{"id":"089df848-444d-4e9c-81cd-6f3310535bd6","arxiv_id":"2608.10087","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Electric-field sweeps show the defect bath of a transmon qubit retains memory for about five seconds, attributed to slowly relaxing field-polarised charge fluctuators.","lead":"Repeated electric-field sweeps reveal that defects near a superconducting qubit remember the field history for seconds, far longer than the defects' own lifetimes. The behavior is explained by slow charge fluctuators, and it matters because long memory can turn qubit noise into correlated, non-Markovian errors that error correction must handle.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed 5.4 s equilibration time is not independently supported: it comes from a two-parameter fit to branch probabilities under Eq. (1), whose single-exponential, voltage-independent form is unchecked.","rationale":"The reader identified the same load-bearing weakness: the 5.4 s timescale is a model-dependent fit using Eq. (1), with V_sym and tau_eq fitted to the very branch-probability data they are then used to interpret. My independent reading of the paper confirms that this is the least secure link in the central quantitative claim. The qualitative memory effect, evidenced by reproducible sweep-direction asymmetries in Fig. 1(c), the three forms of hysteresis in Fig. 2(d-f), and the sweep-rate dependence in Fig. 4, is robust and well supported by repeated experiments over tens of hours. The CF explanation is plausible and is consistent with the observed threshold-like switching in Fig. 3, but no direct observation of the CF is made, and no alternative microscopic model is quantitatively ruled out. Therefore the conclusion that the defect bath 'can retain memory for several seconds' should be regarded as conditional, pending a direct or model-robust determination of the timescale. This does not weaken the existence of non-Markovian memory, but it does mean the specific equilibration time should not be cited as established. The remedy is straightforward: provide error-barred branch probabilities, a model comparison or direct relaxation measurement, and public data or analysis code. Since the reader's verdict was already CONDITIONAL and my concern supports rather than alters that assessment, the verdict should remain unchanged.","tokens_in":10004,"tokens_out":3232,"duration_ms":37961,"concrete_test":"Reanalyse the raw P_e maps behind Fig. 4 with an explicit likelihood model that allows a voltage-dependent switching rate, e.g. gamma(V) = gamma0 exp(-(V_sym - V)/V0), fit to the 'left'/'right'/'both' classifications with bootstrap uncertainties from the single-shot P_e data, and compare this model against Eq. (1) via, say, a likelihood-ratio test. If the inferred equilibration time at V_sym remains within a factor of about 2 of 5.4 s under the generalised model and the exponential model is not strongly rejected, the seconds-timescale claim is supported. A complementary decisive check is to hold the gate voltage just below V_sym for variable waiting times before reading out the TLS branch, measuring P_R(t) directly and fitting its decay; this would test the single-exponential assumption without relying on sweep-rate interpolation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline quantitative claim is the CF equilibration time tau_eq = 5.4 +/- 0.3 s, extracted from Eq. (1): after crossing the CF symmetry point V_sym, the probability of remaining in the initial CF state decays as exp(-(V_sym - V_g)/(v_sweep tau_eq)). This expression assumes (i) a single exponential relaxation with a constant tau_eq, (ii) no voltage dependence of the switching barrier or rate, and (iii) that the CF crossing of V_sym is the only process governing the observed branch probability. In the data analysis of Fig. 4(c,d), V_sym and tau_eq are fitted to the same branch-location probabilities they are then used to interpret, and those probabilities are obtained from a classification of TLS-1 as 'left', 'right', or 'both' without a stated threshold or error model. No uncertainties from the classification, no model comparison, and no raw data or code are provided, so the quoted +/-0.3 s reflects only the fit standard error, not model uncertainty. If the switching is instead produced by multiple interacting fluctuators, by a field-dependent barrier, or by a different microscopic process such as TLS-TLS coupling or voltage-induced trapping dynamics, the inferred tau_eq would not correspond to a physical CF equilibration time. The existence of sweep-direction-dependent resonance positions and probabilistic jumps is convincing evidence of memory in the defect bath, but the specific seconds timescale is not uniquely determined by the presented evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":10422,"tokens_out":5145,"duration_ms":44574,"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":[{"comment":"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.","section":"Timescales of memory effects, Eq. (1)"},{"comment":"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.","section":"Timescales of memory effects, Fig. 4(c,d)"},{"comment":"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.","section":"Timescales of memory effects, Eq. (1)"}],"minor_comments":[{"comment":"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.","section":"Fast defect environment mapping"},{"comment":"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.","section":"Individual TLS tracking"},{"comment":"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.","section":"Phenomenological mechanism"},{"comment":"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'.","section":"Timescales of memory effects"}],"recommendation":"major_revision","confidential_remarks":"The experimental observation of hysteresis is solid and is the paper's main strength. The primary concern is the model-dependent extraction of the 5.4 s timescale, which is not sufficiently supported. I recommend seeking a revision that either provides additional validation of Eq. (1) or downgrades the quantitative claim to a qualitative statement. The paper is otherwise well-organized and the topic is of interest to the journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: this paper gives you direct, repeated evidence that the TLS defect environment of a transmon keeps a memory of its electric-field history for seconds. The sweep-direction asymmetry in the relaxation maps, the double crossings, and the probabilistic jumps all show up clearly and reproduce over tens of hours. That qualitative result is robust and worth taking seriously. The paper's quantitative claim, tau_eq = 5.4 +/- 0.3 s, is a different matter: it comes from fitting Eq. (1), a single-exponential, voltage-independent relaxation model, to the very branch probabilities it is used to interpret. The quoted error is only the fit standard error, and no error bars, raw data, or code are provided. The stress-test note is right about that. Where the paper earns credit: the fast Pe-mapping method is a real practical improvement, the classification of conventional, reappearance, and probabilistic hysteresis is genuinely new as a catalog of behaviors, and the interleaved sweep-rate experiments are the right way to get at a timescale. The authors are also honest about the model's limitations - they explicitly call it approximate and note that it ignores voltage-dependent barriers. That honesty matters. The central observation does not depend on the model; the seconds timescale does. So the soft spot is real but it is a soft spot in the interpretation, not in the data. The citation pattern looks fine, and the connection to prior TLS hysteresis and SET charge-fluctuator work is properly acknowledged. The authors are not overselling QEC impact; they just note possible implications. Who gets value from this: experimentalists working on TLS noise, qubit calibration drift, and anyone trying to understand non-Markovian noise sources in superconducting devices. The qualitative memory effect is the takeaway; the specific tau_eq should be treated as provisional until it is confirmed by a direct relaxation measurement or a model comparison. This deserves a serious referee. The referees should ask for error-barred probabilities, a test of whether the relaxation is actually single-exponential, and ideally public data or code. But those requests are about tightening a good result, not about fixing a broken one.","headline":"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.","tokens_in":709,"tokens_out":811,"would_cite":true,"duration_ms":22241,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["two-level systems","charge fluctuators","transmon qubit","hysteresis","memory effects","non-Markovian noise","electric-field tuning","relaxation times"],"falsifier":"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.","tokens_in":9780,"feed_emoji":"⏳","tokens_out":7766,"duration_ms":68402,"temperature":0.7,"pith_summary":"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.","feed_headline":"Defect bath remembers its electric-field history for seconds","feed_subtitle":"Two-level-system resonances imply a ~5 s charge-fluctuator equilibration time, far beyond qubit coherence.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the standard method of mapping TLS defects by measuring qubit relaxation enhancement as a function of applied electric field.","marker":"[7]"},{"why":"Provides the basis for using the excited-state probability $P_e$ after a delay as a fast proxy for the relaxation rate $\\Gamma_1$.","marker":"[9]"},{"why":"Gives recent evidence for long-lived memory in a superconducting qubit's environment, providing the precedent the paper extends to seconds-scale timescales.","marker":"[16]"},{"why":"Establishes the conventional-hysteresis mechanism by which a slow field-polarised charge fluctuator shifts a TLS resonance depending on sweep direction.","marker":"[22]"},{"why":"Provides the interacting tunneling model in which field-polarised charge fluctuators with large barriers are coupled to TLSs.","marker":"[24]"},{"why":"Demonstrates very long charge-fluctuator equilibration times in single-electron transistors, the experimental precedent for estimating such timescales from threshold-crossing behaviour.","marker":"[25]"}],"fun_headline_variants":["Defect bath holds electric-field memory for seconds","Superconducting qubit's defect bath shows 5-second memory","Qubit's defect environment retains electric history for ~5 s","Memory effects in defect bath persist for seconds, study shows"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Defect bath holds electric-field memory for seconds","Superconducting qubit's defect bath shows 5-second memory","Qubit's defect environment retains electric history for ~5 s","Memory effects in defect bath persist for seconds, study shows"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000648,"raw_usage":{"total_tokens":2920,"prompt_tokens":836,"completion_tokens":2084,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":452,"completion_tokens_details":{"reasoning_tokens":2015}},"tokens_in":452,"tokens_out":2084,"duration_ms":13483,"temperature":1.0,"reasoning_tokens":2015,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:13:58.747046+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Lisenfeld, A","cited_arxiv_id":null,"evidence_quote":"Supplies the standard method of mapping TLS defects by measuring qubit relaxation enhancement as a function of applied electric field."},{"cited_title":"Carroll, S","cited_arxiv_id":null,"evidence_quote":"Provides the basis for using the excited-state probability $P_e$ after a delay as a fast proxy for the relaxation rate $\\Gamma_1$."},{"cited_title":"Gosling, D","cited_arxiv_id":null,"evidence_quote":"Gives recent evidence for long-lived memory in a superconducting qubit's environment, providing the precedent the paper extends to seconds-scale timescales."},{"cited_title":"Faoro and L","cited_arxiv_id":null,"evidence_quote":"Provides the interacting tunneling model in which field-polarised charge fluctuators with large barriers are coupled to TLSs."},{"cited_title":"Pourkabirian, M","cited_arxiv_id":null,"evidence_quote":"Demonstrates very long charge-fluctuator equilibration times in single-electron transistors, the experimental precedent for estimating such timescales from threshold-crossing behaviour."}],"review_version":1}