thermal cycle are highly reproducible (ρ ≈ 0.8), whereas spectrograms from different cycles are essentially uncorrelated (ρ ≈ 0.3). Moreover, the inter‑cycle ρ matches the fidelity observed after >1000 hours of continuous low‑temperature evolution, implying that a single thermal cycle randomizes the TLS landscape to the same extent that would otherwise require months or years of slow spectral diffusion at millikelvin temperatures. The authors argue that the thermal energy supplied during warm‑up overcomes high energy barriers in the TLS configuration space, providing a “hard reset” of the microscopic defect environment.

In summary, the study establishes a clear hierarchy of stability for superconducting hardware: intrinsic parameters (junction energies, capacitances, baseline T₁) are robust against repeated thermal cycling, while environmental variables (flux offsets, TLS defect distribution) are highly stochastic and reset by each cycle. Consequently, large‑scale quantum processors will need automated calibration routines and possibly scheduled thermal cycles to manage the evolving noise landscape, ensuring reliable operation over the device’s lifetime.