{"id":"00eeaecb-bdf8-4dbc-a505-ad0570cf4492","arxiv_id":"2507.05160","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Valley splitting data alone cannot reliably distinguish disordered from deterministic Si/SiGe quantum wells, but g-factor mapping around valley vortices can recover the needed valley phase.","lead":"The paper shows that standard statistical fits of valley splitting data in silicon spin qubits badly overestimate the deterministic valley coupling in disordered samples, and proposes to fix this by extracting the valley phase from g-factor measurements, using loops around valley vortices for calibration. The proposed method could give quantum well engineers a practical way to identify deterministic versus disorder-dominated valley behavior at scale.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (4) yields only cos phi_v, so the proposed g-factor protocol recovers the valley phase only up to sign; the advertised statistical improvement is demonstrated only for full complex Delta, not for the censored observable actually measured.","rationale":"The reader's weakest_assumption identified both the sign ambiguity in Eq. (4) and the reliance on the companion paper for the g-factor relation. My concern sharpens and prioritizes the sign ambiguity: the paper's Fig. 2(g) itself uses absolute valley phases, and the improved maximum-likelihood result in Fig. 1 uses full complex Delta, not the censored observable that a g-factor measurement can provide. This is an internal gap between the proposed protocol and the statistical demonstration, not merely a disagreement with external consensus. The independent numerical check in Fig. 2(g) is real evidence that higher-order disorder corrections to Eq. (4) are small, and the vortex-density derivation in Sec. S.4 is a useful supporting result; neither resolves the censored-observable issue. The concrete test proposed above would settle whether |Delta_0| and sigma_Delta are identifiable from (E_v, cos phi_v) data with the same reliability as from full complex Delta. Since the reader already returned CONDITIONAL and my concern motivates exactly that condition, no verdict change is needed.","tokens_in":16908,"tokens_out":8343,"duration_ms":106249,"concrete_test":"Re-run the maximum-likelihood analysis of Fig. 1 using only the observables the proposed experiment actually provides: for each dot, draw Delta from Eq. (1), form E_v = 2|Delta| and c = cos(phi_v), noting that the g shift in Eq. (4) is proportional to c. Fit the censored likelihood f_cens(E_v, c; |Delta_0|, phi_0, sigma_Delta) = sum_{s=+-1} f(Delta = (E_v/2)(c + i s sqrt(1-c^2)); |Delta_0|, phi_0, sigma_Delta) to groups of 20 dots, and also to larger groups as in Fig. S.1, then compare the inferred |Delta_0|/sigma_Delta distributions with the salmon full-phase results of Fig. 1. If the censored estimator also suppresses false deterministic classifications for |Delta_0|/sigma_Delta = 0, the sign ambiguity is benign; if it does not, g-factor data from Eq.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing gap is that the proposed observable does not determine the signed valley phase used in the statistical argument. Inverting Eq. (4), g - g0 = -g_tau cos(phi_v) sin(2 theta_B), yields only cos(phi_v), and hence |phi_v| up to the sign of sin(phi_v), because g_tau is real and g0 is a scalar. The paper implicitly concedes this: the error metric in Fig. 2(g) is defined with absolute values, |phi_v^(g)| - |phi_v|. Yet the salmon-color maximum-likelihood demonstration in Fig. 1 that knowledge of phi_v improves estimates is generated from the full complex Delta drawn from Eq. (1), assuming access to both Delta_r and Delta_i, or equivalently |Delta| and signed phi_v. The proposed g-factor protocol supplies |Delta| from E_v and cos(phi_v) from g, but not the sign of sin(phi_v). The likelihood for this censored observable is the sum over the two mirror phases, f_cens(|Delta|, cos phi_v) = sum_{s=+-1} f(Delta = |Delta|(cos phi_v + i s sin phi_v)). Neither the main text nor the supplement analyzes this censored likelihood. It is plausible that the two mirror phases are statistically equivalent for estimating |Delta_0|/sigma_Delta, in which case the sign ambiguity is harmless; but this is not established. The central practical claim, that the g-factor protocol recovers the statistical improvement shown by the salmon data, is therefore unsupported as presented. A secondary consequence is that phi_0 is identifiable only up to sign, though phi_0 is not the primary target of the estimation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies statistical characterization of the complex intervalley coupling Δ = Δ0 + Δδ in Si/SiGe quantum dots, where Δδ is a complex Gaussian describing alloy disorder. Using maximum likelihood estimation on valley splitting Ev alone (a Rician distribution), the authors show that the deterministic component |Δ0| is strongly overestimated in the disorder-dominated regime, even for groups of 1000 dots. They then show, via simulations, that adding knowledge of the valley phase φv substantially improves the estimates. Since φv is not directly measurable, they propose to reconstruct it from g-factor measurements, using the relation g = g0 − gτ cos φv sin 2θB (Eq. (4)), with gτ calibrated by measuring g along a loop enclosing a valley vortex, where the phase winds by ±2π and g visits its extrema. The paper derives the vortex density ρVV = (0.184/ℓ^2) exp(−|Δ0|^2/σΔ^2) and validates the phase reconstruction numerically, reporting small errors. The stated outcome is an experimentally implementable protocol for characterizing valley coupling statistics.","tokens_in":1370,"tokens_out":1853,"duration_ms":113065,"significance":"If the central claim holds, the paper provides a practical characterization tool for Si/SiGe spin qubits, where disorder-dominated valley physics is a known obstacle. The MLE overestimation result is well supported by explicit simulations for group sizes up to N = 1000, and the vortex-density derivation in the Supplementary Materials is careful and consistent with the simulated landscape. The g-factor valley-phase mapping is an original and potentially useful proposal. However, the advertised statistical improvement is demonstrated for the full complex Δ, whereas the proposed g-factor protocol supplies only cos φv; the censored-likelihood analysis needed to close this gap is absent. Because that gap is directly load-bearing for the central practical claim, the paper needs additional work before the protocol can be regarded as established.","major_comments":[{"comment":"The observable supplied by the g-factor protocol is not the signed valley phase φv but its cosine: inverting Eq. (4) determines only |φv|, because gτ and g0 are real, so the sign of sin φv is undetermined. The salmon-color maximum-likelihood demonstration in Fig. 1 is generated from the full complex Δ distribution of Eq. (1), which encodes the signed phase. The likelihood appropriate to the actually measurable data, f_cens(|Δ|, cos φv) = Σ_{s=±1} f(|Δ|(cos φv + i s √(1−cos^2 φv)); |Δ0|, φ0, σΔ), is never analyzed in the main text or the Supplementary Materials. The paper should add a maximum-likelihood study using this censored observable and report whether |Δ0|/σΔ and φ0 remain identifiable; at minimum, the statement that g-factor measurements deliver the statistical improvement shown by the salmon data is currently unsupported.","section":"Eq. (4) and Fig. 1"},{"comment":"The numerical validation of the g-to-phase inversion in Fig. 2(g) uses the same effective-mass model that produced Eq. (4) through Ref. [29], and it quantifies only the error in the absolute phase, |φv^(g)| − |φv|. This checks the size of higher-order disorder corrections but does not independently test the validity of Eq. (4) and does not address the sign ambiguity of φv. An independent benchmark, for example computing g and the valley phase from an sp3d5s* tight-binding model for the same disorder realizations, would materially strengthen the claim that Eq. (4) can be inverted in real devices.","section":"Fig. 2(g) and Eq. (4) validation"},{"comment":"The procedure for locating a valley vortex by following a curve of constant g is stated with the dichotomy that the curve either passes through a vortex or forms a closed loop. Since g depends on cos φv, its level sets can in principle have multiple components, saddle points, or open ends, so this dichotomy is not immediate from Eq. (4) alone. The claim is not load-bearing for the statistical argument, but a brief numerical demonstration would substantially clarify the proposed experimental protocol.","section":"Using valley vortices to determine gτ"}],"minor_comments":[{"comment":"The sentence 'Since Ev = 2|Δ| is much easier to measure that Δ' contains a typo: 'that' should be 'than'.","section":"Eq. (2)"},{"comment":"The main text defines ℓ = √(ℏ/(mt ωt)) just above Eq. (5), while the Supplementary Materials use ℓt for the same quantity; the notation should be harmonized.","section":"Eq. (5)"},{"comment":"The statement that a non-zero φ0 can be removed by a global redefinition of the valley degrees of freedom is correct for the Δ distribution but should be reconciled with the g-factor protocol, where gτ is assumed real and positive; the phase convention used for φv extracted from g should be stated explicitly.","section":"Supplementary Materials S.2"}],"recommendation":"major_revision","confidential_remarks":"The main technical gap is the mismatch between the signed-phase data used in the Fig. 1 salmon simulation and the cos φv observable provided by Eq. (4). This is fixable with a censored-likelihood analysis, but it is essential before the central claim can be accepted. The editor may also wish to verify that the companion paper Ref. [29] is available in final form, since Eq. (4) is the load-bearing bridge between g-factor measurements and valley phase."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things worth knowing. First, the Rician MLE overestimation result is solid: the paper shows convincingly that fitting valley-splitting distributions with maximum likelihood routinely misclassifies disorder-dominated samples as deterministically enhanced, even with 1000 dots per group. That is a useful caution for the field. Second, the g-factor protocol for extracting the valley phase has a load-bearing gap. Eq. (4) gives g in terms of cos phi_v, so inverting it yields |phi_v|, not the signed phase. The improvement shown in Fig. 1 (salmon data) is generated from full complex Delta, whereas the proposed protocol supplies only |Delta| from E_v and cos phi_v from g. The paper never analyzes the censored likelihood for this observable, so the central practical claim—that the g-factor protocol recovers the statistical improvement—is unsupported as stated. The paper implicitly concedes the sign issue by plotting |phi_v^(g)| - |phi_v| in Fig. 2(g), but it does not address the consequences.\n\nWhat the paper does well: the VV density derivation in the SM is careful and matches the simulated landscape. The statistical caution about Rician MLE is clearly demonstrated and non-obvious. The writing is honest about some limitations, though not about this one.\n\nSoft spots, in proportion. The sign ambiguity is major, not minor. It is plausible that the two mirror phases are statistically equivalent for estimating |Delta0|/sigma_Delta, which would make the ambiguity harmless, but that needs to be shown. Also, Eq. (4) is cited to a companion paper by overlapping authors, and the numerical validation in Fig. 2(g) uses the same effective-mass model that produced the bridge; that is self-consistency, not independent validation. No code or data are shipped. These are legitimate concerns but not reasons to dismiss the paper.\n\nWho this is for: anyone working on valley characterization in Si/SiGe spin qubits. The statistical caution is the most valuable part. The protocol is an interesting idea that needs more work.\n\nRecommendation: it deserves serious peer review. A strong referee should ask for a censored-likelihood analysis and for independent validation of Eq. (4), and probably for code or data. If those come through, the paper could be quite useful.","headline":"Solid statistical caution, but the g-factor phase extraction has a sign ambiguity that leaves the central claim unsupported as stated.","tokens_in":17783,"tokens_out":2227,"would_cite":true,"duration_ms":23423,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Valley splitting data alone cannot determine valley-coupling statistics in disordered Si/SiGe quantum wells; g-factor loops around valley vortices can.","keywords":["valley splitting","valley phase","Si/SiGe quantum wells","spin qubits","g-factor","alloy disorder","maximum likelihood estimation","valley vortex"],"falsifier":"Map the valley splitting and the g-factor over the same region of a Si/SiGe well while shuttling a single electron, and locate a valley vortex. If the density of points where $E_v = 0$ disagrees with $(0.184/\\ell^2)\\exp(-|\\Delta_0|^2/\\sigma_\\Delta^2)$, the statistical model of valley coupling is wrong; if a loop with winding number one does not send the measured g through both extrema $g_0 \\pm g_\\tau$, or if the g-inferred valley phase contradicts the splitting landscape, Eq. (4) is falsified.","tokens_in":16735,"feed_emoji":"🌀","tokens_out":12897,"duration_ms":115140,"temperature":0.7,"pith_summary":"The paper claims that in disorder-dominated Si/SiGe quantum wells, valley splitting data alone cannot determine the two statistical parameters that set qubit failure rates: the deterministic valley coupling magnitude $|\\Delta_0|$ and the random-alloy disorder strength $\\sigma_\\Delta$. Maximum-likelihood fits to splitting distributions systematically overestimate $|\\Delta_0|$, misclassifying disordered wells as deterministically enhanced even when the data set contains a thousand dots. The paper shows that adding the valley phase $\\varphi_v$ — the argument of the complex valley coupling — makes the inference accurate. Because the phase is hard to measure directly, it proposes to extract it from the electron g-factor, whose measured value depends on $\\cos \\varphi_v$, and to calibrate that dependence by moving the dot in a loop around a valley vortex, where the phase winds by $\\pm 2\\pi$. If the protocol works, it gives an experimentally practical way to certify quantum wells for large-scale spin qubit arrays.","feed_headline":"Valley splittings alone can't certify spin qubits","feed_subtitle":"G-factor loops around a valley vortex recover the valley phase that splitting statistics hide.","key_machinery":"The load-bearing object is the relation between the measurable g-factor and the valley phase, $g = g_0 - g_\\tau \\cos \\varphi_v \\sin(2\\theta_B)$, together with the complex valley coupling $\\Delta = \\Delta_0 + \\Delta_\\delta$ whose argument defines $\\varphi_v$. A valley vortex is a point where $|\\Delta| = 0$: the valley splitting vanishes there, and the valley phase winds by $\\pm 2\\pi$ around it. Measuring $g$ along a loop that winds once around a vortex guarantees that $g$ visits both extrema $g_0 \\pm g_\\tau$, which fixes the calibration constant $g_\\tau$ with certainty. The statistical analysis then uses the Rician distribution of $E_v$ and the complex-normal distribution of $\\Delta$ to show that phase information, not just splitting information, resolves the inference problem.","core_discovery":"On the paper's own terms, the central discovery is that valley splitting statistics alone are unreliable precisely in the regime that matters for large quantum computers, and that the missing observable is the valley phase. The splitting $E_v = 2|\\Delta|$ follows a Rician (magnitude-of-complex-Gaussian) distribution whose shape depends only on the ratio $|\\Delta_0|/\\sigma_\\Delta$, so a disorder-dominated well and a deterministically enhanced well can have nearly identical splitting distributions and the same average splitting; maximum likelihood therefore often reports a large deterministic coupling when the true deterministic coupling is zero. In the disorder-dominated regime, $|\\Delta_0|/\\sigma_\\Delta \\lesssim \\sqrt{\\pi}/2$, realistic samples of 20 dots misclassify the well, and even $N=1000$ dots leave more than half of the fits with a spuriously large deterministic ratio. Measuring the valley phase breaks the degeneracy, and the g-factor provides a practical channel for that information: $g = g_0 - g_\\tau \\cos \\varphi_v \\sin(2\\theta_B)$. The paper also derives the density of valley vortices, points where $E_v = 0$, as $\\rho_{VV} = (0.184/\\ell^2)\\exp(-|\\Delta_0|^2/\\sigma_\\Delta^2)$, which keeps the calibration loop practical in the disordered regime.","pith_inferences":["An implication the authors leave implicit is that Eq. (4) determines only $\\cos \\varphi_v$, so an experimental protocol must either resolve the sign of $\\varphi_v$ or work with $|\\varphi_v|$; the paper's own error statistics use absolute phases, suggesting the latter route.","The same g-factor maps could be used to extract spatial correlation lengths of alloy disorder, not just $|\\Delta_0|$ and $\\sigma_\\Delta$, because the covariance structure of $\\Delta$ shapes the landscapes — an extension the paper does not pursue.","A direct check of the model's random-field assumption would be to count valley vortices in a mapped valley-splitting landscape and compare the density with $\\rho_{VV} = (0.184/\\ell^2)\\exp(-|\\Delta_0|^2/\\sigma_\\Delta^2)$.","If $g_\\tau$ itself fluctuates spatially, through the short-length-scale interface sharpness that generates the spin-orbit term, the phase extraction would inherit that noise; the paper's small-error result assumes a deterministic $g_\\tau$."],"forward_implications":["Valley splitting surveys alone — whether across many dots or along a shuttled dot — cannot certify a quantum well as deterministically enhanced; reported high-splitting distributions may still be disorder-dominated.","Adding valley phase information restores reliable maximum-likelihood estimation of $|\\Delta_0|$ and $\\sigma_\\Delta$ in the disorder-dominated regime, with no misclassification in the demonstrated examples.","The g-factor mapping protocol needs only standard qubit resonance measurements and dot position control, so it can be implemented in current experiments.","A loop enclosing a single valley vortex fixes the calibration constant $g_\\tau$ with certainty, because the valley phase winding sends the measured g-factor through both of its extreme values.","The predicted vortex density implies the calibration step is practical in the disordered regime: a $100 \\times 100$ nm$^2$ region is expected to contain about nine vortices for the parameters shown."],"supporting_citations":[{"why":"Supplies the statistical model of complex valley coupling, including the decomposition into deterministic and random components and the alloy-disorder covariance used throughout the paper.","marker":"[13]"},{"why":"Derives the effective Hamiltonian and the g-factor relation Eq. (4) that the proposed valley-phase extraction protocol inverts.","marker":"[29]"},{"why":"Demonstrates conveyor-mode shuttling that maps valley splitting over large regions, the experimental technique the paper proposes to adapt for g-factor mapping and vortex location.","marker":"[18]"},{"why":"Reports an experiment with low disorder and high valley splitting, the kind of claim the paper argues cannot be certified from splitting data alone.","marker":"[17]"},{"why":"Provides measurements of atomic fluctuations that lift valley degeneracy in Si/SiGe quantum dots, supplying physical parameters used in the numerical model.","marker":"[12]"},{"why":"Shows that the effective-mass model reproduces spin-orbit coefficients, g-factors, and valley splittings of more detailed tight-binding calculations, supporting Eq. (3).","marker":"[31]"},{"why":"Defines the valley splitting theory for SiGe/Si/SiGe quantum wells, including the valley phase as the argument of the inter-valley coupling.","marker":"[19]"}],"fun_headline_variants":["Valley splitting stats mislead; g-factor loops reveal the phase","Splitting distributions fool you; add the valley phase","New g-factor loop method exposes the valley phase hidden in splitting","Valley splitting stats overestimate; g-factor loop recovers phase","Splitting measurements lie about valley coupling; g-factor phase tells truth"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the measured electron g-factor tracks the valley phase through a simple cosine law with a single fixed calibration constant, so that inverting a measured g gives the true valley phase; the authors validate that law only inside their own effective-mass model, and it recovers the phase only up to sign.","fun_headline_variants_meta":{"raw":{"variants":["Valley splitting stats mislead; g-factor loops reveal the phase","Splitting distributions fool you; add the valley phase","New g-factor loop method exposes the valley phase hidden in splitting","Valley splitting stats overestimate; g-factor loop recovers phase","Splitting measurements lie about valley coupling; g-factor phase tells truth"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000685,"raw_usage":{"total_tokens":3123,"prompt_tokens":980,"completion_tokens":2143,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":596,"completion_tokens_details":{"reasoning_tokens":2054}},"tokens_in":596,"tokens_out":2143,"duration_ms":18854,"temperature":1.0,"reasoning_tokens":2054,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:31:08.960968+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Map the valley splitting and the g-factor over the same region of a Si/SiGe well while shuttling a single electron, and locate a valley vortex. If the density of points where $E_v = 0$ disagrees with $(0.184/\\ell^2)\\exp(-|\\Delta_0|^2/\\sigma_\\Delta^2)$, the statistical model of valley coupling is wrong; if a loop with winding number one does not send the measured g through both extrema $g_0 \\pm g_\\tau$, or if the g-inferred valley phase contradicts the splitting landscape, Eq. (4) is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the statistical model of complex valley coupling, including the decomposition into deterministic and random components and the alloy-disorder covariance used throughout the paper."},{"cited_title":"Mapping of valley-splitting by conveyor-mode spin-coherent electron shuttling","cited_arxiv_id":"2312.17694","evidence_quote":"Demonstrates conveyor-mode shuttling that maps valley splitting over large regions, the experimental technique the paper proposes to adapt for g-factor mapping and vortex location."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports an experiment with low disorder and high valley splitting, the kind of claim the paper argues cannot be certified from splitting data alone."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides measurements of atomic fluctuations that lift valley degeneracy in Si/SiGe quantum dots, supplying physical parameters used in the numerical model."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows that the effective-mass model reproduces spin-orbit coefficients, g-factors, and valley splittings of more detailed tight-binding calculations, supporting Eq. (3)."},{"cited_title":"Friesen, S","cited_arxiv_id":null,"evidence_quote":"Defines the valley splitting theory for SiGe/Si/SiGe quantum wells, including the valley phase as the argument of the inter-valley coupling."}],"review_version":1}