{"id":"87755fb4-078d-4e39-83fa-0fc2e121fbc4","arxiv_id":"2608.05435","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A new LNN QFT compilation reaches all-to-all CX counts, and a truncated 'Convolutional' variant was demonstrated on IBM hardware up to 100 qubits with the correct frequency as the mode output.","lead":"The paper introduces a linear-nearest-neighbor compilation of the Quantum Fourier Transform that matches the two-qubit gate count of a fully connected machine, and an approximate version was run on IBM hardware at up to 100 qubits. The correct output appears as the most frequent bitstring, but the reported fidelity numbers mix approximation error with hardware error.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"AQFT truncation error is not separated from hardware error in the Eq. (2) fidelity estimator, so the reported fidelities and the 'above 1% threshold' claim are not yet established.","rationale":"The paper has two separable claims: a compilation claim and an experimental-demonstration claim. The compilation claim -- an LNN QFT/AQFT with n^2-n CX gates, and a convolutional variant with n^2-n+2 CX gates -- is internally plausible and is not contradicted by anything I found in the text. The derivation is presented as a circuit-identity argument; I cannot fully verify Fig. 1d from the text alone, but that is a conventional checkable step and not the weakest point. The experimental claim rests on the fidelity numbers and on the mode-bitstring observations. The mode-bitstring observations are genuine and already give a weak but real signal at up to 100 qubits. The quantitative fidelities, however, depend on Eq. (2), and Eq. (2) is applied to AQFT circuits without reporting the noiseless success probability of those approximate circuits. This is exactly the reader's weakest_assumption, and I agree that it is load-bearing: if the noiseless AQFT baseline is not essentially 1, the reported fidelities are not estimates of the hardware's process fidelity, and the 'largest QFT demonstrated' claim, as quantitatively supported, is not established. The proposed simulation test is straightforward with standard statevector tools and would settle the issue. If the simulation shows q_k near 1, the concern disappears and the experimental claims stand; if q_k is small, the paper must revise its fidelity interpretation or add a truncation-aware estimator. I therefore leave the reader's CONDITIONAL verdict unchanged.","tokens_in":13022,"tokens_out":11495,"duration_ms":113043,"concrete_test":"Run a noiseless statevector simulation of the exact compiled Convolutional AQFT circuits used in the experiment, i.e. with approximation threshold pi/16 and d=3, the same periodic state preparation (H followed by RZ parameterized by each randomly selected frequency), the same layout and transpilation but with ideal gates, for n=50, 80, and 100. For each of the 20 random frequencies, record the ideal success probability q_k of the target bitstring and identify the noiseless mode. Compare the average q_k against the measured p_k values and against the Eq. (2) fidelity estimate. If the average q_k is close to 1, the reader's concern is resolved; if it is appreciably below 1, re-estimate hardware fidelity using a truncation-aware model such as p_k = F q_k + (1-F)/2^n and check whether the corrected hardware fidelity still exceeds the 1% threshold at n=80.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing concern is methodological and sits in Section IV, specifically in the use of Eq. (2) to estimate process fidelity. The estimator from Ref. [38] is derived assuming that, for each randomly selected periodic input state, the ideal circuit returns the target bitstring with probability exactly 1. That assumption is true for the full QFT combined with the stated state-preparation layer, but the experiments do not run the full QFT: all circuits are AQFTs obtained by truncating rotations of pi/16 and below, which corresponds to the d=3 approximation in Table I and Figs. 2-3. For a truncated AQFT, the ideal output is not a computational basis state, so the noiseless success probability q_k of the target bitstring is strictly less than 1. The paper never reports q_k or a noiseless simulation baseline. Consequently, the quoted process fidelities of 11.4% at n=50 and 1.8% at n=80 conflate two distinct error sources: (i) the intentional AQFT truncation error and (ii) hardware/readout noise. If q_k is substantially below 1 at these sizes, then the true hardware fidelity is even lower than reported, and the statement that the process fidelity remains above the conventional 1% threshold up to 80 qubits is not supported. The separate mode-bitstring observation (the target is the most frequent outcome) is a legitimate experimental finding and is less affected by this issue, but it does not validate the quantitative fidelity estimates.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces two LNN compilation strategies for the QFT: a 'Low-CX' compilation using n^2-n CX gates (matching the all-to-all baseline for the full QFT and for AQFTs at any truncation threshold), and a 'Convolutional' variant using one ancilla and two additional CX gates, realized as a translation-invariant kernel gadget. The authors then report experiments on IBM Quantum hardware for AQFT circuits with truncation at rotations of pi/16 and below, claiming process fidelities of 11.4% at 50 qubits and 1.8% at 80 qubits, and that the target bitstring remains the most frequent outcome up to 100 qubits, which they describe as the largest QFT circuit executed to date.","tokens_in":13275,"tokens_out":9744,"duration_ms":90107,"significance":"The compilation derivation is the main strength: it is constructive, parameter-free, and if correct it removes routing overhead entirely for QFT on LNN hardware, giving a CX count that matches all-to-all connectivity. The convolutional form and the kernel-gadget picture are elegant and potentially useful for hardware-aware scheduling. The experimental observation that the target bitstring is the mode outcome at 50-100 qubits is a notable empirical result. However, the quantitative fidelity claims rest on a questionable application of the estimator in Eq. (2) to truncated AQFT circuits, so the headline fidelity numbers and the 'above 1% threshold' claim need support before the paper's central quantitative conclusions can be accepted.","major_comments":[{"comment":"The fidelity estimator in Eq. (2) is applied to circuits that are not the full QFT. The paper states that all executed circuits are AQFTs with rotations of pi/16 and below truncated, and explicitly acknowledges that this 'introduces synthesis error compared to the full QFT unitary definition in Eq. (1)'. For such an AQFT, the ideal probability q_k of observing the full-QFT target bitstring is strictly less than 1 for each random frequency. The estimator in Eq. (2), as used here, is only valid when the ideal success probability of each benchmark circuit is 1; otherwise it conflates AQFT truncation error with hardware noise. The manuscript never reports q_k or a noiseless simulation of the executed AQFT circuits, so the quoted process fidelities of 9.6%/11.4% (n=50) and 1.4%/1.8% (n=80) are not established as process fidelities of the executed unitary relative to its own ideal. Please provide noiseless AQFT success probabilities for the same circuits and either re-estimate the fidelity against the ideal AQFT unitary or explicitly separate the truncation contribution from the hardware contribution.","section":"Section IV, Eq. (2)"},{"comment":"The claims that 'the success probability remains above the previously articulated ~1% threshold up to 80 qubits' and the abstract's 'process fidelity of 11.4% at 50 qubits, and 1.8% at 80 qubits' inherit the issue in the first major comment. Until the noiseless q_k values are supplied, these quantitative thresholds are unsupported. The mode-bitstring observation, namely that the target is the most frequent outcome in each trial, is a separate and more robust empirical result; it should be presented as the primary evidence for the 100-qubit claim, with the fidelity numbers either corrected or removed from the abstract and conclusion.","section":"Section IV, Figs. 4-5"}],"minor_comments":[{"comment":"The typeset expression for Fhat is ambiguous: it is not clear whether the factor m/(m-1) multiplies both terms or only the first; please add brackets to display the formula unambiguously.","section":"Section IV, Eq. (2)"},{"comment":"The sentence 'The chosen threshold maximizes circuit fidelity in the current benchmarking exercise on the selected device' is an unsubstantiated optimization claim; either provide a small threshold scan or soften the wording to indicate that this threshold was selected empirically.","section":"Section IV, paragraph on AQFT threshold"},{"comment":"The paper uses 'process fidelity' to describe the composite 'QFT + measurement' operation and then 'process fidelity of the unitary QFT alone' after readout mitigation; these are different quantities, and the abstract should state explicitly which one is being reported.","section":"Section IV, Figs. 4-5 and Abstract"},{"comment":"At a nominal width of 100 qubits, the executed circuit actually uses 101 physical qubits because of the ancilla. The caption discloses this, but the abstract and conclusion should state explicitly that the claim is for 100 data qubits plus one ancilla.","section":"Section V and Fig. 5 caption"},{"comment":"No statistical uncertainties are reported for the fidelity estimates derived from 20 random frequencies and 4096 shots; please provide confidence intervals (for example, by bootstrapping over the 20 trials).","section":"Section IV, fidelity estimates"},{"comment":"The hexadecimal bitstring labels in Fig. 5a and 5b are dense and partially truncated; they are hard to read and should be reformatted or replaced by abbreviated labels with a mapping table.","section":"Fig. 5"}],"recommendation":"major_revision","confidential_remarks":"The compilation contribution appears sound and publishable, and the mode-bitstring experimental observation is interesting. The main blocker is the fidelity estimator applied to truncated AQFT circuits. I would be willing to accept a revision that supplies noiseless AQFT success probabilities and corrects the fidelity claims accordingly; if the authors cannot provide such a baseline, the quantitative fidelity statements should be removed from the abstract and the paper reframed around the distinguishability result."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, this paper is worth reading for the compilation section alone. The authors give a constructive LNN QFT that uses n^2 - n CX gates, matching the all-to-all count and saving 2n-4 CX over Park/Ahn and n-1 over Klaver. The derivation using the H = S·SX·S identity and the √X commutation through three CX gates is clean and checkable. The convolutional variant with one ancilla and a translation-invariant kernel gadget is a clever extension that lowers gate depth and reduces the light cone of each qubit. That part is solid.\n\nThe experimental side is where the paper needs work. The process fidelity numbers come from Eq. (2), an estimator derived for circuits whose ideal output is a single computational basis state with probability 1. But all the benchmark circuits are truncated AQFTs, omitting rotations of π/16 and below. For those circuits the noiseless success probability of the target bitstring is strictly below 1, and the paper never reports it. Without a noiseless simulation baseline, the 11.4% at n=50 and 1.8% at n=80 conflate truncation error with hardware error, and the \"above 1% up to 80 qubits\" claim is unsupported. The mode bitstring result (target is the most frequent outcome up to 100 qubits) is a legitimate experimental observation, but it is not a process fidelity.\n\nI would not desk-reject this. The compilation result is new, non-trivial, and independently verifiable. But the experimental validation needs a noiseless baseline of the AQFT circuits and a corrected estimator (or a statement of q_k) before the fidelity claims can be taken seriously. A serious referee should ask for those. If the authors can supply the baseline, the paper becomes a solid contribution. If they cannot, the experimental section should be reframed as a mode-identification demonstration, not a fidelity benchmark.","headline":"A genuinely better LNN QFT compilation, but the experimental fidelity claims conflate AQFT truncation error with hardware error.","tokens_in":13901,"tokens_out":3177,"would_cite":true,"duration_ms":27792,"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":"A new compilation strategy gives the quantum Fourier transform the same two-qubit gate count on linear qubit chains as on fully connected hardware, and the circuit works up to 100 qubits.","keywords":["Quantum Fourier transform","Linear nearest neighbor","Convolutional compilation","CX gate count","Approximate QFT","IBM Quantum Platform","Process fidelity","Routing overhead"],"falsifier":"Run the exact truncated AQFT circuits (threshold π/16) on a statevector simulator and compute the ideal probability of the target bitstring for n=50 and n=80. If that probability is substantially below 1, then the Eq (2) fidelity is biased upward as a measure of hardware performance, and the reported 11.4% and 1.8% figures would need to be divided by the ideal probability to separate synthesis error from device error.","tokens_in":12759,"feed_emoji":"⚛️","tokens_out":6419,"duration_ms":54761,"temperature":0.7,"pith_summary":"The paper claims that the quantum Fourier transform (QFT) can be compiled onto a linear nearest-neighbor (LNN) qubit topology with exactly the same number of CX gates as an all-to-all architecture: $n^{2}$ - n for n qubits, and $n^{2}$ - n + 2 for a convolutional variant that adds an ancilla. The authors derive this by starting from a known LNN construction, then using a gate identity that lets a √X gate commute through three CX gates, which aligns CX pairs at layer interfaces so they cancel. They further repackage the circuit as a translation-invariant kernel gadget that steps along the register. On IBM quantum hardware, the correct frequency peak remains the most likely measurement outcome up to 100 qubits, with process fidelity estimates of 11.4% at 50 qubits and 1.8% at 80 qubits. If correct, this removes routing overhead for QFT on any connected device and yields the largest QFT executed to date.","feed_headline":"100-qubit quantum Fourier transform demonstrated on real hardware","feed_subtitle":"A convolutional compiler removes routing overhead on linear qubit chains, and the correct output beats all others up to 100 qubits.","key_machinery":"The load-bearing identity is the commutation of a √X gate through a specific configuration of three CX gates (Fig 1d), which, combined with rewriting H = S·√X·S and moving the diagonal S gates outward, aligns CX pairs at layer boundaries so they cancel as CX² = I. The second mechanism is the convolutional kernel: starting from the Low-CX circuit, one ancilla in |0> and an initial SWAP chain reverse the direction of the long CX chain; because the first CX in each SWAP is controlled by |0>, it can be deleted, and adjacent aligned CXs cancel, leaving a translation-invariant gadget of d+2 qubits that increments along the register. This gadget confines most entangling operations to a brief kernel pass, reducing the average number of causally upstream CX gates per qubit wire.","core_discovery":"The central discovery is a compilation of the QFT onto an LNN architecture that exactly matches the CX gate count of an all-to-all architecture. The derivation rewrites each Hadamard as S·√X·S, moves the diagonal S gates to the circuit edges, and pushes each √X leftward through three preceding CX gates using a proven identity; this makes two CX gates that were separated by an H gate adjacent and aligned, so they cancel at every interface between adjacent QFT layers, saving 2n-4 CX gates over the Park-Ahn construction. A further transformation using an ancilla in |0> and an initial SWAP chain reverses the long initial CX chain and compiles it as late as possible, producing the Convolutional QFT/AQFT: a compact kernel gadget spanning d+2 qubits that strides across the register. Experimentally, the mode of the output distribution equals the encoded frequency for every tested circuit up to n=100, and the process fidelity estimator of Eq (2) yields 11.4% at n=50 and 1.8% at n=80 after readout mitigation.","pith_inferences":["The same kernel-gadget strategy could likely compile other translation-invariant circuits, such as quantum walks or Trotterized translation-invariant Hamiltonians, onto LNN hardware with similar routing savings.","Because the reported fidelities use truncated AQFT circuits, the 11.4% and 1.8% figures probably include synthesis error; a noiseless-simulator baseline would reveal how much headroom remains for hardware improvement.","The linear scaling for fixed d suggests the method could scale to several hundred qubits if the local two-qubit error in the kernel stays low enough.","The ALAP scheduling that confines gates to the kernel naturally pairs with error-detection or quantum-error-correction patches on a linear lattice, so the compilation may remain useful in fault-tolerant settings."],"forward_implications":["QFT and approximate QFT circuits on any LNN device now cost the same number of CX gates as on an all-to-all device, eliminating routing overhead for this subroutine.","For a fixed approximation threshold d, the gate count scales linearly in n (d(2n - d - 1) + 2 for the convolutional AQFT), making larger circuits practical on noisy hardware.","The convolutional kernel structure keeps qubits idle outside a brief kernel pass, so dynamical decoupling sequences can protect them from decoherence and crosstalk.","The experimental demonstration shows that with 4096 shots per circuit, the correct frequency of a periodic quantum state is identifiable up to 100 qubits, the largest QFT execution reported.","The construction is directly compatible with heavy-hex or square-lattice topologies and with grids of code patches in fault-tolerant architectures."],"supporting_citations":[{"why":"Supplies the base LNN QFT compilation that this work modifies via CX cancellations.","marker":"[26]"},{"why":"Defines the all-to-all QFT CX count (n^2 - n) that the new LNN scheme matches.","marker":"[29]"},{"why":"Provides the unbiased process-fidelity estimator (Eq. 2) used to score the hardware results.","marker":"[38]"},{"why":"Klaver et al.'s swap-less LNN QFT is the alternative construction compared in Table I.","marker":"[41]"},{"why":"Nielsen and Chuang gives the standard QFT unitary and the 2-CX synthesis of CP gates.","marker":"[23]"},{"why":"Supplies the benchmarking methodology and periodic-signal state preparation used in the experiments.","marker":"[42]"},{"why":"Provides the dynamical-decoupling embedding that protects idle qubits during kernel traversal.","marker":"[18]"},{"why":"Aumann et al.'s record-fidelity QFT set the 1% fidelity threshold and the comparison baseline.","marker":"[39]"}],"fun_headline_variants":["QFT on 100 qubits: convolutional kernel matches all-to-all","100-qubit QFT on IBM's linear chain with two extra gates","Convolutional QFT compiles to 100 qubits without SWAPs","Quantum Fourier Transform reaches 100 qubits on real hardware","A two-gate kernel strides QFT to 100 qubits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The fidelity calculation assumes the ideal circuit returns the target bitstring with probability exactly 1, yet the tested circuits are approximate QFTs whose noiseless success probability is never reported, so truncation error and hardware error are not separated.","fun_headline_variants_meta":{"raw":{"variants":["QFT on 100 qubits: convolutional kernel matches all-to-all","100-qubit QFT on IBM's linear chain with two extra gates","Convolutional QFT compiles to 100 qubits without SWAPs","Quantum Fourier Transform reaches 100 qubits on real hardware","A two-gate kernel strides QFT to 100 qubits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001543,"raw_usage":{"total_tokens":6184,"prompt_tokens":967,"completion_tokens":5217,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":583,"completion_tokens_details":{"reasoning_tokens":5123}},"tokens_in":583,"tokens_out":5217,"duration_ms":31740,"temperature":1.0,"reasoning_tokens":5123,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T13:09:56.724151+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the exact truncated AQFT circuits (threshold π/16) on a statevector simulator and compute the ideal probability of the target bitstring for n=50 and n=80. If that probability is substantially below 1, then the Eq (2) fidelity is biased upward as a measure of hardware performance, and the reported 11.4% and 1.8% figures would need to be divided by the ideal probability to separate synthesis error from device error.","supporting_citations":[{"cited_title":"Park and D","cited_arxiv_id":null,"evidence_quote":"Defines the all-to-all QFT CX count (n^2 - n) that the new LNN scheme matches."},{"cited_title":"B¨ aumer, V","cited_arxiv_id":null,"evidence_quote":"Klaver et al.'s swap-less LNN QFT is the alternative construction compared in Table I."},{"cited_title":"Karuppasamy, V","cited_arxiv_id":null,"evidence_quote":"Provides the dynamical-decoupling embedding that protects idle qubits during kernel traversal."}],"review_version":1}