{"id":"6ab28836-7897-415d-bacb-ada01ca0677e","arxiv_id":"2504.13041","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":7,"one_line_summary":"A hybrid quantum-classical control algorithm using variational quantum circuits is tested on five systems, with theoretical claims about when it outperforms classical MPC, but the evidence is not convincing.","lead":"This paper proposes a control method that trains a small quantum circuit to choose actions inside a model predictive control loop, and tests it on five simulated systems. The authors also claim general rules for when such quantum-inspired control can work, but the experiments include several failures and no comparison against standard control methods.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Proposition 2's regret advantage rests on Lemma 7, whose classical O(T) baseline is not the standard convex-cost baseline, and no quantum regret or amplitude-estimation construction is supplied; the central claim lacks support.","rationale":"To make Proposition 2 true one would need: (i) a definition of regret for MPC that compares against the best fixed control sequence; (ii) a proof that the VQC parameter updates produce O(sqrt(T)) regret; (iii) a correct classical baseline showing O(T) or worse; and (iv) a quantum circuit that evaluates the MPC cost in O(1/epsilon). None of these are in the paper. The reader and I identify the same weak assumption. I also note that the paper's own experiments undermine rather than support the generality of Proposition 2: Experiments 4 and 5 diverge, and the conclusion admits the compound pendulum result is poor and the approach is suboptimal for oscillatory systems. That makes the positive claim hinge even more heavily on the formal lemmas. Because the main advertised advantage is exactly the regret comparison, the verdict should remain REJECT.","tokens_in":22274,"tokens_out":4259,"duration_ms":42794,"concrete_test":"Independently re-derive Lemma 7 using the standard regret definition: for convex Lipschitz stage costs, classical online gradient descent has regret O(sqrt(T)), not O(T). If the quantum update's regret is also O(sqrt(T)) (or if no explicit regret bound for Algorithm 1 is derived), Proposition 2's strict improvement over classical MPC disappears. As a second check, write down the explicit quantum amplitude-estimation oracle for J(x_k,U) in Eq. (1) over the horizon N; if no such oracle can be constructed without exponential cost in N or the state dimension, Lemma 5 fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The positive headline claim is Proposition 2, and its proof depends entirely on Lemmas 5, 6, and 7. The weakest link is Lemma 7: it asserts, with no derivation, that classical MPC has regret O(T) on a convex cost while quantum gradient updates have regret O(sqrt(T)). For convex Lipschitz stage costs, the standard online convex optimization result is O(sqrt(T)) regret (and O(log T) for strongly convex costs), so the claimed classical baseline is not the standard one; replacing it with the correct baseline removes the strict advantage asserted in Proposition 2. In addition, Algorithm 1 as written is not an online learning procedure with a defined regret benchmark: the parameter-shift update at step 11 minimizes a one-step loss ||x_{k+1}-x_target||^2 + lambda||u_k||^2, not the finite-horizon MPC objective in Eq. (1), and no cumulative-regret analysis is supplied. Lemma 5 is equally unsupported: no explicit circuit is given that evaluates J(x_k,U) over a superposition of control trajectories with quantum amplitude estimation in O(1/epsilon); the claim is asserted rather than constructed. Since Proposition 2 is the formal basis for \"QI-MPC can achieve a lower regret bound than classical MPC,\" the central claim is not established. The experiments do not fill this gap because there is no classical MPC baseline, and the two \"successful\" experiments show either trivial linear tracking (Experiment 1) or constant temperature trajectories (Experiment 2).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes QI-MPC, a hybrid quantum-classical framework in which a Variational Quantum Circuit (VQC) is trained online to generate control inputs that are clipped and applied to a dynamical system under a receding-horizon update. The approach is illustrated on five systems (target tracking, building climate control, autonomous vehicle dynamics, a simple pendulum, and a compound pendulum), and three 'safety guarantees' are stated in Sec. 3.2. On the basis of the five experiments, the paper then derives two propositions: (P1) hybrid quantum-classical MPC cannot achieve globally stable control for nonlinear oscillatory systems with finite-dimensional quantum ansatze, and (P2) QI-MPC can, in theory, achieve a lower regret bound than classical MPC for high-dimensional systems with sufficiently smooth dynamics. The positive claim rests on Lemmas 5-7 in Sec. 5.2 (quantum parallelism, state compression, and regret), and the negative claim rests on Lemmas 1-4 in Sec. 5.1 (sampling rates, energy scales, topology, and decoherence).","tokens_in":22566,"tokens_out":14971,"duration_ms":138144,"significance":"If the two propositions were established, the paper would provide a rare theoretical characterization of when hybrid quantum-classical control can beat classical MPC, and its identification of favorable versus unfavorable application domains (smooth low-bandwidth systems versus oscillatory, chaotic, and ultrafast systems) would interest both the quantum-control and MPC communities. The paper deserves credit for transparency: Experiments 4 and 5 are explicitly reported as suboptimal, the authors list possible reasons for the vacuous temperature trajectories in Experiment 2, Algorithm 1 is given in full pseudocode, and the Conclusion candidly states that only experimentation can determine where the hybrid approach wins or loses. However, the theoretical content consists of lemmas asserted without proof or construction, the stability guarantee is delegated to an unnamed theorem, and the experimental section contains no classical MPC baseline; the significance of the claims therefore cannot be assessed from the present manuscript.","major_comments":[{"comment":"Algorithm 1 does not implement the MPC problem stated in Eq. (1): the update at step 11 minimizes the one-step loss ||x_{k+1} - x_target||^2 + lambda||u_k||^2, not the finite-horizon cost J(x_t, U), and no N-step prediction or open-loop solution u* = arg min_U J is ever formed. The quantities 'prediction horizon N' and 'receding-horizon update' play no role in the optimization, so the procedure is better described as an online-trained feedback policy than as an MPC controller; this mismatch propagates into the safety guarantees and the regret claims, which presuppose that the algorithm solves Eq. (3).","section":"Sec. 3.1, Algorithm 1; Eq. (1)"},{"comment":"The stability guarantee is asserted by invoking 'the stability theorem' without stating or proving it, and no argument shows that the VQC parameter update decreases a control Lyapunov function. Standard MPC stability results require conditions (terminal cost or terminal constraint sets, and exact solution of the open-loop problem) that Algorithm 1 neither assumes nor satisfies; positive-definite stage cost and Lipschitz dynamics do not suffice even in the classical setting. The claimed convergence lim_{k to infinity} x_k = x_target is also contradicted by the paper's own Experiments 4 and 5, which fail to converge under this algorithm.","section":"Sec. 3.2, Formal Verification II"},{"comment":"The four lemmas underpinning Proposition 1 do not support it. Lemma 1 confuses clock speeds with the control sampling rate and misapplies the Nyquist theorem to closed-loop feedback: the sampling rate is a design choice and the relevant constraint is feedback computation latency, not the processor clock; moreover the inequality direction is wrong for the stated numbers, since for a macroscopic oscillator with omega_sys of order 1-10^3 rad/s the required update rate f_control >= omega_sys/pi is orders of magnitude below the GHz clock rate, so the stated condition is satisfied trivially. Lemma 2 is a category error: the VQC output is a classical number that is clipped and mapped to a torque or force applied through classical actuators, so the single-excitation energy hbar*omega of a qubit imposes no bound on control authority. Lemma 3 states that the n-qubit pure-state space is homeomorphic to R^{2n}; the relevant space is the complex projective space CP^{2^n - 1}, and the control output <psi|Z_i|psi> is an element of R^m, not a state vector in the Hilbert space, so no topological obstruction to covering the physical reachable set is established. Lemma 4 is contradicted by the paper's own cited coherence time of up to one year for nuclear spins and in any case does not imply global instability of the closed loop. Proposition 1 therefore has no valid proof.","section":"Sec. 5.1, Lemmas 1-4"},{"comment":"Proposition 2's proof rests on Lemmas 5-7, none of which is established. Lemma 5 asserts without construction that quantum amplitude estimation evaluates the MPC cost in O(1/epsilon) steps; no circuit computing J(x_k, U) over a superposition of control trajectories is given, and the stated classical baseline O(1/epsilon^2) is the Monte Carlo estimation rate, not the cost of evaluating the deterministic objective in Eq. (1). Lemma 6 invokes superposition as exponential state compression with no measurement or retrieval scheme, which is the well-known gap between Hilbert-space dimension and algorithmic speedup. Lemma 7 asserts that classical MPC has regret O(T) on convex costs while quantum gradient updates achieve O(sqrt(T)); the standard online-convex-optimization result for convex Lipschitz costs is O(sqrt(T)) (and O(log T) for strongly convex costs), so the asserted classical baseline is not the standard one, and no regret benchmark for Algorithm 1 is even defined since the algorithm minimizes a one-step loss and no cumulative-regret analysis is supplied. With the correct baseline, the strict advantage claimed in Proposition 2 disappears.","section":"Sec. 5.2, Lemmas 5-7; Proposition 2"},{"comment":"The experiments do not provide the empirical support claimed for the propositions. No classical MPC baseline is run in any of the five experiments, so the section title 'Outperformance of Classical MPC by QI-MPC' (Sec. 5.2) is unsupported numerically. The two experiments invoked as evidence for Proposition 2 are unpersuasive: Experiment 1 (Sec. 4.1) uses the trivially stabilizable dynamics x(t+1) = x(t) + alpha(u(t) - x(t)) and yet reports a non-vanishing final loss of about 0.75, and Experiment 2 (Sec. 4.2) reports all temperature trajectories constant at 20 degrees C although the declared set point is 22 degrees C, a non-result that the paper itself attributes to possibly over-simplified dynamics. The validation is also circular: Propositions 1 and 2 are motivated by the outcomes of Experiments 4-5 and 1-2 (Secs. 5.1-5.2), and the Conclusion then invokes those propositions to explain the experimental outcomes, which provides neither independent evidence for the propositions nor a genuine test of them.","section":"Sec. 4 (Experiments); Sec. 6 (Conclusion)"}],"minor_comments":[{"comment":"The minimization in Eq. (1) is written as min over u_k in U, but the decision variable is the whole sequence U = (u_0, ..., u_{N-1}); the text 'x_N contained in X_f contained in X' also states set inclusions for what is a single terminal state.","section":"Eq. (1), Sec. 1"},{"comment":"The phrase 'the horizon is sifted forward' should read 'shifted forward'.","section":"Sec. 1"},{"comment":"The energy hbar*f_qubit ~ 10^-24 J is described as 'Planck scale energies', which is incorrect; the Planck energy is of order 10^9 J.","section":"Sec. 5.1, Lemma 2"},{"comment":"Fig. 7 shows all temperature trajectories constant at 20 degrees C while the text declares the set point to be 22 degrees C; the paper should reconcile the set point with the observed trajectories or correct the experimental description.","section":"Sec. 4.2, Fig. 7"},{"comment":"Measurement outcomes are modeled as Gaussian noise, eta ~ N(0, sigma^2), and then bounded with Hoeffding's inequality, which requires bounded random variables; the relationship between the two noise models should be clarified.","section":"Sec. 3.2, Formal Verification III"},{"comment":"The shaded regions are described as confidence intervals, but the paper does not state how many independent runs or seeds they are computed from, so the uncertainty bands cannot be interpreted.","section":"Figs. 2-4, 6-8, 10-12, 15-17, 20-22"},{"comment":"The title uses 'Quantum-Inspired' while the body describes 'hybrid quantum-classical' control and the experiments appear to be classical simulations of quantum circuits; the distinction between these terms should be clarified.","section":"Title and Abstract"},{"comment":"The derivation f_control >= 2 f_sys = 2 omega_sys/(2 pi) = omega_sys/pi mixes angular and cyclic frequencies; with f_sys = omega_sys/(2 pi) the bound is f_control >= omega_sys/pi in Hz, and the units should be stated consistently throughout the lemma.","section":"Sec. 5.1, Lemma 1"}],"recommendation":"reject","confidential_remarks":"The manuscript describes a plausible empirical direction, but the theoretical results as stated are not defensible: Proposition 1 rests on four lemmas that are individually flawed (including an internally inconsistent sampling-rate argument and a physically incorrect energy argument), and Proposition 2's regret comparison uses a classical baseline of O(T) that contradicts standard online-convex-optimization results without discussion or citation. The circular structure, in which the propositions are motivated by the experiments and then used to explain those same experiments, is a further concern. My rejection is based on the load-bearing gaps described in the major comments rather than on disagreement with the empirical observation that VQC-based controllers struggle on oscillatory systems; a reframed empirical study with a classical MPC baseline and honest benchmarking could form the basis of a different and more defensible paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a plausible hybrid quantum-classical control scheme with an honest experimental write-up, but the formal claims are not supported.\n\nWhat's new: the specific combination of a VQC generating Pauli-Z expectation controls in a receding-horizon MPC loop (Algorithm 1) is new. The paper also gets credit for reporting bad results on pendulum systems rather than hiding them.\n\nThe problems are in Section 5. The regret advantage in Proposition 2 rests on Lemma 7, which asserts classical MPC has O(T) regret on convex costs. The standard online convex optimization baseline is O(sqrt(T)) (or O(log T) for strongly convex), so the strict advantage vanishes. Lemma 5 claims quantum amplitude estimation evaluates the MPC cost in O(1/epsilon) steps without giving any circuit construction. And Algorithm 1 as written minimizes a one-step loss, not the finite-horizon objective in Eq. (1), so the regret analysis isn't about the algorithm. Formal Verification II (stability) is asserted via an unnamed stability theorem; no proof that VQC updates decrease a Lyapunov function.\n\nThe other lemmas have category errors. Lemma 1 compares qubit clock speed with the MPC sampling rate; Lemma 2 compares the energy of a control signal with the energy of a qubit. Those are different things. The topology argument in Lemma 3 is too hand-wavy to support Proposition 1.\n\nThe experiments don't rescue the theory. There are no classical MPC baselines, so \"viability\" is only demonstrated on simple target tracking. The building control experiment has an internal contradiction about the set point temperature (22 C in the text, 20 C in the description), and the pendulum experiments visibly don't converge. The authors admit the compound pendulum result is suboptimal; that honesty is good, but it conflicts with the sweep of Proposition 1.\n\nWho is this for? A reader exploring hybrid quantum-classical control might get a quick sense of one way to wire a VQC into MPC, but the formal sections need major reworking. I would not cite it in its current form. It does deserve a careful referee, though: the claims are important and the failures are instructive. My recommendation: send to peer review, but expect rejection or a fundamental revision.","headline":"New VQC-in-the-loop MPC recipe with honest experimental reporting, but the regret and stability claims do not hold up under scrutiny.","tokens_in":23135,"tokens_out":4383,"would_cite":false,"duration_ms":39661,"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":"QI-MPC claims that a variational-quantum-circuit controller can in theory beat classical MPC on smooth high-dimensional control problems, while failing globally on nonlinear oscillatory systems.","keywords":["model predictive control","variational quantum circuits","quantum-inspired control","hybrid quantum-classical","regret bounds","oscillatory systems","nonlinear control","control stability guarantees"],"falsifier":"Take a smooth high-dimensional linear-quadratic tracking problem, run Algorithm 1 with a fixed VQC ansatz over many steps, and compare cumulative regret against a standard interior-point MPC solver; if the classical solver's regret grows at or below $O(\\sqrt{T})$ while the quantum loop's regret does not, Proposition 2's advantage claim is contradicted.","tokens_in":21968,"feed_emoji":"⚡️","tokens_out":6455,"duration_ms":69340,"temperature":0.7,"pith_summary":"QI-MPC wraps a variational quantum circuit inside the standard model-predictive-control loop: the circuit encodes the current state, a parameterized ansatz produces candidate control actions, and only the first action is applied before the horizon shifts. The paper reports five experiments — target tracking, building climate control, autonomous vehicle dynamics, a simple pendulum, and a compound pendulum — and finds the approach works cleanly for the smooth, low-frequency cases and poorly for the oscillatory ones. From those observations it derives two results: hybrid quantum-classical control cannot achieve globally stable MPC for nonlinear oscillatory systems with finite-dimensional quantum ansätze, and for systems with high-dimensional state spaces and sufficiently smooth dynamics, QI-MPC can in theory attain a lower regret bound than classical MPC. A sympathetic reader would take the paper's aim to be identifying, with experiments and supporting arguments, the class of control problems where a VQC-based MPC loop is viable and the class where it is not.","feed_headline":"Quantum MPC could beat classical on smooth problems, not oscillators","feed_subtitle":"Five experiments and two theorems map when variational quantum circuits help or fail in model predictive control.","key_machinery":"The central object is Algorithm 1's hybrid loop: encode the current state into a quantum state $|\\psi(x_k)\\rangle$, apply the parameterized ansatz $U(\\theta)$ built from single-qubit rotations $\\mathrm{Rot}(\\theta)=R_Z(\\theta_1)R_Y(\\theta_2)R_X(\\theta_3)$ and CNOT entanglers, measure Pauli-Z expectations to obtain controls $u_k$, clip to the admissible range, evolve the system dynamics $x_{k+1}=f(x_k,\\tilde{u}_k)$, compute the loss, and update $\\theta$ with a gradient-based rule under a receding horizon. The two theorems are carried by four lemmas for the oscillatory negative result (Nyquist feedback-delay violation, energy-scale mismatch, non-contractible reachable sets in phase space, and decoherence timescales) and three lemmas for the positive result (quantum parallelism in cost evaluation, exponential state compression, and quantum gradient regret). Proposition 2 also states explicit conditions: polynomial qubit scaling, polylogarithmic circuit depth in the horizon, smooth dynamics, and no ultra-fast feedback requirement.","core_discovery":"The paper's central claim is that wrapping a variational quantum circuit around the standard receding-horizon MPC loop is a viable way to learn control policies, and that its viability has a sharp boundary. On one side, Proposition 1 asserts that for nonlinear oscillatory systems, any hybrid quantum-classical control method using a finite-dimensional quantum ansatz fails to achieve globally stable MPC because the classical-optimizer feedback delay violates the Nyquist rate for the oscillation, qubit-level energies are orders of magnitude below mechanical energies, a finite-dimensional Hilbert space cannot topologically cover the non-contractible reachable sets such as tori that oscillatory phase spaces contain, and decoherence acts before mechanical damping. On the other side, Proposition 2 asserts that for high-dimensional state spaces with sufficiently smooth dynamics, QI-MPC with polynomially many qubits can in theory achieve lower regret than classical MPC, relying on quantum parallelism for $O(1/\\epsilon)$ cost evaluation, exponential state compression, and a claimed $O(\\sqrt{T})$ quantum-gradient regret. The empirical section shows clean success only in the smooth low-frequency cases, with marginal results for the vehicle model and clear divergence for the two pendula.","pith_inferences":["The negative result for oscillatory systems may reflect the finite ansatz and measurement noise rather than a fundamental quantum limit; continuous-variable quantum control or adaptive ansätze could evade the topological obstruction, as the paper itself leaves open.","The claimed $O(\\sqrt{T})$ versus $O(T)$ regret comparison is not the standard regret baseline for convex MPC, where strongly convex costs often yield logarithmic regret; replacing the baseline with standard bounds would likely shrink or eliminate the stated quantum advantage.","If Lemmas 5 through 7 were made constructive with explicit circuits for the MPC cost evaluation, QI-MPC could be benchmarked directly against an interior-point MPC solver on a smooth high-dimensional problem, giving a practical test of the regret claim."],"forward_implications":["For classical oscillatory control tasks, such as pendula or vibrating mechanical systems, classical MPC remains the recommended tool because QI-MPC cannot be globally stable under the paper's assumptions.","For nanoscale or quantum-mechanical systems, the timescale and energy scales match quantum hardware capabilities, so the hybrid loop is identified as a plausible control approach.","For smooth, high-dimensional, low-frequency control problems, QI-MPC can in theory achieve a lower regret bound than classical MPC while requiring exponentially less memory to discretize the state space.","The three safety guarantees imply that, under Lipschitz dynamics and positive-definite stage costs, the closed loop is stable, constraints are satisfied by clipping, and measurement noise can be exponentially suppressed by additional circuit readouts.","The experiments indicate the approach performs best on target-tracking and building climate control, marginally on autonomous vehicle dynamics, and poorly on the two pendulum systems."],"supporting_citations":[{"why":"Supplies the motivating example of quantum-inspired stochastic optimal control applied to a real-time spacecraft trajectory problem.","marker":"[48]"},{"why":"Provides the quantum-annealer MPC baseline that reformulates control selection as a QUBO problem and reports superior results on finite-input systems.","marker":"[49]"},{"why":"Shows MPC applied to quantum state preparation with real-time feedback and constraints, motivating the hybrid quantum-classical control loop.","marker":"[50]"},{"why":"Supplies the approach of reformulating nonlinear MPC in polynomial form for quantum annealers, which the paper positions against its variational method.","marker":"[52]"},{"why":"Is the stated source for the Nyquist-Shannon sampling theorem used in Lemma 1 to argue that hybrid feedback delay exceeds the oscillatory timescale.","marker":"[55]"},{"why":"Is the stated source for quantum coherence timescales used in Lemma 4 to argue that decoherence disrupts control before mechanical damping acts.","marker":"[56]"}],"fun_headline_variants":["QI-MPC: smooth wins, oscillators fail","Quantum MPC: only smooth dynamics benefit","Smooth systems yes, oscillatory systems no","Hybrid quantum MPC fails on oscillators, wins on smooth","Quantum-inspired MPC: smooth wins, oscillators fail"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The positive advantage claim rests on an unproven comparison: quantum gradient updates are assumed to accumulate regret like the square root of the time horizon while classical MPC accumulates regret linearly, and the paper supplies no circuit construction and no online-learning proof for that comparison, so if it fails, Proposition 2 has no basis.","fun_headline_variants_meta":{"raw":{"variants":["QI-MPC: smooth wins, oscillators fail","Quantum MPC: only smooth dynamics benefit","Smooth systems yes, oscillatory systems no","Hybrid quantum MPC fails on oscillators, wins on smooth","Quantum-inspired MPC: smooth wins, oscillators fail"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000696,"raw_usage":{"total_tokens":3106,"prompt_tokens":865,"completion_tokens":2241,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":481,"completion_tokens_details":{"reasoning_tokens":2167}},"tokens_in":481,"tokens_out":2241,"duration_ms":16735,"temperature":1.0,"reasoning_tokens":2167,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T12:16:20.063126+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a smooth high-dimensional linear-quadratic tracking problem, run Algorithm 1 with a fixed VQC ansatz over many steps, and compare cumulative regret against a standard interior-point MPC solver; if the classical solver's regret grows at or below $O(\\sqrt{T})$ while the quantum loop's regret does not, Proposition 2's advantage claim is contradicted.","supporting_citations":[{"cited_title":"Acta Astro- nautica 205, 68–79 (2023)","cited_arxiv_id":null,"evidence_quote":"Supplies the motivating example of quantum-inspired stochastic optimal control applied to a real-time spacecraft trajectory problem."},{"cited_title":"Scientific Reports 10(1), 1591 (2020)","cited_arxiv_id":null,"evidence_quote":"Provides the quantum-annealer MPC baseline that reformulates control selection as a QUBO problem and reports superior results on finite-input systems."},{"cited_title":"Quantum 6, 837 (2022)","cited_arxiv_id":null,"evidence_quote":"Shows MPC applied to quantum state preparation with real-time feedback and constraints, motivating the hybrid quantum-classical control loop."},{"cited_title":"Quantum optimization for Nonlinear Model Predictive Control","cited_arxiv_id":"2410.19467","evidence_quote":"Supplies the approach of reformulating nonlinear MPC in polynomial form for quantum annealers, which the paper positions against its variational method."},{"cited_title":"TMH (1991)","cited_arxiv_id":null,"evidence_quote":"Is the stated source for the Nyquist-Shannon sampling theorem used in Lemma 1 to argue that hybrid feedback delay exceeds the oscillatory timescale."},{"cited_title":"Advances in Computers, vol","cited_arxiv_id":null,"evidence_quote":"Is the stated source for quantum coherence timescales used in Lemma 4 to argue that decoherence disrupts control before mechanical damping acts."}],"review_version":1}