{"id":"381e4e63-392d-4bf1-9eda-77eb66a56689","arxiv_id":"2511.10978","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"An adaptive readout protocol that switches to non-perturbing negative-result measurements after one positive outcome improves nuclear-qudit QND readout fidelity to 99.61% with a 3x speedup.","lead":"This paper demonstrates a new way to read out quantum nuclear spins that disturbs them less: after the first sign of the spin state, the protocol checks only the remaining possibilities without triggering an ionization event. On a 123Sb nucleus in silicon, readout fidelity rose from about 98.9% to 99.6% with a threefold speedup, and the authors show similar disturbances affect a 73Ge nuclear spin.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The AR protocol's 'truly QND' dark-subspace claim ignores the reload (T_couple) event; the reported 99.61% is secure only if T_couple flips are negligible.","rationale":"The reader's weakest assumption is exactly the load-bearing point: the dark-subspace readout is called 'truly QND', but the protocol must reload the electron after the initial blip, and the paper's own T_couple matrix is nonzero. This attacks the mechanism that motivates the entire protocol, not just the secondary 73Ge analysis or the shot-number selection. If T_couple-induced flips are significant, the reported 99.61% fidelity is not explained by the stated single-ionization-shock argument, and the protocol's claimed maximization of QND behavior is overstated. The proposed control experiment would settle the question directly. The paper has real strengths: direct fidelity data, a consistent simulation, and an acknowledgement that decoupling is stronger than coupling. But this specific assumption is unverified, and the data/code are not yet available. The reader's CONDITIONAL verdict remains appropriate; no change is needed.","tokens_in":20953,"tokens_out":18161,"duration_ms":183688,"concrete_test":"Measure T_couple directly: prepare each of the 8 nuclear states in the ionized donor, apply exactly one electron load (|∅>→|↓>) with no ESR pulse, then immediately ionize and read out the nuclear state; repeat to extract the experimental T_couple matrix (compare to Supp. Eq. S6). Then simulate the AR protocol including one T_couple event for the reload after the first blip (plus the initial load) and compare predicted fidelity to the reported 99.61±0.04%. If the predicted fidelity drops by more than the error bar, the 'one ionization shock' explanation is unsupported and the headline fidelity needs correction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The protocol's central premise (Section III.B) is that after the first positive blip, probing the dark subspace is 'truly QND' because the Hamiltonian remains unchanged. That is only true for the interval between loading and a possible tunnel-out. The first blip leaves the donor ionized, so the dark-subspace readout requires a new tunnel-in (|∅>→|↓>) before the 7 ESR pulses can be applied. This coupling step changes H_C from 0 to A I·S and has a nonzero transition matrix T_couple (Supp. Eq. S6; Fig. S3). The statement 'just a single electron tunneling event per nuclear spin readout' counts only detected blips, not these undetected loading tunnel events, which also induce flips because [H_C,H_S]≠0. AR does reduce the number of tunnel-out events, but its advantage over RR is quantitatively secure only if T_couple-induced flips are negligible relative to T_decouple. The paper does not measure T_couple separately; it only states that decoupling produces a stronger eigenbasis rotation (Section II.C). The coincidence of the AR data with the one-shot ionization-shock y-intercept (Fig. 3e) is consistent with a small T_couple, but it could also be reproduced by a simulation that folds the loading event into the per-QND-cycle matrix. With data/code withheld, this key modeling assumption cannot be checked. If T_couple is non-negligible, the true AR fidelity is lower than reported and the 'nondemolition nature' is not maximized as claimed.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an adaptive readout protocol for a D-dimensional nuclear spin qudit, applied to an 123Sb donor (D=8). After a first positive detection, the protocol switches to collectively probing the remaining D-1 states with negative-result measurements, aiming to reduce measurement-induced nuclear spin flips and readout time. The authors report an increase in average readout fidelity from (98.93±0.07)% to (99.61±0.04)% compared with repeated QND readout, together with a threefold speed-up. They model measurement-induced transitions via eigenstate overlaps of coupled/decoupled Hamiltonians, using independently measured Hamiltonian parameters, and extend the study to a 73Ge qudit read out through Pauli spin blockade.","tokens_in":21358,"tokens_out":7595,"duration_ms":74239,"significance":"The core experimental demonstration is valuable: the direct fidelity measurement is statistically strong, and the reported improvement is not derived from the model, so it is robust to model uncertainties. If the protocol works as described, it provides a practical way to improve QND readout of high-spin donor qudits, with direct relevance to spin-cat QEC schemes. The supporting simulation is also helpful, though it depends on a number of empirical inputs. The main weakness is conceptual: the manuscript repeatedly claims that the dark-subspace negative-result probing is 'truly QND' and involves 'just a single tunneling event', while the protocol necessarily includes reload (tunnel-in) events whose backaction is nonzero in the authors' own model. This overstatement needs correction, but it does not invalidate the measured fidelity gain.","major_comments":[{"comment":"The statement that 'a negative measurement outcome within the dark state subspace is truly QND, because the Hamiltonian remains unchanged throughout the process' is inaccurate as written. The dark-subspace subroutine begins with a |∅>→|↓> reload step, which changes H_C from 0 to A I·S and has nonzero transition matrix T_couple (Supp. Eq. S6, Fig. S3). The measured AR fidelity is direct and therefore remains credible, but the mechanism claimed in the abstract ('negative-result ... do not perturb the Hamiltonian') is not supported unless T_couple-induced flips are shown to be negligible. Please revise the wording and provide a quantitative estimate of the reload contribution, either from the model or from a dedicated measurement.","section":"Section III.B; Supp. Eq. S6"},{"comment":"The argument that the NAR=2 datapoint 'coincides with the y-intercept' of the single-shot ionization-shock curve and therefore 'confirms that the AR protocol indeed requires only one tunneling event' conflates detected blips with total tunneling events. An accepted AR readout includes a reload after the first positive blip, and the Maxwell-demon initialization can itself involve multiple loading attempts (Supp. Fig. S4 reports an average of 4.47 tunneling events per QND cycle). The agreement with the y-intercept is not sufficient evidence for a single tunneling event. The authors should specify exactly which tunnel-in/out events are counted, and how reloads are included in the stated 'one tunneling event per readout'.","section":"Section III.B; Fig. 3e"},{"comment":"The Monte-Carlo AR simulation is stated to use 'the experimentally obtained transition matrix (Fig. 2)', i.e., the per-QND-cycle matrix for repeated readout. However, the AR dark-subspace step is structurally different: seven ESR pulses are applied while the electron remains coupled, and the reload/tunnel-out pattern is not the same as in the standard RR cycle. It is not clear whether the per-cycle matrix is applied to each of the seven ESR pulses, or whether a separate dark-subspace transition rule is used. Without this detail, the claimed consistency between the simulated and measured AR fidelities cannot be fully assessed. Please specify the simulation update rule and, if possible, release the simulation code.","section":"Section III.C; Fig. 3e-f"}],"minor_comments":[{"comment":"The phrase 'negative-result measurement results that do not perturb the Hamiltonian' should be qualified, since the protocol includes a reload step that does change the Hamiltonian. A phrase such as 'do not cause additional tunnel-out events' would be more accurate.","section":"Abstract; Introduction"},{"comment":"The definition of the projection operator P↕ is ambiguous (the displayed matrix has three rows and two columns, which seems inconsistent with the intended projection onto the coupled subspace). Please clarify the notation.","section":"Supp. Eq. S3"},{"comment":"There is a typo in the caption: '180 degree s periodicity' should read '180-degree periodicity'. Also, 'quadruople' appears elsewhere in the text; please proofread.","section":"Fig. S2 caption"},{"comment":"The statement that data and code 'will be made available after publication' is standard but, given that the simulation comparison is part of the central evidence, consider releasing the simulation code with the submitted revision to enable full reproducibility.","section":"Data and Code Availability"},{"comment":"The threefold speed-up claim would benefit from a clear statement of whether it refers to wall-clock time or number of QND cycles. The text explains the differing pulse durations, but the definition should appear earlier and be used consistently.","section":"Section III.B"}],"recommendation":"major_revision","confidential_remarks":"The experimental core of the paper is sound: the AR fidelity is directly measured, and the reported improvement is statistically convincing. The main issue is conceptual overreach in the 'truly QND' and 'single tunneling event' claims, which can be fixed by quantifying the reload (T_couple) contribution and clarifying the counting conventions. I see no circularity in the fidelity measurement itself. The paper should be publishable after these revisions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: this paper demonstrates a real, measured improvement in QND readout fidelity for a 123Sb nuclear qudit, from 98.93% to 99.61% with a threefold speedup, using an adaptive protocol that switches to dark-subspace probing after the first positive event. The core idea is new, well explained, and the headline result is backed by direct measurement, not by fitting the model to the reported fidelities.\n\nWhat it does well: the adaptive strategy is simple and generic for any D-dimensional system, and the implementation on an 8-dimensional qudit is clean. The simulation uses independently measured Hamiltonian parameters (quadrupole from angular NMR, hyperfine from ESR) and a separately measured tunnel-event count, and it reproduces the AR data. That is a meaningful check. The 73Ge study adds breadth by showing similar measurement-induced flips in a different readout platform.\n\nWhere the soft spots are, in order of severity: (1) The wording in Section III.B that a negative dark-subspace outcome is 'truly QND because the Hamiltonian remains unchanged' overstates the case. Loading the electron for the dark-subspace readout is itself a coupling event with a nonzero T_couple, so the Hamiltonian does change at the start. That said, the authors' own Fig. S3 shows T_couple is smaller than T_decouple, and the simulation includes both. The measured fidelity stands; this is a phrasing issue rather than a fundamental flaw. (2) Data and code are not yet released, which makes it hard to verify the 73Ge matrix-logarithm extraction or the choice of optimal shot counts. These are addressable before publication. (3) The 73Ge per-shot flip probabilities are inferred via a matrix logarithm over 201 tunnel events and come without error bars, so treat them as indicative.\n\nThe central argument holds up: the adaptive protocol reduces the number of the more perturbing decoupling events, and the data confirm it. The paper deserves a serious referee. It is primarily for the spin-qubit and qudit-QEC community, where the protocol should be straightforward to adopt.\n\nRecommendation: send it to peer review. The soft spots are wording and reproducibility details, not fatal flaws.","headline":"Solid adaptive-readout result on a nuclear qudit: the fidelity gain is directly measured and the model supports it; the 'truly QND' claim about the dark subspace is loose, but that is a wording issue, not a load-bearing flaw.","tokens_in":21908,"tokens_out":6536,"would_cite":true,"duration_ms":58469,"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":"The paper claims that measurement-induced errors in repeated QND readout of a high-dimensional nuclear spin can be minimized by switching, after one positive detection, to negative-result probing of the remaining dark-state subspace, which","keywords":["quantum non-demolition measurement","adaptive readout protocol","negative-result measurement","nuclear qudit","ionization shock","spin-cat code","silicon donor","quadrupole interaction"],"falsifier":"Measure the single-cycle flip probability when the electron is loaded once and then repeatedly checked by dark-subspace negative-result measurements without ever re-ionizing; if the flip probability per negative check equals the per-ionization flip probability rather than being much smaller, the central premise fails. More directly, compare adaptive-readout fidelity in a regime where T_couple dominates T_decouple: the predicted advantage should vanish.","tokens_in":20862,"feed_emoji":"⚛️","tokens_out":3095,"duration_ms":32816,"temperature":0.7,"pith_summary":"The paper argues that the main source of error in repeated QND readout of a high-dimensional nuclear spin is not the measurement collapse itself but the electron tunneling events used to detect the ancilla, each of which perturbs the nuclear Hamiltonian. It introduces an adaptive protocol: after one positive detection, instead of re-testing all D states, it collectively probes the remaining D−1 states by negative-result measurements that leave the Hamiltonian unchanged. On an 8-dimensional antimony-123 nucleus in silicon this raises average readout fidelity from about 98.93% to 99.61% and cuts readout time about threefold. The same measurement-induced-flip signature appears in a 10-dimensional germanium-73 system read through Pauli spin blockade, suggesting the problem and the fix are generic across platforms.","feed_headline":"Adaptive readout hits 99.61% qudit fidelity","feed_subtitle":"By probing only the remaining states after the first hit, the protocol cuts spin flips and time threefold.","key_machinery":"The dark-state subspace probe: after a first positive tunnel event identifies a candidate state m, the protocol applies ESR pulses for all other D−1 states while the electron stays coupled, then allows a single possible tunnel event. If no blip appears (below a threshold), m is accepted. This is a negative-result measurement: the absence of tunneling carries information without the basis-rotation penalty of ionization. The eigenstate-overlap transition matrices T_couple and T_decouple from the coupled/decoupled Hamiltonians model the flips and justify why decoupling (|↑>→|∅>) is the dominant error channel.","core_discovery":"The central claim is that a negative-result measurement confined to the dark-state subspace is effectively QND even when the full readout is not: once the electron ancilla remains loaded and no tunneling occurs, the Hamiltonian is unchanged, so no basis rotation and no spin flip is induced. The adaptive protocol exploits this by reading all remaining states in one collective check; the only ionization event is the initial one. The measured data reproduce the simulated transition matrix, and the adaptive protocol's fidelity at the optimum coincides with the single-shot ionization-shock limit, confirming one tunnel event per readout. The improvement is robust in simulation even when ancilla re","pith_inferences":["Extension: The protocol's logic generalizes to any D-level system whose readout uses an ancilla with a no-tunnel outcome, including trapped ions, NV centers, and other spin qudits, wherever a dark-state subspace can be collectively probed.","The one-ionization floor suggests a fundamental limit: readout fidelity cannot exceed the no-flip probability of a single coupling/decoupling cycle; further gains would require reducing the coupling event itself, for example by keeping the electron loaded and reading out without a tunnel-out step.","Because the initial-guess subroutine averages about 4 shots and about 13% of guesses are rejected, lowering the false-positive (dark count) rate would reduce rejections and improve both fidelity and speed further.","A testable extension: applying the adaptive protocol at lower magnetic field in the germanium system, where measurement-induced flips are stronger, should yield a larger fidelity gain than at high field."],"forward_implications":["Average readout fidelity improves from (98.93±0.07)% to (99.61±0.04)% while readout time is reduced by about a factor of three, with only one ionization event per accepted readout.","The protocol can be implemented on existing hardware with minimal FPGA logic and no new control hardware.","For quantum error correction, the demonstrated fidelity meets typical fault-tolerance threshold estimates for spin-cat codes and is compatible with symmetric-subspace syndrome extraction.","Simulated robustness shows adaptive readout fidelity stays nearly flat as ancilla fidelity degrades, whereas repeated readout requires more shots and then decays, so the protocol is more resilient to imperfect ancilla readout.","The same flip statistics in germanium-73 show measurement-induced errors are platform-wide, and increasing magnetic field reduces flips by restoring eigenstate overlap."],"fun_headline_variants":["Adaptive readout lifts qudit fidelity to 99.61%","Quantum nondemolition readout made less invasive","Adaptive protocol cuts readout time threefold","Negative-result readout preserves qudit states"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The whole advantage rests on the claim that a negative result in the dark-state subspace leaves the nuclear state untouched; in practice the probe still begins with an electron-loading (coupling) event, whose own transition matrix is nonzero, so the protocol helps only if ionization events dominate the flip rate.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive readout lifts qudit fidelity to 99.61%","Quantum nondemolition readout made less invasive","Adaptive protocol cuts readout time threefold","Negative-result readout preserves qudit states"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000349,"raw_usage":{"total_tokens":1741,"prompt_tokens":741,"completion_tokens":1000,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":485,"completion_tokens_details":{"reasoning_tokens":936}},"tokens_in":485,"tokens_out":1000,"duration_ms":9656,"temperature":1.0,"reasoning_tokens":936,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T22:18:14.709823+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the single-cycle flip probability when the electron is loaded once and then repeatedly checked by dark-subspace negative-result measurements without ever re-ionizing; if the flip probability per negative check equals the per-ionization flip probability rather than being much smaller, the central premise fails. More directly, compare adaptive-readout fidelity in a regime where T_couple dominates T_decouple: the predicted advantage should vanish.","supporting_citations":[],"review_version":1}