{"id":"fb1f76f3-bc76-40b7-b7f2-a99c6a7bc83e","arxiv_id":"2504.14453","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A postselected random quantum cellular automaton driven by a 2-gram corpus state converges faster when two-site gates are added, and its information scrambling shows a percolation-like threshold in gate density.","lead":"Researchers propose an iterative algorithm in which a random quantum circuit is guided by word-pair statistics from a simple three-word corpus, accepting only updates that bring the state closer to the target corpus state. Adding two-site quantum gates speeds convergence, while information spreading turns off when such gates are too rare, a behavior the authors compare to bond percolation.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'bond percolation' claim is inferred from visual plateaus in TMI and D with no percolation observable computed; this is the least-supported link in the central argument.","rationale":"I agree with the reader's conditional verdict but identify a different weakest assumption. The reader's postselection concern is real: Eq. (2) requires two-site reduced density matrices, and measuring them is destructive, so a direct hardware implementation is not described. This caveat, however, could be addressed by reframing the work as a classical simulation of a postselected quantum process; the reported D, EA, and TMI curves would survive that reframing. The percolation claim is more fragile because it is the paper's headline and is inferred from the shape of curves without computing the percolation variable it names. No spanning probability, no cluster-size analysis, no finite-size scaling, and no derivation connects Sts to a percolation lattice, so the threshold identification is effectively an eye-fit. The paper explicitly defers numerical details to an SM that is not present in the supplied text, and it reports a fitted floor c≈1.1, so the claimed speedup is not a convergence rate. For these reasons I recommend keeping the conditional verdict but requiring a direct percolation check as a condition of acceptance.","tokens_in":12049,"tokens_out":10940,"duration_ms":106769,"concrete_test":"Compute the actual percolation observables for the same ensemble: for each sampled circuit at each Sts, build the spacetime graph whose directed edges are the two-site gates that are sampled as effective (CF_you, CF_are, CF_here) and measure (i) the probability that a connected path of effective gates spans the L sites within t=5000, (ii) the mean cluster size, and (iii) the crossing of spanning probabilities for L=6,8,10,12 at fixed t/L. Compare the finite-size crossing point with the claimed Sts=2 and Sts=3 thresholds. If the crossing is absent or occurs at a different Sts, the TMI and D plateaus are not evidence for bond percolation. This check also reveals whether the two claimed thresholds correspond to one or two distinct connectivity transitions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The strongest claim—that information scrambling exhibits a bond percolation transition with critical point Sts=2 (Fig. 4(c)) and that the update rate crosses a second percolation threshold at Sts=3 (Fig. 3(b))—is not supported by any percolation calculation. The paper never samples the spacetime network of effective two-site gates, never computes a spanning probability or cluster-size distribution, and gives no relation between Sts and a bond-occupation probability on a known percolation lattice. On L=6, t≈5×10^3, a plateau in TMI or D can be a finite-size or saturation effect; a true percolation threshold is a property of the infinite lattice and would require finite-size scaling. Moreover, the text assigns two different thresholds (Sts=2 and Sts=3) to 'bond percolation' without explaining how one connectivity transition yields two critical Sts values. The D=at^b+c fit (Eq. 8) also fixes c≈1.1, meaning D does not go to zero; the fitted exponent b, the basis of the 'search speedup', describes a transient approach to a nonzero floor, not convergence to the target state. Since the abstract's headline findings are the speedup and the percolation transition, this unsupported threshold identification is the main risk to the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an iterative, postselected search algorithm on a one-dimensional random quantum cellular automaton. The update rule (Eq. 2) accepts a random circuit step only if the average Frobenius distance D from the two-site reduced density matrices to a 2-gram 'Corpus State' |CS⟩ decreases; otherwise the previous state is kept. The authors study how adding two-site gates affects the evolution, reporting (i) a 'search speedup' characterized by the fitted exponent b in the power law D = a t^b + c (Eq. 8), (ii) block-diagonalization of the reduced density matrices quantified by an entanglement asymmetry, and (iii) two distinct 'bond percolation' thresholds: Sts = 3 for the update rate (Fig. 3(b)) and Sts = 2 for the tripartite mutual information (Fig. 4(c)). The central claims are that the two-site gates directionally optimize initial states toward the target entangled state and that information scrambling undergoes a percolation transition.","tokens_in":12238,"tokens_out":4352,"duration_ms":38833,"significance":"If the claims were fully supported, the paper would offer a novel connection between n-gram-inspired cooperative interactions and quantum many-body dynamics, and a potentially useful postselected search paradigm. The authors provide a concrete numerical protocol, explicit gate sets, and averaged simulations over 500 configurations; the raw decrease of D under the accept-if-closer rule is a direct consequence of the rule and is reproduced in the simulations. Nevertheless, the two headline findings — the speedup and the bond-percolation transition — are currently supported only by fitted or visual evidence, and the physical implementability of the postselection rule is not addressed. The paper is therefore of moderate significance as a proposal, but its quantitative claims need substantial revision or re-scoping before they can be accepted.","major_comments":[{"comment":"The postselection rule requires evaluating D, which needs all nearest-neighbor two-site reduced density matrices of the full state at every step. The paper gives no measurement protocol that would obtain these reduced density matrices without destroying the state or otherwise paying a cost; on actual hardware such measurements generally collapse the state, while on a classical simulator the updating 'state' is a classical data structure and the phrase 'quantum search speedup' is not justified. The authors should either provide a non-demolition measurement/feedback scheme that makes the rule physically implementable, or explicitly state that the algorithm is analyzed as a classical postprocessing protocol on a simulated state and revise the quantum-search framing accordingly.","section":"Setup, Eq. (2)"},{"comment":"The claimed bond-percolation thresholds, Sts = 3 in Fig. 3(b) and Sts = 2 in Fig. 4(c), are inferred from visual plateaus in the final-state distance D and the tripartite mutual information TMI. No percolation observable is computed: there is no spanning probability, cluster-size distribution, or finite-size scaling, and no mapping is given between Sts and a bond-occupation probability on a known percolation lattice. For L = 6 and t ≈ 5 × 10^3, the plateaus could be finite-size or saturation effects. Moreover, the text assigns two different threshold values to 'bond percolation' without explaining how one connectivity transition produces two critical points. Please provide a genuine percolation analysis with finite-size scaling, or relabel these observations as crossover or plateau features.","section":"Results, Figs. 3(b) and 4(c)"},{"comment":"The 'search speedup' is quantified by the fitted exponent b in D = a t^b + c. With c ≈ 1.1, D approaches a nonzero floor rather than converging to the target |CS⟩, so the fitted exponent describes a transient approach to a finite residual distance. No error bars or goodness-of-fit measures are reported for a, b, or c, and b is fitted to the same quantity D that defines the acceptance rule, making the 'speedup' a fitted characterization of the rule's own dynamics rather than an independent prediction. Please provide confidence intervals, model comparison (e.g., against a logarithmic or exponential decay), and a threshold-based definition of convergence (for example, time to reach a fixed small D) before claiming a quantum search speedup.","section":"Results, Eq. (8) and Fig. 2(a)"}],"minor_comments":[{"comment":"The sentence 'the the evolution of D is a smooth concave function' contains a duplicated article 'the'; please remove the duplicate.","section":"Fig. 2 caption"},{"comment":"The caption lists 'Sts = log10(1), log10(2), log10(3) and 1', which gives values 0, 0.301, 0.477, and 1, yet the text later discusses thresholds at Sts = 2 and Sts = 3. Please clarify the scale and the meaning of the plotted Sts values, presumably Sts = -log10(P) with P the sampling probability of effective two-site gates.","section":"Fig. 2(b) caption"},{"comment":"All results are averaged over 500 configurations, but no error bars or standard deviations are shown; please add error bars or state that they are smaller than the marker size.","section":"All figures"},{"comment":"The statement 'the update for Sts > 3 is totally determined by one-site gates' is too strong, because two-site gates are still sampled with nonzero probability in that regime; please rephrase as 'dominated by one-site gates' or give a precise quantitative criterion.","section":"Results, paragraph near Fig. 3(b)"},{"comment":"The phrase 'information scrambling dependent of gate sampling' should be 'information scrambling dependent on gate sampling'; please correct the grammar.","section":"Abstract and Introduction"}],"recommendation":"major_revision","confidential_remarks":"The manuscript has a fresh idea and the numerical protocol is easy to reproduce, but the central quantitative claims are currently overreaching. The bond-percolation identification is the largest risk: it is based on plateaus in small-system data with no percolation observable, and the two different threshold values (Sts = 2 and 3) are not reconciled. The postselection implementability issue also needs to be faced head-on; if the algorithm is meant to be a classical postprocessing scheme, the 'quantum speedup' language must be removed from the abstract and title. I believe the paper could become publishable after a major revision that adds proper statistical and percolation analyses and carefully re-scopes the claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe model in 2504.14453 is genuinely new: a postselected random quantum cellular automaton whose update rule is driven by a 2-gram corpus state, with the two-site gate sampling controlled by a gate entropy. That combination is not in the literature, and the raw observation—accept-if-closer reduces the Frobenius distance D, and adding two-site gates changes the decay—seems to hold in the simulations. The authors are also candid about the c=1.1 floor and the failed D=at^b fit. That part is solid enough.\n\nThe soft spots are the two headline claims. The 'search speedup' is the fitted exponent b in D=at^b+c, with no error bars and with the acknowledged nonzero floor; it describes a transient approach to a nonzero value, not convergence to the target. The 'bond percolation' claim is the least supported. No percolation observable is computed anywhere—no spanning probability, no cluster-size distribution, no finite-size scaling. The thresholds at Sts=2 and Sts=3 are read off visual plateaus in TMI and D at L=6, and the paper calls both a 'bond percolation threshold' without explaining how one connectivity transition yields two different values. That is overreach.\n\nThe postselection step is also a structural concern. Computing D requires two-site reduced density matrices. On real hardware that means measurements, which collapse the state; no non-demolition or feedback scheme is given. If the scheme is run on a classical simulator, the state is a classical data structure and calling it a quantum search speedup is not justified. This does not sink the numerical observation, but it weakens the quantum meaning of the claims.\n\nWho this is for: people working on postselected circuits, state preparation, and quantum-inspired optimization. The paper deserves a serious referee—the idea is fresh and the numerics are reproducible in principle—but the referee should require error bars, a proper percolation analysis or a toned-down claim, and a clear discussion of measurement cost. I would not cite it as evidence for a speedup or a transition, but I might cite it as an example of a postselected corpus-state scheme.","headline":"Novel postselected corpus-state circuit with plausible numerics, but the percolation threshold and search speedup are both under-supported.","tokens_in":12839,"tokens_out":2800,"would_cite":false,"duration_ms":22984,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Ud","03.67.Ac","03.67.Mn","05.50.+q"],"model":"deepseek-v4-flash","headline":"This paper claims that postselected random quantum circuits with effective two-site gates steer product states toward a target entangled state, with distinct gate-density thresholds for state update and information scrambling.","keywords":["quantum cellular automata","2-gram model","postselection","random unitary circuits","information scrambling","bond percolation","entanglement asymmetry","tripartite mutual information"],"falsifier":"Simulate or implement the same update rule on a system with L = 8 or larger and d = 3, sampling gates from the stated distributions, and measure the final-state tripartite mutual information as a function of Sts: if the vanishing above Sts = 2 does not persist, or if the same step-function appears in a classical simulation that stores the full state without any quantum measurement, then the bond-percolation identification for information scrambling is not established.","tokens_in":11666,"feed_emoji":"⚛️","tokens_out":11765,"duration_ms":93553,"temperature":0.7,"pith_summary":"Adding effective two-site gates to a postselected random quantum circuit makes the search converge faster to a target entangled 'corpus state' built from a 2-gram word model, and the dynamics exhibits two distinct gate-density thresholds. The authors identify Sts = 3 as the point where the final-state distance to the corpus state stops improving, and Sts = 2 as the point where the tripartite mutual information vanishes, marking the critical density for information scrambling. The algorithm therefore provides a way to tune between local state refinement and global information spreading by changing only the probability of sampling two-site gates. If the results hold, they point to a postselection-driven protocol for directed preparation of entangled states that is governed by the structure of a corpus rather than by a Hamiltonian.","feed_headline":"Two-site gates speed convergence to a target entangled state","feed_subtitle":"A postselected automaton scrambles information only above a two-site gate-density threshold.","key_machinery":"The load-bearing object is the corpus state |CS⟩ = (2|you⟩|are⟩ + |are⟩|here⟩ + |here⟩|you⟩)/√6, a superposition of the allowed adjacent word pairs in the two-sentence corpus, together with the postselection rule: a random circuit proposes an update via one-site and two-site gates, and the update is kept only if the Frobenius distance D (averaged over nearest-neighbor pairs) between ρ_{j,j+1} and |CS⟩⟨CS| decreases. The circuit itself is a four-layer brickwork of staggered two-site gates on alternating bonds plus one-site gates, with gate entropies Sos and Sts controlling how often effective operations are sampled. The thresholds for update saturation (Sts = 3) and scrambling (Sts = 2) are extracted from the final-state distance and the tripartite mutual information respectively.","core_discovery":"The paper's central claim is that effective two-site gates 'directionally optimize initial states to the target many-body entangled state' and that the resulting dynamics is organized by a bond-percolation threshold in gate sampling. With two-site gates, the average Frobenius distance D between the updating state's nearest-neighbor reduced density matrices and the corpus state decays faster than logarithmic, following a power law with an exponent controlled by the gate entropy; without them, the decay is essentially logarithmic. The final-state D saturates once the two-site gate entropy Sts exceeds 3, interpreted as the two-site bond-percolation threshold for the state-update process. In parallel, the tripartite mutual information of the final state vanishes for Sts > 2, interpreted as the critical point of information scrambling; the separation between the two thresholds shows that two-site gates can still update local blocks while long-range quantum information is localized. A modified indicator that groups two sites at a time suppresses scrambling entirely, which the authors take as evidence that the two-site interaction channel is what transmits quantum correlations.","pith_inferences":["A physical implementation would likely use mid-circuit measurements or weak measurements; if the thresholds survive that replacement, the model becomes an instance of measurement-induced criticality in a language-motivated setting.","The gap between the update threshold (Sts=3) and scrambling threshold (Sts=2) suggests a design principle: a protocol can keep refining local structure while leaving long-range correlations localized, which may be useful when one wants to prepare a state without first scrambling the whole system.","A quick test: replace the Frobenius distance with the trace distance or swap the two-site gate set; if the thresholds do not move, the phenomenon is tied to the postselection statistic, and if they do, the gate details matter.","Because the corpus state resembles a valence-bond entangled state, replacing it with a matrix-product target state should allow the same algorithm to be tested at larger system sizes and the thresholds checked for finite-size scaling."],"forward_implications":["Replacing the corpus state with a more complex n-gram state gives a family of directed state-preparation protocols that target entangled states beyond the three-word example.","Varying the two-site gate density alone lets one move between a regime where local updates occur but global scrambling is suppressed and a regime where quantum information spreads through the chain.","If the percolation interpretation is correct, the scrambling threshold is controlled by the connectivity of two-site bonds rather than by the detailed form of the two-site unitaries.","Changing the postselection statistic from single-site pairs to two-site groupings (the D' modification) suppresses long-range correlation, showing that the geometry of the update check determines whether information scrambles."],"supporting_citations":[{"why":"Supplies the 2-gram/Markov-chain model that motivates the corpus state and local cooperative interactions.","marker":"[22–25]"},{"why":"Establishes the AKLT valence-bond analogy used to interpret the corpus state as a target entangled state.","marker":"[47–49]"},{"why":"Provides the Frobenius-distance measure used to define the postselection indicator D in Eq. (2).","marker":"[50]"},{"why":"Supplies the random unitary circuit/cellular automaton framework for the discrete-time dynamics.","marker":"[51, 52]"},{"why":"Provides the entanglement-asymmetry tool used to quantify block diagonalization during evolution.","marker":"[57–60]"},{"why":"Gives the bond-percolation theory and thresholds that the claimed Sts=2 and Sts=3 values are identified with.","marker":"[64–66]"},{"why":"Supplies the tripartite mutual information measure used to diagnose information scrambling.","marker":"[67–69]"}],"fun_headline_variants":["Two-site gates accelerate entanglement convergence","Gate entropy threshold marks percolation crossover","Power-law speedup from two-site quantum gates","Bond percolation emerges in gate-sampled dynamics","Two-site gates beat logarithmic convergence"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole construction rests on being able to check at every step whether a proposed random update moves the local state closer to the target, and to accept or reject the update on that basis; if that check cannot be done without destroying or measuring the state, the claimed quantum search protocol does not run as described.","fun_headline_variants_meta":{"raw":{"variants":["Two-site gates accelerate entanglement convergence","Gate entropy threshold marks percolation crossover","Power-law speedup from two-site quantum gates","Bond percolation emerges in gate-sampled dynamics","Two-site gates beat logarithmic convergence"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000341,"raw_usage":{"total_tokens":1834,"prompt_tokens":853,"completion_tokens":981,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":469,"completion_tokens_details":{"reasoning_tokens":914}},"tokens_in":469,"tokens_out":981,"duration_ms":7232,"temperature":1.0,"reasoning_tokens":914,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T11:49:13.874885+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate or implement the same update rule on a system with L = 8 or larger and d = 3, sampling gates from the stated distributions, and measure the final-state tripartite mutual information as a function of Sts: if the vanishing above Sts = 2 does not persist, or if the same step-function appears in a classical simulation that stores the full state without any quantum measurement, then the bond-percolation identification for information scrambling is not established.","supporting_citations":[{"cited_title":"Fagotti and F","cited_arxiv_id":null,"evidence_quote":"Provides the Frobenius-distance measure used to define the postselection indicator D in Eq. (2)."}],"review_version":1}