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Adaptive spectroscopy reveals qubit defects switching and drifting on second timescales.

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2026-08-04 15:21 UTC pith:QVSLYFIN

load-bearing objection Likely real observation of seconds-scale TLS dynamics, but the quantitative timescales are not secure without a static-TLS null control. the 3 major comments →

arxiv 2608.02086 v1 pith:QVSLYFIN submitted 2026-08-03 quant-ph cond-mat.mes-hall

Adaptive Spectroscopy of Fast Two-Level-System Dynamics in Superconducting Qubits

Fabrizio Berritta , David Pahl , Lukas Pahl , William P. Banner , Gabriel Cutter , Jan A. Krzywda , Spencer Weeden , Shravan Patel
show 10 more authors
Paul Buttles Stanislav Eilhart Michael Gingras Bethany M. Niedzielski Robert McDermott Mollie E. Schwartz Kyle Serniak Max Hays Jeffrey A. Grover William D. Oliver
This is my paper
classification quant-ph cond-mat.mes-hall
keywords two-level systemsspectral diffusiontelegraphic switchingadaptive spectroscopysuperconducting qubitstransmonrandomized benchmarkingrelaxation rate
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper claims that in flux-tunable superconducting qubits, individual two-level-system defects change their transition frequency on timescales of seconds—roughly 300 times faster than conventional nonadaptive spectroscopy has been able to see. Using an FPGA-based adaptive Bayesian estimator of the qubit decay rate, the authors produce time-resolved maps of relaxation rate versus frequency and time, and extract a telegraphic switching time of about 2.2 seconds and a spectral diffusivity of about 0.93 MHz²/s. They also interleave randomized benchmarking and find that gate infidelity tracks the relaxation-rate fluctuations when the qubit is biased on a TLS resonance. If correct, these results mean that TLS-aware calibration and error mitigation in superconducting processors must operate on much shorter timescales than the hours-long intervals currently used.

Core claim

The central discovery is that TLS-induced energy-relaxation peaks in flux-tunable transmons are not static on the timescales of conventional spectroscopy: a single TLS switches between two transition frequencies with correlation time 2.2 seconds, and another TLS diffuses in frequency with diffusivity 0.93 MHz²/s. These dynamics become observable because each point in the relaxation-rate map is obtained in about 1.5 ms by adaptive Bayesian estimation, making a full sweep of 500 frequencies take about 0.78 seconds. The authors argue that the same fast dynamics appear in two independently fabricated device platforms, and that the fluctuation of the relaxation rate at a TLS resonance is correlat

What carries the argument

The key machinery is the real-time adaptive Bayesian estimator of the decay rate Γ1, implemented on an FPGA. The controller stores the posterior over Γ1 as a two-parameter distribution, chooses each probe wait time τ = 0.1/Γ̂ from the current estimate, updates after every single-shot readout, and reinitializes the prior at each flux point. Repeated sweeps of the flux-tunable qubit frequency turn these estimates into time-resolved TLS maps; a two-state hidden Markov model and an Ornstein-Uhlenbeck fit to the tracked trajectory then convert the maps into a switching time and a diffusivity.

Load-bearing premise

The results stand or fall on whether the adaptive estimator's Γ̂ values at N=30 probe cycles faithfully reflect the qubit's true decay rate at each frequency point; if estimator noise is mistaken for TLS motion, the inferred switching and diffusion are artifacts.

What would settle it

Repeat the same adaptive sweep while the qubit is parked on a TLS that is independently known to be static, for example verified by repeated conventional T1 measurements at much slower sampling; if the adaptive map still shows telegraphic switching or diffusion of that feature, or if the extracted timescales shift when N is raised from 30 to several hundred, the reported dynamics are tool artifacts rather than TLS motion.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • TLS-induced relaxation fluctuations in flux-tunable transmons occur on seconds timescales, so standard T1 tracking with minutes-to-hours sampling averages over the very dynamics that limit gate performance.
  • Spectroscopy with sub-second sampling can map these dynamics across a 500 MHz band in under a second per sweep, making two-dimensional TLS maps practical for routine qubit characterization.
  • The same seconds-scale dynamics appear in two independently fabricated, differently architected devices, suggesting a generic property of current transmon TLS environments rather than a single-device quirk.
  • Gate infidelity measured by randomized benchmarking tracks the relaxation-limited prediction when the qubit is on a TLS resonance, while a few MHz away the correlation vanishes, so fast TLS motion is a real gate-error contributor.
  • The low-latency online estimate of Γ1 is fast enough to be embedded in adaptive control loops for error mitigation, for example pausing operation when the estimated relaxation rate is high.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Inference: the same interleaving scheme could be extended to multi-qubit operations, where a TLS hitting one qubit during a two-qubit gate may produce correlated errors that the adaptive map would reveal in real time.
  • Inference: if confirmed on more devices, the measured diffusivity of about 0.9 MHz²/s and switching rates provide quantitative targets for microscopic models of TLS spectral diffusion, such as coupling to a fluctuating defect bath.
  • Inference: a direct stress test—tracking a known static TLS with the same N=30 estimator settings and with higher N—would separate physical TLS motion from estimator-induced fluctuations; the paper does not report such a control.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reports an FPGA-implemented adaptive Bayesian relaxation-rate estimation protocol applied to flux-tunable transmon qubits, producing time-resolved TLS loss maps with per-column sampling times near 0.78 s. From these maps it claims (i) telegraphic TLS switching with characteristic time τsw ≈ 2.2 s for one feature, (ii) spectral diffusion with D ≈ 0.93 MHz²/s for a second feature, stated as roughly 300× faster than previous nonadaptive spectroscopy, (iii) qualitatively similar dynamics on a second, independently fabricated device in a different laboratory, and (iv) a statistically significant correlation between tracked Γ1 fluctuations and randomized-benchmarking gate infidelity at the TLS resonance (ρ0 = 0.618) that is absent a few MHz away (ρ0 = −0.0507). The statistical treatment in the Supplemental Material includes an HMM with forward-filtering backward-sampling, credible intervals, block-bootstrap uncertainties, a permutation test, and a 3×3×3 robustness grid.

Significance. If the measurements are faithful, the paper opens a new observational regime: it would show that individual TLSs in flux-tunable transmons undergo telegraphic and diffusive spectral motion on seconds timescales, with direct implications for TLS-aware calibration, qubit screening, and error mitigation. The paper has real strengths: the adaptive estimator achieves a substantial speedup over conventional T1 measurements, the statistical analyses are unusually careful (posterior credible intervals, bootstrap, permutation tests, robustness grid), the central RB correlation is tested against an off-TLS control, and the effect is reproduced on two devices in different laboratories. The main open risk is estimator fidelity: whether the reported fast dynamics could be injected by the adaptive estimation procedure itself rather than by the TLS. This is a correctness question, not a stylistic one, and it is the primary reason the paper needs revision.

major comments (3)
  1. [Sec. II; Supp. Eqs. (S.18)–(S.22), (S.4)–(S.7)] The central claim—that the time-dependent features are physical TLS motion—requires a validation that the estimator does not generate spurious fast fluctuations. The protocol uses only N = 30 adaptive probe cycles per frequency point and reinitializes the prior at every flux-time point. No null control is reported. The problem is concrete: Eq. (S.18) subtracts the time median at each frequency, so a perfectly static TLS is removed by construction and only estimation noise remains; the Viterbi tracker of Eq. (S.19) will then produce a center-frequency trajectory even for a static TLS, and fitting its MSD to the OU form of Eq. (S.22) will return a nonzero D. Similarly, the two-component Gaussian HMM of Eqs. (S.4)–(S.7) can split a noise-only score sequence into two clusters and yield a nonzero switching rate. The off-TLS RB control in Supp. Sec. IV validates the correlation analysis, not t
  2. [Fig. 2; Eqs. (S.3), (S.14), (S.23)] The two headline numbers are each extracted from a single TLS feature, and the frequency bands B0 and B1 in Eq. (S.3) are chosen after inspecting the same data. The abstract and discussion state these as 'a characteristic timescale of a few seconds' and D ≈ 0.9 MHz²/s, which reads as a general property of TLS dynamics. The cross-device reproducibility in Fig. 3(a) is qualitative and is not analyzed with the same HMM/OU pipeline. A single feature is sufficient for an observation, but for a claimed characteristic timescale the authors should either apply the same analysis to all resolvable features across both devices and report the distribution, or explicitly temper the wording to 'one observed feature' for each quantitative value. The post hoc band choice should also be acknowledged as a selection effect; the current uncertainty intervals (S.14) and (S.23) do not include this selection.
  3. [Supp. Sec. II C] The Allan-deviation comparison is described in the text as an 'independent check' of the HMM rate, but it is not independent: the credible band in Fig. S7 is generated by simulating trajectories from the posterior draws of (k01, k10), so the agreement of the empirical curve with that band is a posterior predictive consistency check, not a validation against a null or against an independent estimator. This does not invalidate the HMM analysis, but the wording should be corrected, and the analysis should be supplemented by the null control requested above before the Allan-deviation curve can be used as supporting evidence.
minor comments (5)
  1. [Sec. III A; Supp. Sec. III] The 300× comparison with previous diffusivities should be made reproducible: please give the exact previous D values used, the conversion to the same short-time MSD convention, and the references for each number. As written, this claim is difficult to verify.
  2. [Supp. Eq. (S.4) and Fig. S3] The raw band-score correlation ρ = −0.36 and integrated-weight correlation ρ = −0.52 are not exact conservation checks. The text should avoid implying quantitative spectral-weight transfer between the two TLS states unless a conservation test with uncertainties is provided.
  3. [Fig. 3(b)] The moving-average correlation is computed after smoothing with a 5 s window. This is appropriate for trend-level comparison, but the p-value should be interpreted as testing correlation of the smoothed traces, not of the raw single-repetition values. A sentence clarifying this would help.
  4. [Abstract and Sec. IV] The phrase 'redefine the timescales relevant to TLS-aware characterization' is stronger than the single-feature evidence supports. I suggest a more measured formulation such as 'reveal a previously inaccessible regime.'
  5. [General] A data-availability statement and, if possible, release of the analysis code would strengthen reproducibility, given that the full pipeline (smoothing, median subtraction, Viterbi tracking, HMM, bootstrap) is described only in prose.

Circularity Check

0 steps flagged

No significant circularity: empirical measurement with independent cross-checks; self-cited estimator is an external tool.

full rationale

The paper's central claims are empirical observations of TLS dynamics, not derivations from assumptions. The adaptive estimator is taken from the authors' prior work (Ref. [27]), but that prior work is a published, independently validated measurement method; using it does not make the observed dynamics circular, because the TLS maps are new data and are not constructed to equal the estimator's assumptions. The spectral-diffusion analysis fits an OU model to the MSD of a Viterbi-tracked trajectory, and the telegraphic analysis fits a two-state HMM; these are standard descriptive model fits, not predictions forced by the choice of model, and the paper includes robustness checks and an Allan-deviation cross-check. The RB correlation compares measured gate infidelity to an independently estimated relaxation-limited contribution from interleaved T1 data, with an off-TLS null control; it is not a fit to the same data. The absence of a static-TLS null control is a potential correctness risk (estimator noise could masquerade as dynamics), but it is not a circularity: no equation in the paper reduces a claimed prediction to an input by definition.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The paper introduces no new physical entities. Its accounting rests on a set of analysis choices (OU model, Viterbi penalty, HMM bands) and on the fidelity of the prior adaptive method. The central measured quantities D and tau_sw are outputs of fits, not free parameters, but the analysis hyperparameters are listed above.

free parameters (5)
  • OU correlation time tau_c = 32 s (68% CI 21-45 s; 95% CI 13-61 s)
    Fitted to the MSD of the tracked TLS trajectory in the OU model; a model output, not a central claim.
  • Viterbi jump penalty lambda = 10
    Chosen by hand for trajectory extraction; robustness grid (5, 10, 20) shows modest effect, so it is not critical.
  • Bayesian wait-time constant c = 0.1
    From Ref [27]; sets the adaptive wait time tau=c/hat_Gamma1. Not fitted here, but load-bearing for the estimator's behavior.
  • Telegraphic band edges B0, B1 = [-335,-285] MHz and [-230,-185] MHz
    Chosen post hoc from the data to define the two TLS states; HMM results depend on this choice, and no band sensitivity analysis is provided.
  • HMM emission and transition parameters = Fitted by Baum-Welch (500 iterations)
    Gaussian means, covariances, and transition matrix fitted to the band-score sequence; part of the statistical analysis, not the physics claim per se.
axioms (6)
  • domain assumption Exponential-decay likelihood with misclassification probabilities alpha and beta
    The Bayesian update assumes a single exponential decay during each wait time; if TLS switching occurs within a probe cycle, estimates would be biased.
  • domain assumption Quasistatic approximation for TLS during each probe cycle
    The likelihood treats Gamma1 as constant over the ~10-100 us wait time; the authors assume this holds.
  • ad hoc to paper Two-parameter posterior approximation of Ref [27] is faithful
    The FPGA stores only two parameters for the posterior; this is a simplification from the prior work and is not independently validated here.
  • domain assumption Ornstein-Uhlenbeck model for spectral diffusion
    The MSD is fit to the OU form MSD=2D/gamma (1 - exp(-gamma tau)); deviations could bias D.
  • domain assumption Viterbi tracker with penalty lambda recovers the true TLS trajectory
    The extracted frequency trajectory is the output of a regularized optimization; robustness grid suggests stability.
  • domain assumption Observed fluctuations are TLS dynamics rather than qubit-frequency noise
    Interleaved Ramsey checks keep frequency drift within +/-1 MHz, supporting the interpretation but not eliminating other noise sources.

pith-pipeline@v1.3.0-daily-deepseek · 19037 in / 13973 out tokens · 94986 ms · 2026-08-04T15:21:25.867723+00:00 · methodology

0 comments
read the original abstract

Parasitic two-level-system (TLS) defects are a major source of energy relaxation and temporal instability in superconducting quantum processors. Our sub-second adaptive spectroscopy reveals telegraphic switching of TLSs with a characteristic timescale of a few seconds and spectral diffusion with diffusivity $D \approx 0.9~\mathrm{MHz}^2/\mathrm{s}$. These timescales are about $3 \times 10^2$ times faster than what is observed in conventional nonadaptive spectroscopy, which typically requires hours of measurement time. We resolve such fast dynamics on a field-programmable gate array (FPGA)-based controller that enables measurement of frequency- and time-resolved relaxations with sub-second temporal resolution in flux-tunable superconducting qubits. We observe similar defect dynamics across multiple qubits in independently fabricated devices measured in different laboratories. We correlate TLS-induced fluctuations with gate-level errors using randomized benchmarking. Our results reveal a previously inaccessible regime of frequency-resolved TLS dynamics and redefine the timescales relevant to TLS-aware characterization and calibration of superconducting quantum processors.

Figures

Figures reproduced from arXiv: 2608.02086 by Bethany M. Niedzielski, David Pahl, Fabrizio Berritta, Gabriel Cutter, Jan A. Krzywda, Jeffrey A. Grover, Kyle Serniak, Lukas Pahl, Max Hays, Michael Gingras, Mollie E. Schwartz, Paul Buttles, Robert McDermott, Shravan Patel, Spencer Weeden, Stanislav Eilhart, William D. Oliver, William P. Banner.

Figure 1
Figure 1. Figure 1: (c), which is a zoom-in of the data in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) shows the controller estimates Γˆ 1 in Q1. The controller estimates Γ1 using N = 30 probe cy￾cles [47] at each value of Φ, sweeping the flux so that fQ1 spans a 500 MHz detuning range from the upper degen￾eracy point in 1 MHz steps. Each Γ1 estimate requires only about 1.5 ms of laboratory time. Every frequency sweep is interleaved with a Ramsey experiment at Φ = 0 to verify afterwards that the qubit f… view at source ↗
Figure 3
Figure 3. Figure 3: (a), is qualitatively similar in terms of timescales to [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

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