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REVIEW 3 major objections 4 minor 42 references

Long-lived memory effects in the defect bath of superconducting qubits

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Gate-voltage sweeps show that the TLS defect environment of a transmon qubit can remember its electric-field history for several seconds, with a charge-fluctuator equilibration time of about five seconds.

desk verdict Solid evidence that a transmon's defect bath retains field history for seconds; the 5.4 s number is a model-dependent estimate, not a direct measurement, but the qualitative memory claim holds. read the letter →

arxiv 2608.10087 v1 pith:QDNKZ6YR submitted 2026-08-10 quant-ph

Abhishek Agarwal , Masum Uddin , Shroya Vaidya , Lachlan P. Lindoy , Ehsaneh Daghigh Ahmadi , Tobias Lindström , Sebastian E. de Graaf , Ivan Rungger This is my paper · ORCID
classification quant-ph
keywords two-levelsystemschargefluctuatorstransmonqubithysteresismemoryeffectsnon-Markoviannoiseelectric-fieldtuningrelaxationtimes
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Using a fast relaxation-probability mapping of a transmon qubit under repeated gate-voltage sweeps, the paper shows that individual two-level-system (TLS) defects respond to the electric field in a history-dependent way: their resonance voltages differ between upward and downward sweeps, occasionally cross the qubit resonance twice in one direction, and sometimes jump probabilistically between positions. The paper argues that these hysteresis effects, reproduced over many hours, cannot be explained by independent short-lived TLSs and are instead the signature of field-polarised charge fluctuators in the defect bath with a long-lived metastable configuration. From the sweep-rate dependence of the probabilistic jumps it extracts an effective charge-fluctuator equilibration time of $\tau_{\rm eq}=5.4\pm0.3$ s, orders of magnitude longer than the qubit lifetime. If correct, the defect environment is not a Markovian bath but contains correlated, slowly evolving degrees of freedom, which matters for qubit calibration, stabilisation, and quantum error correction.

What carries the argument

The central object is a field-polarised charge fluctuator, a two-state defect with a large tunnelling barrier whose asymmetry energy shifts linearly with gate voltage, $\epsilon_{\rm CF}(V_g)=\epsilon_{\rm CF}(0)+\nu_{\rm CF}V_g$. As the voltage sweeps through the fluctuator's symmetry point, the occupied configuration becomes metastable, so the shift it imposes on a nearby TLS depends on sweep direction and on how much time has elapsed since the crossing. The quantitative workhorse is Eq. (1), a single-exponential survival probability for the initial CF state, fitted to the sweep-rate-dependent branch probabilities of TLS-1 to extract $V_{\rm sym}\sim-4.6$ V and $\tau_{\rm eq}=5.4$ s.

What would settle it

Perform the same interleaved sweep-rate experiment over a wider range of sweep rates and check whether the left-branch probability for TLS-1 is exactly $\exp[-(V_{\rm sym}-V_g)/(v_{\rm sweep}\tau_{\rm eq})]$ with a single $V_{\rm sym}$ and $\tau_{\rm eq}$ across all rates and both sweep directions. Alternatively, park the gate voltage at a point just past $V_{\rm sym}$ and watch the TLS branch population relax in real time: the single-CF model predicts a single exponential with $\tau_{\rm eq}\approx5$ s, while multi-fluctuator or voltage-dependent-barrier mechanisms would show clear deviations from that form.

Watch

Extended reading notes

Core claim

The central claim is that the microscopic defect environment of a superconducting transmon retains a memory of its electric-field history for several seconds. The evidence is the reproducible hysteresis in the gate-voltage positions of individual TLS resonances, including conventional sweep-direction dependence, 'reappearance' events where a TLS crosses resonance twice in one sweep direction, and probabilistic jumps that become more frequent at slower sweep rates. The paper attributes these observations to field-polarised charge fluctuators with large tunnelling barriers that are metastable near their symmetry point; after the sweep passes $V_{\rm sym}$, the probability that a fluctuator has not yet switched is modelled as $\exp[-(V_{\rm sym}-V_g)/(v_{\rm sweep}\tau_{\rm eq})]$, giving $\tau_{\rm eq}\simeq5$ s. The same mechanism explains why the two dominant TLSs switch together, since they share the same electric environment.

Load-bearing premise

The quantitative five-second timescale stands or falls on the assumption that, after the charge fluctuator crosses its symmetry point, its probability of remaining in the initial configuration decays exponentially with one fixed equilibration time that does not change as the voltage continues to sweep; if the switching is driven by multiple interacting fluctuators or by a voltage-dependent barrier, the fitted $\tau_{\rm eq}$ is not the true memory time.

Editorial extensions

If this is right

  • The defect environment of a transmon carries temporally correlated, non-Markovian noise that persists for seconds, so any protocol that repeatedly sweeps electric fields must account for the field history.
  • Qubit stabilisation and error-correction schemes that rely on electric-field tuning of TLS defects will need to incorporate these long memory timescales into their calibration schedules.
  • The fast $P_e$ mapping method can track individual fluctuator dynamics over tens of hours, enabling microscopic studies of the coupled defect bath rather than ensemble averages.
  • Because TLS-1 and TLS-2 switch together, the common electric environment implies that a single charge fluctuator can shift multiple TLSs, so defect interactions matter for noise modelling.
  • The timescale $\tau_{\rm eq}\sim5$ s is many orders of magnitude larger than typical TLS coherence and qubit $T_1$, placing the memory process in a distinct slow regime.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If confirmed on other devices, the seconds-long charge-fluctuator memory implies that stationary-noise characterisations of TLS baths underestimate their non-Markovian content, because the relevant correlations live in the field-history dependence, not in spontaneous fluctuations.
  • A testable extension is to hold the gate voltage fixed just beyond $V_{\rm sym}$ and observe the TLS branch population relax directly; the paper's single-CF model predicts an exponential approach with a fixed $\tau_{\rm eq}$, while a more complex bath would show stretched or multi-exponential relaxation.
  • The same hysteretic mechanism may explain some of the device-to-device and day-to-day drift in qubit relaxation times reported elsewhere, since a slowly equilibrating charge fluctuator could produce correlated shifts in TLS resonance frequencies over long times.
  • Multi-gate or scanning-probe variants of this method could map the spatial distribution of charge fluctuators and test whether the inferred $\tau_{\rm eq}$ is a property of individual fluctuators or of the local environment.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper presents an experimental study of two-level-system (TLS) defects in a transmon qubit, mapping the qubit relaxation probability as a function of a swept gate voltage. It reports that individual TLS resonance positions exhibit hysteresis (sweep-direction dependence), double crossings, and probabilistic jumps, with these behaviors persisting across tens of hours. The authors attribute these effects to coupling between TLS defects and slow, field-polarised charge fluctuators (CFs), and they extract an equilibration time of tau_eq = 5.4 +/- 0.3 s from a fit to a two-parameter model (Eq. (1)). The paper argues that the defect bath contains long-lived internal degrees of freedom that produce temporally correlated, non-Markovian noise relevant for error correction and qubit stabilisation.

Significance. If the quantitative timescale is correct, this is a significant advance: it demonstrates that TLS environments in superconducting qubits can retain memory for seconds, far beyond typical TLS coherence times, and provides a microscopic mechanism (field-polarised charge fluctuators). The fast mapping method is a useful technique for probing defect dynamics. The observed hysteresis itself is a robust, directly evidenced phenomenon and is a valuable empirical contribution regardless of the model details. The paper also offers falsifiable predictions through threshold behavior and sweep-rate dependence, which are partially evidenced in the data.

major comments (3)
  1. [Timescales of memory effects, Eq. (1)] The central quantitative claim of tau_eq = 5.4 +/- 0.3 s is extracted from a two-parameter fit of V_sym and tau_eq to the same branch-probability data that Eq. (1) is used to interpret. The model assumes a single-exponential relaxation with a constant tau_eq and no voltage dependence of the barrier, yet the paper provides no independent test of these assumptions, such as comparing alternative functional forms or checking consistency across different voltage regions or sweep rates. The quoted uncertainty therefore reflects only fit standard error, not model uncertainty, and the 5.4 s number is not robustly supported. To make the timescale claim load-bearing, the authors should either validate the model against independent predictions (e.g., using different TLSs, different voltage offsets, or direct time-domain measurements) or explicitly restrict the claim to a qualitative estimate of seconds.
  2. [Timescales of memory effects, Fig. 4(c,d)] The classification of TLS-1 location as 'Left', 'Right', or 'Both' is not described. No detection threshold for a resonance dip, no voltage tolerance, and no error model are stated, so the probabilities in Fig. 4(c,d) are not reproducible from the manuscript. The authors should specify the algorithm used to classify each sweep and provide the raw data or code, or at least a detailed description of the classification criteria.
  3. [Timescales of memory effects, Eq. (1)] The model in Eq. (1) describes a two-state CF and predicts only the probability of being in state R, but the data include a third category 'Both' where the TLS appears at both locations in a single sweep. The relation between the model and the three-outcome probabilities is unclear. The authors should either extend the model to account for 'Both' events, or explicitly state that sweeps classified as 'Both' are excluded from the fit and show that the fit is insensitive to that choice.
minor comments (4)
  1. [Fast defect environment mapping] The statement that 'a change in the background P_e occurs near ~38 h... does not affect the sweep-direction comparison below' is reassuring but would be strengthened by a brief discussion of how the background was subtracted or normalized.
  2. [Individual TLS tracking] In Fig. 2, the labeling of the highlighted regions in panels (a-c) and the corresponding boxes in (d-f) is not fully explicit; adding the time and voltage ranges of each box would improve readability.
  3. [Phenomenological mechanism] The last paragraph of this section mentions that the CF switching can cause the TLS to go undetected, but this is not quantified or included in the model; it may affect the branch probabilities and should be discussed in the analysis.
  4. [Timescales of memory effects] The paper uses a single strongly coupled TLS (TLS-1) for the quantitative analysis; a statement about how many other defects show similar behavior and whether the same timescale is recovered from them would strengthen the generalization to the 'defect bath'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the memory effect is a direct experimental observation, and the quoted equilibration time is an openly fitted model parameter rather than a prediction forced by the fit.

full rationale

The paper's central claim is the observation of sweep-direction-dependent TLS resonance positions, double crossings, and probabilistic jumps in P_e(V_g), which are read directly from the measured data (Figs. 1(c) and 2) and are not derived from any model. The charge-fluctuator mechanism is introduced as a phenomenological interpretation, and Eq. (1) is explicitly stated as a model in which the probability of the CF remaining in its initial state decays as exp(-(V_sym - V_g)/(v_sweep tau_eq)). The two parameters V_sym and tau_eq are then fitted to the observed branch probabilities, with the paper honestly reporting that the quoted uncertainty is the fit standard error and does not account for model uncertainty. This is parameter estimation, not 'prediction' of a closely related fitted quantity: the hysteresis itself does not depend on the fit, and the paper does not present the 5.4 s value as an independent prediction. The statement that the model 'predicts a sharp onset or termination' is a qualitative consistency check against an observed threshold, not a statistically forced output of the fitted parameters. Self-citations [27] and [28] concern the fast TLS mapping method and non-Markovian noise modelling respectively; neither is load-bearing for the central memory claim, and no uniqueness theorem is imported from the authors' prior work. The model dependence of tau_eq is a legitimate robustness concern, but it is not circularity: the observed memory effects remain a direct experimental finding, and the timescale is a transparently reported fit rather than a quantity made equivalent to its inputs by construction.

Assumptions & free parameters 2 free parameters · 3 assumptions · 1 invented entities

The direct observation (sweep-direction hysteresis, sweep-rate-dependent branch probabilities) is self-contained from the experiment. The interpretation as a field-polarised charge fluctuator is carried by prior literature and by two fitted parameters (V_sym, tau_eq); a single unobserved CF entity is invoked. The central memory effect does not depend on those fitted parameters, but the quantitative timescale does.

free parameters (2)
  • V_sym (CF symmetry point) = -4.6 V (best fit)
    Fitted in Eq. (1) to the sweep-rate-dependent probability that TLS-1 appears on the left or right branch in Fig. 4(c,d). The value is combined with tau_eq to construct the memory model.
  • tau_eq (CF equilibration time) = 5.4 +/- 0.3 s
    Fitted simultaneously with V_sym in Eq. (1); the central claim of seconds-long memory rests on this fitted timescale. The quoted uncertainty is the fit standard error and excludes model uncertainty.
assumptions (3)
  • domain assumption A coupled TLS shifts the qubit relaxation rate only when it is resonant; Pe = exp(-Gamma1 tau_delay) with ideal zero-temperature preparation and measurement.
    Used throughout to convert relaxation probability dips into TLS resonance positions; ignores measurement errors, residual thermal population, and multi-exponential decay.
  • domain assumption Field-polarised charge fluctuators with large tunnelling barriers have metastable localised configurations and linear asymmetry vs voltage: epsilon_CF(Vg) = epsilon_CF(0) + nu_CF Vg.
    Basis of the phenomenological mechanism; taken from prior literature [22,25], not independently measured in this device.
  • ad hoc to paper After crossing the CF symmetry point, the probability the CF remains in its initial state is exp(-t/tau_eq) with a constant tau_eq, as in Eq. (1).
    Introduced for this analysis; it ignores voltage-dependent barrier renormalisation, as the authors explicitly note. The seconds timescale is derived from this assumed functional form.
invented entities (1)
  • Slow field-polarised charge fluctuator (CF) with large tunnelling barrier
    purpose: Explains conventional, reappearance, and probabilistic hysteresis and provides the degrees of freedom for the fitted 5.4 s equilibration time.
    The CF is not directly observed; its state, symmetry point, and switching threshold are inferred from the same qubit relaxation data used to establish the memory effect. It is borrowed from prior SET literature, not invented de novo, but in this paper it functions as an unobserved explanatory entity.

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Pith. "Pith review of Long-lived memory effects in the defect bath of superconducting qubits." pith.science (2026). https://pith.science/paper/QDNKZ6YR

@misc{pith2026260810087,
  author       = {Pith},
  title        = {Pith review of: Long-lived memory effects in the defect bath of superconducting qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QDNKZ6YR}},
  note         = {Machine review of arXiv:2608.10087}
}
read the original abstract

We reveal long-lived memory effects in the defect bath of a superconducting transmon qubit through electric-field tuning of two-level system (TLS) defects coupled to the qubit. Using a fast TLS mapping method we observe several hysteretic effects in the TLS environment with memory timescales of the order of seconds, far beyond the lifetimes of individual TLS defects. The observations can be explained by TLS coupling to electric field-polarised charge fluctuators in the defect bath. Our method enables detailed mapping of the dynamics of the bath's coupled microscopic degrees of freedom and the associated memory effects which can introduce temporally correlated noise. This information may be used to improve qubit-stabilisation and quantum error correction protocols.

Figures

Figures reproduced from arXiv: 2608.10087 by the authors.

Figure 1
Figure 1. FIG. 1. (a) The experimental protocol showing the circuit [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Two sets of repeated experiments are performed with sweep rates 50 Vs [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Zoomed-in view of the results in Fig. 2(a,b) show [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Results of interleaved experiments with different sweep rates [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Reviewed August 14, 2026 · model on record in the stance chip above.