{"id":"cb0e8161-43dc-42ae-b37e-402538b49ac0","arxiv_id":"1908.04229","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"The simulated breakpoints for 90 percent average success are about 99 to 99.9 percent gate fidelity for short circuits and above 99.99 percent for Grover, with coherence times of 50 to 500 microseconds.","lead":"This paper simulates three quantum algorithms with realistic limitations of current quantum chips, adding noise from imperfect gates and memory decay. It reports the minimum qubit quality levels needed for the algorithms to succeed most of the time.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Decoherence thresholds hinge on a nonstandard T1/T*_1 collapse model; standard amplitude-damping/dephasing channels could shift the reported T1 requirements.","rationale":"The reader's weakest assumption concerned the timing discretization and the arbitrary T1*=T1/2 relation. My check sharpens this: the larger issue is the type of decoherence channel, not just the timing. Modeling T*_1 as a projective measurement on superpositions and restricting T1 to qubits already in |1⟩ changes the physical meaning of the reported T1 thresholds. The paper is internally consistent and the qualitative ordering (larger circuits need better hardware, combined errors are worse) is robust, so this is not a rejection. But the central quantitative benchmarking claim is not secure until the decoherence model is replaced or explicitly validated against a standard amplitude-damping/dephasing simulation. That is an addressable revision, consistent with a conditional verdict.","tokens_in":16547,"tokens_out":7586,"duration_ms":77437,"concrete_test":"Re-run the decoherence and combined-error simulations with standard Markovian channels: per circuit moment, apply amplitude damping with Kraus operators governed by exp(-dt/T1) and pure dephasing with T_phi chosen so that 1/T2 = 1/(2T1) + 1/T_phi, keeping the same circuits, gate times, and fidelity model. Record the T1 values at which each algorithm's average success crosses 90% and 95%. If any threshold shifts by more than ~20% relative to Figs. 17/18/22, the central T1 benchmarking values are model-dependent rather than device-relevant.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's headline T1 bounds (roughly 50–500 µs in Figs. 17/18/22) are produced by the §V.A decoherence rules, not by standard open-system channels. T1 is applied only when a qubit is already in the |1⟩ computational basis state; any qubit in a superposition is instead subjected to T*_1, modeled as a projective partial measurement onto |0⟩ or |1⟩ with amplitude-squared probabilities. Physical T1 is amplitude damping: it reduces the |1⟩ amplitude of a superposition continuously and does not require the qubit to be classically |1⟩. Physical dephasing (T2/T2*) randomizes phase; it does not project the qubit onto a basis state. The paper then sets T*_1 = T1/2 (§VI), which is not the standard 1/T2 = 1/(2T1) + 1/T_phi relation, and introduces an extra measurement channel into every superposition. Because Fig. 22 shows combined-error thresholds track the decoherence-only curves more than the fidelity-only curves, the reported 'required coherence times' are sensitive to this modeling choice. The paper itself lists missing T2 and per-qubit parameter variation as future work, but the abstract and conclusion present the thresholds without that caveat.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a connectivity-limited qubit geometry, constructs adapted circuits for the Bernstein-Vazirani, QFT, and Grover algorithms on that geometry, and simulates them under two error models: a coherent amplitude-error model parameterized by average gate fidelity, and a decoherence model combining T1 energy relaxation with a partial-collapse process T1*. The simulations report average success rates and derive benchmark thresholds for gate fidelity and coherence time needed for high-probability success. The central quantitative claims are that smaller algorithms require average fidelities around 0.99-0.999 and T1 of order 50-500 microseconds, while Grover iterations require fidelities above 0.9999 and longer coherence times. The paper concludes that circuit depth and gate count dominate the success rates and that decoherence errors are the main limiting factor.","tokens_in":16839,"tokens_out":5449,"duration_ms":57399,"significance":"If the reported thresholds were robust, they would give useful NISQ-era hardware targets. The paper has several genuine strengths: the simulation methodology is a forward state-vector evolution rather than a fit to the success metric; the fidelity constraints in Eqs. (5)-(6) and (13)-(16) are internally consistent; and the comparison of two zero-mean error distributions is a reasonable first test of model sensitivity. The paper also makes a concrete attempt to include realistic connectivity constraints. However, the significance is substantially weakened by the nonstandard decoherence model and by representative, uncited gate times, so the quantitative thresholds are not directly comparable to standard T1/T2 hardware specifications. The qualitative conclusions about circuit depth and error accumulation are credible, but the headline numbers require either a reformulation using standard amplitude-damping/dephasing channels or a clear limitation statement.","major_comments":[{"comment":"The decoherence model is nonstandard: T1 is applied only to qubits that are in the |1> computational basis state, while superpositions are subjected to T1* as a projective partial measurement onto |0> or |1>. Physical T1 amplitude damping acts continuously on the |1> amplitude of any superposition, and physical dephasing does not project onto basis states. The paper sets T1* = T1/2 (Section VI) without a physical justification and acknowledges in Section VIII that T2 is missing. Because Fig. 22 shows the combined-error thresholds tracking the decoherence-only curves more than the fidelity-only curves, the reported required coherence times (Section VIII) are an artifact of this modeling choice. This issue is load-bearing for the central claim and needs to be addressed either by rerunning with standard amplitude-damping and dephasing channels or by explicitly restricting the claims to this specific collapse model and justifying its physical relevance.","section":"V.A and Eqs. (20)-(22)"},{"comment":"The gate times used to compute circuit times are described as 'based on average results found from reports for 1 and 2-qubit gates on superconducting qubits,' but no references are given. The T1 thresholds scale directly with the total circuit time through Eq. (19), so changing these representative times shifts the reported 50-500 microsecond range. Without citations or a sensitivity analysis over plausible gate times, the quantitative coherence-time thresholds are not robust. A revision should provide sources for these values or demonstrate how the conclusions change when they are varied.","section":"V.A and Fig. 16"},{"comment":"The conclusion states that the required fidelities 'ranged from 0.99≥⟨f⟩≥0.999' and the required coherence times 'were of the order 50µs≥T1≥500µs.' The inequality directions are reversed: these should presumably read 0.99≤⟨f⟩≤0.999 and 50µs≤T1≤500µs. More importantly, the T1 range contradicts Fig. 18, where the Grover iterations reach 90% success only at T1 = 425µs, 745µs, and 975µs. As written, the central summary misstates the paper's own results and should be corrected.","section":"VIII and Abstract"}],"minor_comments":[{"comment":"The phrase 'isolated isolate each source of error' contains a typo and should read 'isolate each source of error.'","section":"III.A"},{"comment":"The text says 'the effects of the noisty gates' — 'noisty' should be 'noisy.'","section":"IV.B"},{"comment":"The relation T1 = 2T1* is introduced 'for simplicity reasons' but not connected to the standard relation 1/T2 = 1/(2T1) + 1/Tφ; if T1* is meant to capture dephasing-like processes, this connection should be clarified.","section":"VI"},{"comment":"The notation '2N computational qubits' is ambiguous; it should be clear whether this means 2^N or 2N, and the example N=2 suggests the latter but could be stated explicitly.","section":"II.A"},{"comment":"The conclusion that the choice of P(ε) has no impact is based on two zero-mean Gaussian distributions; the paper correctly notes that biased distributions could change this, but the statement 'any probability distribution that satisfies ⟨ϵ⟩=0 will lead to the same average success' is stronger than the evidence supports.","section":"IV.A"}],"recommendation":"major_revision","confidential_remarks":"The paper's headline numbers are presented without sufficient caveats about the nonstandard T1/T1* model and the uncited gate times. I would encourage the editor to require either a simulation with standard amplitude-damping and dephasing channels or a clearly framed statement that the thresholds apply only to the paper's specific collapse model. The inequality typos in the conclusion should be fixed as part of that revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Daniel, here's the short version. This is a legitimate forward simulation of Bernstein-Vazirani, QFT, and Grover on a ladder connectivity graph, with noisy gates and decoherence. What's actually new is the specific combination: the coherent amplitude error model with Gaussian-sampled epsilon, the connectivity-restricted circuits, and the breakpoint numbers—roughly 0.99–0.999 average fidelity for small circuits, above 0.9999 for Grover, and T1 around 50–500 µs for decoherence-only. The math of the coherent error model checks out: equations 13–16 enforce the average fidelity constraints, and f=1-epsilon^2 is consistent with a unitary implementation. The authors also test two epsilon distributions and show the average-success results don't depend on which one you use, which is a good robustness check.\n\nThe soft spots are real but mostly addressable. The decoherence model is not standard. They let T1 collapse only qubits already in |1>, and for superpositions they use a T*1 partial-measurement channel with probability decay, then set T*1 = T1/2. Physical amplitude damping acts on the |1> amplitude of a superposition continuously and doesn't require the qubit to be classical |1>; and the T*1 = T1/2 relation isn't the usual 1/T2 = 1/(2T1) + 1/T_phi. So the headline T1 thresholds are sensitive to a modeling choice rather than a direct description of open-system dynamics. The paper acknowledges missing T2 and per-qubit variation as future work, but the abstract and conclusion don't carry that caveat. That's a load-bearing weakness for the coherence-time claims, though not for the fidelity thresholds.\n\nAlso minor: gate times in figure 16 are uncited representative values, and no code or data accompanies the paper, so the numbers are hard to reproduce exactly. And calling 90% average success 'reliably successful' is too strong given the large standard deviations shown in their own figures.\n\nBottom line: the fidelity-side results are worth taking seriously, and the study is a reasonable order-of-magnitude benchmark. The T1 numbers should not be quoted without the model caveat. The paper deserves a serious referee; I'd send it out, with requests for code/data and a sensitivity analysis on the T1/T*1 ratio and gate times. I wouldn't cite the coherence thresholds as physical, but the circuit-construction and fidelity-model portions are solid enough for a reading-group discussion.","headline":"A useful benchmark study of noisy circuits whose coherent-error half is clean but whose decoherence half uses a nonstandard collapse model, so the reported T1 thresholds should be read as specific to that model.","tokens_in":17341,"tokens_out":2185,"would_cite":false,"duration_ms":22023,"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":"Under the paper's two error models, small quantum circuits reach 90% average success only with gate fidelities between 0.99 and 0.999, and Grover iterations need fidelity above 0.9999 or coherence times of about a millisecond.","keywords":["quantum algorithms","gate fidelity","coherence time","energy relaxation","error model","Grover's algorithm","quantum Fourier transform","NISQ"],"falsifier":"Take one of the simulated circuits, such as one-iteration Grover or QFT, run it on a real device whose per-gate average fidelity and $T_1$ are independently characterized using the same connectivity, and compare the measured average success and run-to-run spread with the paper's curves; if the measurements fall outside the simulation's statistical spread, or if changing only the grouping of gates into parallel moments changes success more than the model predicts, the discrete-moment collapse assumption fails.","tokens_in":16296,"feed_emoji":"⚛️","tokens_out":16066,"duration_ms":141673,"temperature":0.7,"pith_summary":"This paper simulates how two hardware benchmarks—average gate fidelity and coherence time—determine whether small quantum algorithms succeed. The authors build hardware-like circuits for the Bernstein–Vazirani hidden-bit algorithm, the quantum Fourier transform, a controlled-controlled-NOT (CCNOT) gate, and Grover search on a fixed qubit geometry, then inject two single-parameter error models: coherent amplitude errors controlled by $\\langle f \\rangle$, and energy-relaxation/partial-collapse errors controlled by $T_1$. They report that circuits of roughly 20–30 gates exceed 90% average success once average fidelity lies between 0.99 and 0.999, or once $T_1$ is in the tens to hundreds of microseconds; the deeper Grover circuit needs fidelity above 0.9999 or coherence times near a millisecond. When both error types act together, decoherence is the dominant limit, and the simulated thresholds sit at the edge of what current NISQ hardware promises.","feed_headline":"Small quantum circuits need 99.9% gate fidelity for reliable success","feed_subtitle":"Simulations also show Grover's algorithm needs 99.99%+ fidelity or near-millisecond coherence.","key_machinery":"The carrying mechanism is a pair of single-parameter error models plus a discretized time structure. Each coherent error gate is built from a unitary amplitude error: the average gate fidelity is $f = 1 - \\epsilon^2$ for one-qubit gates and $f = (1 - \\epsilon_1^2)(1 - \\epsilon_2^2)$ for two-qubit gates, with $\\epsilon$ drawn from one of two zero-mean Gaussian-based distributions whose width is fixed by $\\langle f \\rangle$. Decoherence is governed by the exponential survival probability $P(\\Delta t) = e^{-\\Delta t / T_j}$, where $T_j$ is $T_1$ for energy relaxation to $|0\\rangle$ and $T_1^* = T_1/2$ for a partial-measurement collapse that renormalizes the superposition. Circuit time is divided into moments, each moment lasting as long as its slowest parallel gate, and after every moment each qubit is randomly collapsed according to $P(\\Delta t)$; the identity $\\prod_i e^{-\\Delta t_i / T_j} = e^{-\\sum_i \\Delta t_i / T_j}$ makes sequential moment sampling equivalent to one total-time decay. These ingredients convert the two benchmark numbers into predicted success probabilities for each circuit, which is what the paper's thresholds are.","core_discovery":"The paper claims that, for these circuits, the average success probability is controlled almost entirely by the aggregate quality numbers $\\langle f \\rangle$ and $T_1$, with partial-measurement collapse time set to $T_1^* = T_1/2$. Under gate fidelity errors alone, the smaller Bernstein–Vazirani, CCNOT, and QFT circuits achieve greater than 90% average success for average fidelities in the range 0.99–0.999, while one to three Grover iterations require fidelities upward of 0.9999. Under decoherence errors alone, the same 90% threshold needs coherence times of order 50–500 µs: about 30 µs for the shortest circuit, 61 µs for QFT, and 425–975 µs for one to three Grover iterations. With both error models combined, the small circuits cross 90% only near $\\langle f \\rangle \\approx 0.997$ and $T_1 \\approx 80$ µs, and the authors conclude that improving coherence time, not fidelity, yields the largest near-term gains. They also find that the detailed shape of the underlying error distribution matters little, and that a single decoherence collapse, especially the first, accounts for most of the damage.","pith_inferences":["Because the simulations omit dephasing ($T_2$), which the paper lists as future work, the reported $T_1$ thresholds are likely optimistic for full device noise; adding $T_2$ should push the required coherence times and fidelities upward.","The moment-based timing model implies that circuit scheduling is itself a noise parameter: recompiling the same algorithm to balance parallel moments and shorten each moment's longest gate should reduce decoherence without changing the gate count, a testable extension the paper does not run.","The observed favorable single-collapse boosts in Grover suggest a possible error-mitigation strategy for algorithms whose ideal final state has probability below 1: deliberately steering a partial collapse toward the desired outcome. This is an extension, not something the paper proposes.","The insensitivity to the error distribution $P_1(\\epsilon)$ versus $P_2(\\epsilon)$ assumes zero-mean errors; real devices with biased errors could make average fidelity alone an incomplete benchmark, and bias-aware metrics would need testing."],"forward_implications":["Smaller circuits—Bernstein–Vazirani, CCNOT, and QFT—exceed 90% average success with gate fidelities between 0.99 and 0.999 when gate error is the only noise source.","The same small circuits reach 90% average success under decoherence alone with coherence times near 30–60 µs, while one to three Grover iterations need 425–975 µs.","With both error sources active, the small circuits cross 90% only near $\\langle f \\rangle \\approx 0.997$ and $T_1 \\approx 80$ µs, and coherence time, not gate fidelity, is the limiting resource.","Grover circuits of the depth studied are beyond current NISQ devices: they need gate fidelity above 0.9999 or near-millisecond $T_1$.","The first decoherence collapse causes the largest drop in average success; subsequent collapses have smaller additional impact, so preventing early collapses matters most."],"supporting_citations":[{"why":"Supplies the definition of gate fidelity as state closeness, which the coherent-error model parameterizes through $f = 1 - \\epsilon^2$.","marker":"[5]"},{"why":"Cited with [7,8] for the coherence-time formalism that the decoherence model uses for $T_1$ and $T_1^*$ collapses.","marker":"[6]"},{"why":"Cited alongside [6,8] for the exponential relaxation and partial-measurement error models.","marker":"[7]"},{"why":"The third source in the paper's coherence-time citation group, supporting the exponential-decay error model.","marker":"[8]"},{"why":"Defines the Grover search algorithm whose one-, two-, and three-iteration circuits are benchmarked.","marker":"[16]"},{"why":"Defines the Bernstein–Vazirani algorithm circuit used as one of the smaller benchmarks.","marker":"[25]"},{"why":"Defines the quantum Fourier transform circuit used as the QFT benchmark.","marker":"[26]"}],"fun_headline_variants":["Coherence time beats fidelity for near-term quantum gains","Grover's algorithm needs 99.99% fidelity or millisecond coherence","Small circuits cross 90% success at 99.7% fidelity and 80µs coherence","First decoherence collapse does most harm to quantum circuits","Improve coherence time, not fidelity, for biggest near-term quantum wins"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported thresholds rest on the modeling premise that decoherence happens only as instantaneous collapses at discrete moments between parallel gate groups, and that the partial-measurement time $T_1^*$ is exactly half of $T_1$; if real qubits decohere continuously during gates, or if that half-times relation is wrong, the 50–500 µs numbers shift substantially.","fun_headline_variants_meta":{"raw":{"variants":["Coherence time beats fidelity for near-term quantum gains","Grover's algorithm needs 99.99% fidelity or millisecond coherence","Small circuits cross 90% success at 99.7% fidelity and 80µs coherence","First decoherence collapse does most harm to quantum circuits","Improve coherence time, not fidelity, for biggest near-term quantum wins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000995,"raw_usage":{"total_tokens":4203,"prompt_tokens":926,"completion_tokens":3277,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":542,"completion_tokens_details":{"reasoning_tokens":3195}},"tokens_in":542,"tokens_out":3277,"duration_ms":24912,"temperature":1.0,"reasoning_tokens":3195,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:48:33.336561+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take one of the simulated circuits, such as one-iteration Grover or QFT, run it on a real device whose per-gate average fidelity and $T_1$ are independently characterized using the same connectivity, and compare the measured average success and run-to-run spread with the paper's curves; if the measurements fall outside the simulation's statistical spread, or if changing only the grouping of gates into parallel moments changes success more than the model predicts, the discrete-moment collapse assumption fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the definition of gate fidelity as state closeness, which the coherent-error model parameterizes through $f = 1 - \\epsilon^2$."},{"cited_title":"The matrix forms for all of the coherent amplitude error gates are given in figure 8 FIG","cited_arxiv_id":null,"evidence_quote":"Cited with [7,8] for the coherence-time formalism that the decoherence model uses for $T_1$ and $T_1^*$ collapses."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Cited alongside [6,8] for the exponential relaxation and partial-measurement error models."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The third source in the paper's coherence-time citation group, supporting the exponential-decay error model."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the Grover search algorithm whose one-, two-, and three-iteration circuits are benchmarked."},{"cited_title":"Kapit, Phys","cited_arxiv_id":null,"evidence_quote":"Defines the Bernstein–Vazirani algorithm circuit used as one of the smaller benchmarks."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the quantum Fourier transform circuit used as the QFT benchmark."}],"review_version":1}