{"id":"4275ae8f-f790-44e1-9be9-c68a585874c0","arxiv_id":"2510.06725","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Repeated measurements of slowly rotated stabilizer generators confine a code state to a moving code space and apply a logical unitary holonomy, with derived success probabilities and a path-correction method.","lead":"This paper proposes a measurement-only way to perform logical quantum gates on quantum error-correcting codes by repeatedly measuring slightly rotated stabilizers, using the Quantum Zeno effect to keep the state inside the moving code space. It derives success probabilities and a scheme to correct the errors the measurements themselves introduce, making a step toward fault-tolerant holonomic quantum computation.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Continuous-path protocol's final logical unitary is assumed rather than derived from the SSE; only the average survival probability is computed (Eq. 104), leaving the central continuous HQC claim unverified.","rationale":"The reader's weakest assumption correctly identifies the gap between the average survival probability computed in the continuous case and the claimed logical unitary. This is the most load-bearing concern because the abstract and Section III C explicitly extend the holonomic construction to continuous measurement, and the central claim for that extension is not derived. The discrete-path results are well supported by explicit projector products and Lemma 1, and the survival-probability calculation is internally consistent; nevertheless, survival probability alone does not fix the conditional unitary. The proposed numerical check would settle whether the SSE actually produces the claimed holonomy. Since the reader already returned CONDITIONAL and this concern is exactly the reader's main condition, the verdict should remain CONDITIONAL, i.e. unchanged.","tokens_in":812,"tokens_out":1534,"duration_ms":58207,"concrete_test":"Simulate the SSE (Eq. 90) for the [[3,1,3]] bit-flip code with H=σ_x^{⊗3}, θ=π/2, X=σ_x^1 σ_z^3, for ω/κ from 10^{-4} to 10^{-1}, using Euler-Maruyama with dt ≪ 1/κ and κ=1. For each trajectory ending in the code space, apply the inverse of G=exp(iθH) to the final state and compute the residual norm; also reconstruct the conditional logical channel from these trajectories. If the residual tends to 0 and the channel approaches the ideal logical X gate as ω/κ→0, the continuous protocol's unitary claim is supported. If a state-dependent logical rotation remains, the continuous HQC claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing premise is that the diffusive-measurement trajectory described by Eq. (90) implements the same logical holonomy G=exp(iθH) as the discrete projective sequence. The paper never derives the conditional (no-jump) final unitary from the stochastic Schrödinger equation. Section III C computes only the unconditional average 1−p_jump = 1/2[1 + (1 − ωθ²/(2πκ)) exp(−4πω/κ)] (Eq. 104) from the Lindblad equation (Eq. 91), and then asserts that the code state should have acquired the desired holonomy. This does not follow from the Lindblad average: different unravelings with the same average survival probability can have different conditional unitary rotations, and the measurement record can carry logical information. In the discrete case the unitary follows from the explicit product of projectors (Eq. 44); no analogous product or adiabatic-elimination derivation is given for continuous measurements. The numerical Example 3 checks only fidelity to |111⟩ for one gate and one initial state, and does not replace a derivation of the conditional channel. Thus the central continuous-HQC claim rests on an unverified premise.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a measurement-based holonomic quantum computation scheme for stabilizer codes. The code space is rotated by a family of unitaries V(ϕ), and frequent projective or weak measurements of rotated stabilizer generators confine the state to the instantaneous code space by the Zeno effect. Over a closed loop the sequence of rotated projectors is claimed to implement the logical unitary G=exp(iθH). For discrete projective steps, Lemma 1 gives the small-step operator and Theorem 1 gives the no-jump survival probability; Theorem 2 gives modified paths after a single measurement-induced jump. For continuous weak measurements, Section III C computes an average no-jump probability via a Lindblad-equation perturbative expansion. Section IV derives sufficient conditions for the instantaneous codes to preserve correctability and proposes ancilla-augmentation for codes that do not satisfy them.","tokens_in":27103,"tokens_out":18958,"duration_ms":129450,"significance":"If the central claims are correct, the paper introduces a genuinely measurement-driven route to holonomic logical gates, with the attractive feature that the measurement outcomes provide syndrome information along the way. The discrete-path algebra is clean and self-contained: Lemma 1 and Theorem 1 give explicit, checkable expressions, and the path-modification construction in Theorem 2 is an interesting contribution. The correctability analysis and ancilla-augmentation idea are also useful. However, the continuous-path protocol — which is central to the title and abstract — is not actually derived: the paper computes only an averaged survival probability and then asserts the holonomy. The numerical example does not substitute for a derivation of the conditional logical channel. The paper is therefore not yet ready for publication in its present form.","major_comments":[{"comment":"The central claim of the continuous-path protocol is that the diffusive measurement dynamics implements the same logical unitary G=exp(iθH) as the discrete projective sequence. The paper never derives the conditional final unitary from the stochastic Schrödinger equation (Eq. 90). It computes only the average code-space probability 1−p_jump = 1/2[1+(1−ωθ²/(2πκ))exp(−4πω/κ)] from the Lindblad equation (Eq. 91), and then asserts that the state has acquired the desired holonomy. This does not follow: different unravelings of the same Lindblad equation have the same average state but different conditional operations, and the measurement record itself can carry logical information. Moreover, the quantity defined in Eq. (95) is the average probability of being in the code space at the final time T, not the probability that no jump occurred during the interval. The numerical Example 3 checks on","section":"Section III C, Eqs. (90)–(104)"},{"comment":"Theorem 5 claims that 'the number of ancilla qubits required ... for an arbitrary stabilizer code' is at most two. The proof of the two-ancilla case relies on an unstated assumption: in the case D=E_bE_a with one factor on the ancilla register, the proof requires that the ancilla error acts on only a single ancilla qubit ('by assumption of no spatially correlated errors among the ancilla qubits'). This assumption is absent from the theorem statement and from the abstract's claim 'at most two ancilla qubits.' If the correctable set contains a weight-2 error on the two ancillas, the factor ⟨00|E_b|11⟩ need not vanish, and the expression in Eq. (129) is not automatically zero. The theorem should either state this restriction explicitly or provide a proof for general error sets.","section":"Section IV, Theorem 5 and Eq. (129)"},{"comment":"Proposition 7 as stated is false. For D∈E^(2) a stabilizer, P0HDP0 = P0HP0, which is HP0 for a logical Pauli H and is not proportional to P0. The proof appears to analyze only the Table I cases in which HD does not appear; in the cases where HD does appear (D anticommutes with H), D cannot be a stabilizer, so the conclusion P0HDP0=0 follows from Lemma 3. The proposition and its use in Theorem 4 need to be restated with this qualification. The same subsection contains the incorrect sentence 'P0HP0 ∝ P0' in the X=D case: for a non-scalar logical Pauli, P0HP0 is HP0, which is exactly the type of term that violates the Knill–Laflamme condition.","section":"Section IV, Proposition 7 and Theorem 4 proof"}],"minor_comments":[{"comment":"The statement that the sum ∑ξ_lδϕ vanishes exactly is only true when 2π/δϕ is an integer. With the ceiling function used in Eq. (41), the sum is O(δϕ), not zero. The authors should either choose δϕ such that 2π/δϕ is an integer or retain the O(δϕ) correction in the final logical rotation.","section":"Eq. (45)"},{"comment":"The stochastic Schrödinger equation in Eq. (90) contains no explicit rotation Hamiltonian term, even though the observables g_j(t) are time-dependent. The relationship between the time-dependence of the measured observables and the rotation V(t) should be clarified, or a rotating-frame derivation should be given explicitly.","section":"Section III C, Eq. (90)"},{"comment":"The text describes Fig. 5 as a plot of the probability of a jump, but Example 3 states that the average fidelity to |111⟩ was computed. Please clarify the quantity plotted and whether it is obtained by Monte Carlo simulation of Eq. (90) or from Eq. (104). If it is simulated, specify the number of trajectories and the estimator.","section":"Example 3 and Fig. 5"}],"recommendation":"major_revision","confidential_remarks":"The discrete-path part is a solid contribution and could be published after revision. The main obstacle is Section III C: the continuous-path protocol's final logical unitary is assumed rather than derived. If the authors cannot derive the conditional channel, the continuous claim should be removed from the title and abstract, or reframed as a conjecture supported only by numerics. Theorem 5's missing assumption also needs to be fixed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The discrete-path side of this paper is genuinely good. The authors generalize measurement-based holonomies from the spin-coherent-state construction of Mommers and Sjöqvist to arbitrary stabilizer codes, and they derive the success probability, the logical unitary from the projector product, and a dynamic path-correction protocol for a single jump. Lemma 1 and Theorem 1 are clean and self-contained; the algebraic structure of V(φ) is exploited carefully. I expect the discrete part to be useful for people building measurement-only gate schemes on QEC codes, and the error-correctability conditions in Sec. IV are a sensible contribution, with the ancilla-augmentation result a nice bonus.\n\nWhere I agree with the stress-test note is the continuous-path section. The paper computes the average no-jump probability (Eq. 104) from the Lindblad equation and then asserts that the state acquires the desired holonomy. That does not follow from the Lindblad average: different unravelings can produce the same survival probability but different conditional unitaries, and the measurement record itself can carry logical information. For the discrete case, the unitary comes from the explicit product of projectors; for the continuous case, there is no analogous derivation from the stochastic Schrödinger equation. The numerical example checks only fidelity to one state for one gate and does not substitute. So the continuous HQC claim rests on an unproven premise. This does not undercut the discrete results, but it is a load-bearing gap for roughly a third of the paper.\n\nSmaller soft spots, in proportion: the correction protocol is explicitly limited to a single jump, which the authors acknowledge. Theorem 5 contains an unstated assumption of no spatially correlated errors on the ancilla qubits—the proof uses it when the second factor vanishes. And the numerical sections provide no code or data, so the ensemble plots are not independently checkable. These are all fixable with revision.\n\nThe paper is clearly written and the authors are honest about limitations. It deserves a serious referee, especially because the discrete part is worth publishing and the continuous part needs precisely the kind of scrutiny a referee can apply. My recommendation: send it to peer review, and ask the authors to either derive the conditional channel for the continuous protocol or soften the claim to a conjecture with the survival probability as the evidence.","headline":"Discrete measurement-based holonomies on stabilizer codes are a real result; the continuous-weak-measurement claim is plausible but not yet derived, and that is the thing referees should pressure.","tokens_in":27563,"tokens_out":1677,"would_cite":true,"duration_ms":13510,"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":"This paper proposes that logical gates on stabilizer codes can be generated purely by measurements, by slowly rotating the code space and letting the Quantum Zeno effect confine the state.","keywords":["quantum Zeno effect","holonomic quantum computation","stabilizer codes","weak measurements","holonomy","logical gates","measurement-induced errors","quantum error correction"],"falsifier":"Simulate or experimentally run the continuous protocol on the smallest nontrivial code, e.g. the [[3,1,3]] bit-flip code with a logical Pauli rotation, for several values of ω/κ. Perform quantum process tomography conditioned on no detected jump: if the resulting logical map differs from exp(iθH) by a rotation angle that scales with ω/κ, or is not a pure unitary, the continuous-path central claim fails.","tokens_in":26713,"feed_emoji":"🌀","tokens_out":4110,"duration_ms":39359,"temperature":0.7,"pith_summary":"The paper proposes a way to perform logical quantum gates on stabilizer codes using only measurements, no coherent Hamiltonian driving. The code space is adiabatically rotated by measuring a succession of rotated stabilizer generators; when the rotation is slow, the Quantum Zeno effect keeps the state inside the instantaneous code space, and when the rotation returns to the starting point, the accumulated holonomy is the logical unitary exp(iθH). The paper derives the success probability for both discrete projective measurements and continuous weak measurements, and it shows how to detect and correct the measurement-induced jumps that occur when the rotation is not perfectly adiabatic. If correct, this offers a measurement-only route to holonomic quantum computation that naturally integrates with the syndrome information already available in quantum error correction.","feed_headline":"Measurements alone can run holonomic quantum logic gates","feed_subtitle":"Slowly rotating which stabilizers are measured confines the state and adds up to a logical unitary.","key_machinery":"The central object is the holonomic path (V, Φ), where V(ϕ) = exp(iθϕH/2π)exp(iϕX) rotates the code projector P(ϕ) = V(ϕ)P₀V†(ϕ) through a loop. Measuring the rotated stabilizers (or the projector) at small increments produces the Zeno confinement, and the per-step operator P₀V†(φ)V(φ−δφ)P₀ = c_φ exp(−iξ_φH)P₀ carries the accumulated logical phase; the ξ_φ terms cancel over a full loop, leaving exactly exp(iθH). The horizontal lift of the curve on the Grassmannian supplies the geometric holonomy that makes the final logical transformation path-dependent but independent of the state.","core_discovery":"The paper establishes that rotating the code space of a stabilizer code along a closed loop, while continuously or projectively measuring the rotated stabilizer generators, implements a holonomy equal to a desired logical unitary G = exp(iθH). For a rotation family V(ϕ) = exp(iθϕH/2π)exp(iϕX), with X chosen to anticommute with H and at least one stabilizer, each small measurement step confines the state to the instantaneous code space with probability near one, and the product of the step operators reduces to the target logical gate. The paper derives the no-jump probability for discrete steps as exp[−(δϕ/2π)(θ²/2 + 4π²)] and for continuous measurements as (1/2)[1 + (1 − ωθ²/(2πκ))exp(−4πω/κ","pith_inferences":["The paper derives the continuous-path success probability from the averaged Lindblad dynamics, but it does not explicitly derive the final logical unitary from the stochastic Schrödinger equation; a direct derivation or trajectory simulation would be a natural test of whether the continuous protocol really implements exp(iθH) rather than an additional measurement-backaction rotation.","The jump-detection hypothesis test on the measurement current suggests a practical avenue: the same current used to detect measurement-induced jumps could be reused as an online fault-detection signal in a larger error-corrected computation.","The constant-rotation-rate assumption could be relaxed; an optimized, time-dependent rotation schedule might reduce the total gate time for a fixed success probability while preserving the holonomy.","The framework is stated for Pauli stabilizer codes, but the geometric mechanism is general enough that a similar measurement-loop construction could be explored for qudit stabilizer codes or subsystem codes."],"forward_implications":["Any stabilizer-code logical gate of the form exp(iθH) can, in principle, be implemented without Hamiltonian control, using only rotated stabilizer measurements.","The explicit success probabilities give a direct trade-off between gate speed and fidelity: smaller rotation increments or slower continuous rotations exponentially suppress the chance of a measurement-induced jump.","Measurement-induced jumps can be corrected during the protocol by dynamically switching to a modified path, so the gate still completes with the right logical action instead of aborting.","The sufficient error-correcting conditions, combined with the at-most-two-ancilla construction, mean the protocol can be made compatible with a desired error set for any stabilizer code.","Because the measurements themselves provide syndrome information, the scheme is naturally compatible with ongoing quantum error correction rather than being a separate control layer."],"fun_headline_variants":["Zeno effect enables measurement-only holonomic gates","Rotating stabilizer measurements implement logical unitaries","Measurement-based Zeno holonomy for quantum error-correcting codes","Holonomic gates via slow measurement rotation"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The continuous-path claim assumes that the diffusive measurement dynamics produces the same logical unitary as the discrete projective sequence, but the paper only computes the average no-jump probability from the Lindblad equation and never derives the conditional final unitary from the stochastic Schrödinger equation; extra measurement backaction or residual mixing could break the continuous holonomy.","fun_headline_variants_meta":{"raw":{"variants":["Zeno effect enables measurement-only holonomic gates","Rotating stabilizer measurements implement logical unitaries","Measurement-based Zeno holonomy for quantum error-correcting codes","Holonomic gates via slow measurement rotation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000616,"raw_usage":{"total_tokens":2715,"prompt_tokens":776,"completion_tokens":1939,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":520,"completion_tokens_details":{"reasoning_tokens":1878}},"tokens_in":520,"tokens_out":1939,"duration_ms":11382,"temperature":1.0,"reasoning_tokens":1878,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T11:16:20.545739+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate or experimentally run the continuous protocol on the smallest nontrivial code, e.g. the [[3,1,3]] bit-flip code with a logical Pauli rotation, for several values of ω/κ. Perform quantum process tomography conditioned on no detected jump: if the resulting logical map differs from exp(iθH) by a rotation angle that scales with ω/κ, or is not a pure unitary, the continuous-path central claim fails.","supporting_citations":[],"review_version":1}