{"id":"b18605c8-2045-4ced-8f41-6d845e1cdf4d","arxiv_id":"2608.06145","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"The paper proposes QAE for expected path travel time estimation in stochastic networks, but the post-processing correction uses the true expectation, making the method circular and the empirical errors inconsistent with the description.","lead":"This paper applies a quantum computing method, Quantum Amplitude Estimation (QAE), to estimate expected travel times on routes with random travel times, aiming to replace slow Monte Carlo sampling with a faster quantum routine. It tests four QAE variants and several rotation-angle mappings, but the described post-processing appears to use the true travel-time expectation to correct the estimate, which would make the method circular.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section III.F post-processing is circular: the correction term c = E[theta_h] - theta_tilde is computed from the true expected value, so the final estimate returns E[T_h] by construction and the QAE estimate cancels out.","rationale":"The reader's weakest_assumption identifies exactly the circular post-processing in Section III.F, and my independent reading agrees: the correction term uses the true expected value, so the estimator either returns the input or, without the correction, has no valid inversion from E[cos(T_h)] to E[T_h]. I considered other potential concerns, including the reliance on exact probability loading despite the 'no distribution assumptions' claim, and the selection of rotation-angle ranges based on test data. Those are real secondary issues, but the inversion step is logically prior: if the post-processing is circular, the QAE output does no work in the final estimate, and the empirical accuracy claims cannot be attributed to the described method. The reported nonzero errors strengthen the concern, because a literal implementation of the correction term would produce zero error by construction. No independent support, such as formal verification or released code, is present in the manuscript to resolve the ambiguity. Therefore the central claim is not supported as written, and the reader's REJECT verdict remains appropriate.","tokens_in":16570,"tokens_out":4685,"duration_ms":52052,"concrete_test":"Take the two-link example from Table II with T_h in {20, 30, 40} and probabilities {0.25, 0.5, 0.25}. Compute q = sum_j p_j cos(theta_j) for each scaling method, set theta_tilde = arccos(q), define c = E[theta_h] - theta_tilde as in Section III.F, and output theta_tilde + c. Repeat for several arbitrary q values (e.g., q = 0.2, 0.5, 0.8). If the corrected output is exactly E[theta_h] in every case, the correction term is circular and the QAE estimate contributes nothing. Then rerun without the correction term and compare arccos(q) to E[T_h]; this quantifies the bias that any valid inversion would have to remove without access to E[theta_h].","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the claimed recovery of E[T_h] from the QAE estimate of E[cos(T_h)]. In Section III.F, Scaling Method 1 sets theta_l = t_l and post-processes via theta_tilde = arccos(E[cos(T_h)]) with correction c = E[theta_h] - theta_tilde, where E[theta_h] = sum_j p^2(j) theta_j is computed from the known distribution. Since theta_h = T_h under Method 1, E[theta_h] is exactly the target E[T_h]. Adding c gives theta_h* = theta_tilde + E[theta_h] - theta_tilde = E[theta_h], so the QAE measurement cancels completely. The same structure appears in Methods 2-4: in each case theta_h is an affine function of T_h (or of the per-link travel times), so E[theta_h] already contains the desired expectation, and the correction term forces the final answer to equal it. If the correction is omitted, arccos(E[cos(T_h)]) is a biased proxy for E[T_h], because arccos is nonlinear and non-injective and no valid inversion formula is supplied. The reported nonzero absolute errors (Section V, 0.0058 to 1.0531) are inconsistent with this literal implementation, which would return the ground truth exactly; this suggests either the post-processing was implemented differently or the experiments use an estimator not described in the paper. Thus the central accuracy claim rests on an unresolved circular step.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a quantum amplitude estimation (QAE) framework for estimating expected path travel times in stochastic transportation networks (STNs). Link travel times are encoded as Ry rotations of a data qubit, QAE variants estimate the probability of the |1> state, and a post-processing step involving arccos and a correction term is claimed to recover the expected path travel time E[T_h]. Four QAE variants (CAE, IAE, MLAE, FAE) and four rotation-angle scaling methods are benchmarked on a small three-node network under uniform, normal, and lognormal link travel time distributions. The central claims are that the estimator eliminates classical sampling, offers a quadratic speed-up over Monte Carlo, and works without prior distributional assumptions.","tokens_in":16854,"tokens_out":6066,"duration_ms":68958,"significance":"If it worked, this would be a novel first application of QAE to stochastic routing, with clear practical relevance for simulation-based optimization in intelligent transportation systems. The manuscript is pedagogically useful: it introduces QAE concepts for an ITS audience, presents a concrete circuit construction, and provides an empirical comparison of four QAE variants under several encoding strategies. However, the central post-processing step is circular: the correction term is computed from the true expected angle, so the final estimate equals the classical expectation and the QAE measurement cancels out. The numerical results are therefore not evidence for the proposed method. The quadratic-speed-up claim, while standard for QAE, does not apply to the estimator as written, because the post-processing already requires the full joint distribution needed to compute E[T_h] classically. The paper does not currently establish the significance it claims.","major_comments":[{"comment":"The post-processing in Section III.F is circular and cancels the QAE estimate. For Scaling Method 1, theta_h = T_h, so the corrected angle is theta_h^* = theta_tilde + c = arccos(E[cos(T_h)]) + E[theta_h] - theta_tilde = E[T_h] by the definition of c. Thus the QAE measurement drops out and the output equals the classically computed expected value. Under Scaling Methods 2-4 the same cancellation occurs, because theta_h is an affine function of T_h and E[theta_h] already encodes the target expectation. The reported nonzero errors in Section V (0.0058 to 1.0531) are inconsistent with this literal implementation, indicating that the estimator used in the experiments is not the estimator described in the paper, or that the correction was not applied as written.","section":"Section III.F"},{"comment":"The claim that the estimator 'operates without prior assumptions on the travel time distributions' is contradicted by the method itself. Computing c = E[theta_h] - theta_tilde requires the full joint distribution p^2(j) and the realization angles, which is exactly the information needed to evaluate E[T_h] directly by the classical formula in Eq. (7). If the correction term is omitted, theta_tilde = arccos(E[cos(T_h)]) is a biased proxy for E[T_h], because arccos is nonlinear and non-injective; the paper provides no valid inversion formula in that case. Either way, the proposed post-processing does not yield a legitimate QAE-based estimator of E[T_h].","section":"Section III.F and Abstract"},{"comment":"The 'rotation-angle range' parameter used in Experiment 2 is not defined precisely. Scaling Methods 2-4 fix gamma = pi/(S_max^h - S_min^h) or gamma = pi/(t_max^l - t_min^l), so the constructed angles lie in [0, pi] by construction. Combining a scaling method with ranges [0, 2pi], [0, 3pi], [0, 4pi], or [0, 5pi] requires an additional modification of gamma or of theta_l that is never specified. Without this definition, the central empirical finding that even multiples of pi outperform odd multiples is not reproducible.","section":"Section IV.B and Section V.B"}],"minor_comments":[{"comment":"The word 'rerspectively' appears in the discussion of basis states and should read 'respectively.'","section":"Section III.A"},{"comment":"The notation for the good and bad subspaces is inconsistent: Eq. (5) uses |psi_0> and |psi_1>, while the preceding text uses |Psi_0> and |Psi_1>.","section":"Section III.D.2"},{"comment":"The post-processing formula for Scaling Method 4, E[T_h] = sum theta_h^* / n / gamma + t_min^l over l, is ambiguous because gamma is link-specific; it should be written as a per-link inversion followed by a sum.","section":"Section III.F"},{"comment":"The comparison of variants reports counts of smallest errors without statistical significance or error bars; given that the experiments run on a simulator with 1024 shots, reporting variances or confidence intervals would strengthen the comparison.","section":"Section V.A"},{"comment":"The complexity discussion is standard and correct for QAE in general, but it should acknowledge that the state-preparation operator A for arbitrary discrete distributions may itself be nontrivial to implement; the paper assumes exact preparation without discussing the cost.","section":"Section III.G"}],"recommendation":"reject","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Briefly: this is the first paper to apply QAE to expected path travel time estimation in stochastic transportation networks, and it does a decent job explaining QAE to an ITS audience. The comparison of four QAE variants and four scaling methods on a small network is clean, and the takeaway — scaling and rotation-angle range matter more than variant choice — is plausible. But Section III.F's post-processing is circular. Under Scaling Method 1, the correction term c = E[theta_h] - theta_tilde is computed from the true expectation of the angle, which equals the target quantity E[T_h]. Adding it cancels the QAE estimate completely. The same affine structure applies to Methods 2-4. So as written, the estimator returns the ground truth by construction, which makes the reported nonzero errors impossible. If the correction is omitted, arccos(E[cos(T_h)]) is a biased proxy for E[T_h] and no valid inversion is offered. Either way, the central accuracy claim is unsupported.\n\nThe paper also overstates the 'no prior assumptions' point: loading the travel time realizations requires exact probabilities for state preparation. It is non-parametric in form, but it is not assumption-free. The selection of the best rotation-angle ranges from the same test data is a mild overfitting concern, not a major one.\n\nCredit where due: the paper is clearly organized, honestly credits Blank et al. and Filipovska, and the conceptual mapping table and circuit details are genuinely helpful for transportation researchers. The experiments, apart from the post-processing issue, are carefully reported.\n\nWho this is for: ITS readers who want a gentle introduction to QAE and a benchmark of variants. Quantum algorithm researchers will find it a straightforward adaptation of known methods.\n\nRecommendation: I would not desk reject it. The circular step is clearly identifiable and fixable in principle, and a serious referee could give the authors a concrete path — redefine what the estimator actually returns, drop the circular correction, or restrict the claims to what is actually estimated. But as it stands, the paper should not be accepted.","headline":"A useful QAE tutorial for ITS, but the post-processing step makes the estimator circular and the reported errors inconsistent with the described method.","tokens_in":17394,"tokens_out":4664,"would_cite":false,"duration_ms":47445,"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":"The paper argues that Quantum Amplitude Estimation can replace Monte Carlo sampling for expected path travel times in stochastic transportation networks, with a theoretical quadratic speed-up, and validates four variants on a small network.","keywords":["quantum amplitude estimation","stochastic vehicle routing","travel time estimation","Monte Carlo speedup","stochastic transportation networks","expectation estimation","rotation-angle scaling","simulation-based optimization"],"falsifier":"Take a skewed lognormal path whose true expected travel time is known analytically, run each scaling method while withholding $\\mathbb{E}[\\theta_h]$ from the post-processing step, and compare the output with the analytic value; if the estimates miss by more than the reported error range, the accuracy claim depends on feeding the answer back into the correction.","tokens_in":16316,"feed_emoji":"🚚","tokens_out":10564,"duration_ms":98263,"temperature":0.7,"pith_summary":"The paper tries to establish that Quantum Amplitude Estimation (QAE) can estimate the expected travel time of a path in a stochastic transportation network by reading a probability out of a quantum superposition instead of drawing many random samples. If true, this would replace Monte Carlo sampling in the inner loop of simulation-based stochastic vehicle routing with a quantum estimator that has a theoretical quadratic speed-up, using $O(1/\\epsilon)$ quantum queries where classical sampling needs $O(1/\\epsilon^2)$ samples for error $\\epsilon$, and without assuming a parametric form for the link travel time distributions. The authors implement four QAE variants and four rotation-angle scaling strategies, and their small-network experiments report that all variants give comparable low absolute errors, with accuracy governed mainly by the scaling method and rotation-angle range rather than by the variant. A reader should care because repeated travel-time expectation evaluation is the computational bottleneck that a hybrid quantum-classical routing solver would need to accelerate.","feed_headline":"Quantum method cuts travel-time sampling from quadratic to linear","feed_subtitle":"Amplitude estimation promises quadratic speedup over sampling; scaling and angle range, not variant, set accuracy.","key_machinery":"The carrying object is the amplitude-estimation sandwich: a state-preparation operator $\\mathcal{A}$ that loads all path realizations and their probabilities into an index register, an amplification operator $\\mathcal{Q}$ that amplifies the component marked as 'good', and the identity $\\mathbb{E}[\\cos(T_h)] = 1 - 2a$ that converts the measured amplitude $a$ into a cosine expectation. Around this sits the data encoding via controlled $R_y(\\theta)$ rotations, with four scaling methods that map link travel times $t_l$ to rotation angles $\\theta_l$, and a post-processing step that tries to invert the cosine through the correction term $c = \\mathbb{E}[\\theta_h] - \\tilde{\\theta}_h$. The choice of scaling method and rotation-angle range controls how much the cosine nonlinearity distorts the difference between realizations, which is why the experiments find those choices more influential than the QAE variant.","core_discovery":"The central claim is that the expected path travel time $\\mathbb{E}[T_h]$ can be recovered from a measured quantum amplitude rather than from repeated simulation. The construction encodes each joint realization of link travel times into a basis state of an index register, with amplitude equal to the square root of the realization probability, and rotates a data qubit by an angle derived from the realized path travel time. QAE then estimates the amplitude $a$ of the $|1\\rangle$ component, and the paper's measurement identity converts it to $\\mathbb{E}[\\cos(T_h)] = 1 - 2a$; post-processing rescales this cosine expectation into an estimate of $\\mathbb{E}[T_h]$. Experiments on a four-node network with uniform, normal, and lognormal link travel times report absolute errors roughly between 0.006 and 1.05, with iterative amplitude estimation the most stable variant and the combination of link-level scaling with rotation-angle ranges $[0,2\\pi]$ or $[0,4\\pi]$ giving the smallest errors.","pith_inferences":["The paper leaves implicit that $\\arccos(\\mathbb{E}[\\cos(T_h)])$ is not a generally valid proxy for $\\mathbb{E}[T_h]$; for skewed distributions this inversion is biased, so the numerical accuracy claims should be read as contingent on the ground-truth correction being supplied from outside the quantum routine.","The repeated finding that even multiples of $\\pi$ outperform odd multiples is consistent with the periodicity of the cosine: ranges that keep the encoded angles on a monotonic branch of the cosine reduce the ambiguity in the arccos inversion, which suggests a direct test on a single monotonic branch such as $[0,\\pi/2]$.","A natural extension would be to encode the expectation linearly into the amplitude or phase rather than through $\\cos(T_h)$, which would remove the nonlinear inversion step and make the estimator genuinely distribution-free in post-processing."],"forward_implications":["If the estimator works as claimed, expectation evaluation in simulation-based VRPSTT drops from $O(1/\\epsilon^2)$ classical samples to $O(1/\\epsilon)$ quantum queries, removing sample size as the dominant cost.","The same circuit can be reused across uniform, normal, lognormal, or empirical link travel times without re-deriving parametric formulas, since the distribution is loaded through state preparation rather than assumed.","A hybrid routing solver should fix the scaling method and rotation-angle range first (link-level scaling with $[0,2\\pi]$ or $[0,4\\pi]$ worked best) and then treat the QAE variant as a secondary choice, with IAE as the stable default.","The QAE module produces path cost estimates that can be fed directly into classical or quantum routing optimizers, so the contribution is an acceleration of a subproblem rather than a complete VRP solver."],"supporting_citations":[{"why":"Supplies the original quantum amplitude estimation algorithm and its error bound, which the canonical variant is built on.","marker":"[11]"},{"why":"Establishes the $O(1/\\epsilon)$ versus $O(1/\\epsilon^2)$ comparison with Monte Carlo and the simulation-based optimization setting the paper targets.","marker":"[12]"},{"why":"Provides the theoretical quadratic speed-up result for quantum Monte Carlo methods that motivates the complexity claim.","marker":"[24]"},{"why":"Supplies the discrete stochastic process encoding, the $R_y(\\theta)$ data rotation, and the $\\mathbb{E}[\\cos(T_h)] = 1 - 2a$ measurement scheme used here.","marker":"[27]"},{"why":"Provides the iterative QAE variant, the most stable performer in the experiments.","marker":"[14]"},{"why":"Provides the maximum likelihood QAE variant used in the comparison.","marker":"[15]"},{"why":"Provides the faster QAE variant used in the comparison.","marker":"[16]"},{"why":"Supplies the foundational encoding of stochastic travel times as quantum states that this path-level estimator builds on.","marker":"[31]"}],"fun_headline_variants":["QAE speeds travel time estimation quadratically over sampling","Quantum amplitude estimation: travel times with quadratic speedup","Quantum travel time: scaling and angle range, not variant, matter","Quadratic speedup for stochastic VRP travel times via QAE"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the post-processing step can recover $\\mathbb{E}[T_h]$ from $\\arccos(\\mathbb{E}[\\cos(T_h)])$ using a correction term $c = \\mathbb{E}[\\theta_h] - \\tilde{\\theta}_h$, because computing that correction requires knowing the true expectation $\\mathbb{E}[\\theta_h]$ that the algorithm is supposed to estimate.","fun_headline_variants_meta":{"raw":{"variants":["QAE speeds travel time estimation quadratically over sampling","Quantum amplitude estimation: travel times with quadratic speedup","Quantum travel time: scaling and angle range, not variant, matter","Quadratic speedup for stochastic VRP travel times via QAE"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00013,"raw_usage":{"total_tokens":1151,"prompt_tokens":1000,"completion_tokens":151,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":616,"completion_tokens_details":{"reasoning_tokens":81}},"tokens_in":616,"tokens_out":151,"duration_ms":4388,"temperature":1.0,"reasoning_tokens":81,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:03:38.903738+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a skewed lognormal path whose true expected travel time is known analytically, run each scaling method while withholding $\\mathbb{E}[\\theta_h]$ from the post-processing step, and compare the output with the analytic value; if the estimates miss by more than the reported error range, the accuracy claim depends on feeding the answer back into the correction.","supporting_citations":[{"cited_title":"Iterative quantum amplitude estimation,","cited_arxiv_id":null,"evidence_quote":"Provides the iterative QAE variant, the most stable performer in the experiments."},{"cited_title":"Foundations of quantum information science for transportation networks,","cited_arxiv_id":null,"evidence_quote":"Supplies the foundational encoding of stochastic travel times as quantum states that this path-level estimator builds on."}],"review_version":1}