{"id":"1c348c5b-6eb7-449f-835c-e57d5db249f7","arxiv_id":"2608.05140","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Clustered non-Abelian fractional quantum Hall trial states can be prepared on quantum processors at constant circuit depth, and a catalog of 18 families is demonstrated on up to 156 qubits.","lead":"This paper shows that exotic clustered fractional quantum Hall states can be built on IBM quantum chips with a circuit depth that stays constant as the system grows, while the simpler Laughlin state needs a longer chain. It demonstrates 18 families of these states on up to 156 qubits, opening a practical route to probing non-Abelian topological matter on quantum hardware.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed Laughlin linear-depth 'requirement' is asserted but not proven; the paper itself concedes constant-depth preparation is not excluded, so the headline dichotomy is only established for its specific circuit family.","rationale":"Good-faith reading: the central positive result—constant-depth circuits for clustered Read-Rezayi/Moore-Read states—is convincingly supported by exact overlaps in the ED window, MPS-contraction fidelities at the largest sizes, and extensive hardware root recovery. The internal acceptance tests and cross-device replications are appropriate. The most defensible weak point is the comparative claim that Laughlin requires linear depth, because the paper's own Discussion explicitly leaves constant-depth preparation open. The reader's chosen weakest assumption (adiabatic connection to isotropic FQH phases) is also legitimate but less directly tied to the depth dichotomy; the paper's circuits prepare exact zero modes of model parent Hamiltonians, so even a failed adiabatic connection would leave the circuit-depth result intact as a statement about trial-wavefunction preparation. By contrast, the linear-depth 'requirement' is part of the headline claim and is asserted without proof. This is an internal inconsistency (abstract vs. Sec. VI), not merely a disagreement with consensus, so it is the more load-bearing concern. The test—searching for a shallow circuit for the thin-torus Laughlin state—would settle it. The verdict remains conditional: the positive constant-depth result is credible, but the abstract should qualify the Laughlin lower bound to 'our construction' or provide a proven lower bound.","tokens_in":28173,"tokens_out":12871,"duration_ms":179225,"concrete_test":"Optimize a shallow brickwork circuit of depth d=2,3,4 (nearest-neighbor two-qubit gates on the orbital chain, with one layer of ancillas or mid-circuit measurement allowed) to maximize fidelity with the exact ν=1/3 Laughlin thin-torus state at Ly=5-8 for N=12-16 orbitals, using tensor-network or variational circuit optimization. If any d≤4 circuit reaches fidelity ≥0.99, the linear-depth 'requirement' is disproven. A null result would strengthen the dichotomy but should be paired with an explicit lower bound to justify the abstract's 'requires.'","verdict_should_be":"UNCHANGED","load_bearing_attack":"The dichotomy's second half—that Laughlin state preparation 'requires' linear depth—is not supported by the paper's own analysis. The linear depth is demonstrated only for the sequential chained recursion of Sec. II C; no lower bound rules out constant-depth circuits for the same thin-torus state. Section VI concedes: 'Constant depth is not excluded for the chained states in principle, since their thin-torus circuits are exact low-bond-dimension sequential matrix-product states, and measurement-assisted protocols for such states are a separate question.' The cited no-go theorems (Refs. 75-76) apply to circuits local in two dimensions in the thermodynamic limit, not to the quasi-1D thin-torus circuits used here, so they do not provide the missing lower bound. Since the abstract's first sentence and the 'clustering dichotomy' framing assert the Laughlin state is fundamentally more costly, this is a load-bearing overclaim: if any constant-depth circuit (e.g., using commuting gates, ancillas, or feedforward) prepares the thin-torus Laughlin state, the comparison 'more exotic FQH excitations are the less costly ones' fails, even though the constant-depth clustered circuits remain correct.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a parent-Hamiltonian-to-circuit pipeline for preparing thin-torus representatives of fractional quantum Hall (FQH) trial states on IBM Heron quantum processors. The central claim is a 'clustering dichotomy': clustered states (Moore–Read, Read–Rezayi, Gaffnian, Haffnian, Halperin, and multicomponent families) admit parallel preparation circuits whose two-qubit depth is independent of system size, while Laughlin states are claimed to require sequential circuits with linearly growing depth. Hardware results include an 18-family catalog up to 156 qubits, exact-overlap checks in a diagonalization window, transfer-matrix fidelity estimates at larger sizes, fractional charge measurements at -e/3, -e/4, and -e/5, spectral flow, momentum polarization, and interferometric braiding data. The paper also reports closed-form squeezing amplitudes, a symmetry-selected postselection procedure, and a bond-dimension route toward the isotropic limit.","tokens_in":28426,"tokens_out":6085,"duration_ms":85136,"significance":"The constant-depth construction for clustered root patterns is a genuinely useful structural observation, and the paper supports it with exact overlaps, transfer-matrix contractions, closed-form amplitudes, and an unusually complete data-availability statement. If the thin-torus representatives are adiabatically connected to the corresponding isotropic FQH liquids, this is an important scaling result for quantum simulation of FQH physics. However, the advertised dichotomy overreaches as stated: the paper explicitly concedes that constant-depth preparation of the Laughlin thin-torus state is not excluded, so the abstract's 'requires a sequential circuit chain' is stronger than what is proven. In addition, the parent-Hamiltonian certification is an internal consistency check against the same pattern-of-zeros data, not an independent validation, and all hardware runs lie in the thin-torus regime; the FQH interpretation therefore rests on a stated but untested adiabatic-continuity assumption, especially for the non-unitary Gaffnian and Haffnian. These issues are correctable and do not undermine the core circuit-scaling construction.","major_comments":[{"comment":"The statement that constructing the Laughlin state 'requires a sequential circuit chain with linear depth' is not established by the paper. The linear-depth demonstration applies only to the static thin-torus sequential recursion of Sec. II C, and the Introduction explicitly concedes: 'Constant depth is not excluded for the chained states in principle, since their thin-torus circuits are exact low-bond-dimension sequential matrix-product states, and measurement-assisted protocols for such states are a separate question beyond the scope of this work.' The no-go theorems cited in Sec. V (Refs. 75-76) constrain circuits local in the two-dimensional geometry in the thermodynamic limit, not quasi-1D thin-torus circuits, so they do not supply the missing lower bound. Because the 'clustering dichotomy' and the abstract's first sentence rest on this claimed linear-depth requirement, the wording should be revised to something like: 'within the static thin-torus unitary circuit family considered here, Laughlin preparation has linearly growing depth, while clustered states are prepared at constant depth; whether constant-depth alternatives exist for the Laughlin thin-torus state is open.'","section":"Abstract and §I (Clustering criterion; §VI)"},{"comment":"The parent Hamiltonians are constructed from each family's pattern-of-zeros data and then 'certified' by checking that the kernel dimension matches the (k,r)-admissibility count computed from the same pattern-of-zeros rule. This is a consistency check, not an independent certification of the state's FQH status. Since the paper states that all hardware implementations lie in the thin-torus regime (§V: 'All implementations reported here lie in the thin-torus regime') and the adiabatic connection from thin-torus representatives to isotropic FQH liquids is assumed rather than demonstrated, the 'certified' language in Fig. 3 and the workflow should be qualified. In particular, for the non-unitary Gaffnian and Haffnian the adiabatic continuity to a gapped isotropic phase is not guaranteed by the present data, so the manuscript should either provide independent small-size evidence for the FQH interpretation or explicitly state this as an assumption.","section":"§II A and Fig. 3"},{"comment":"The per-shot exactness of the -e/4 and -e/5 charges is presented as a counting statement, but it is established only on symmetry-selected shots after (N,K) postselection. The paper correctly notes that the (N,K) sector contains configurations with many different charge drops, so the absence of non-quantized drops is evidence that the retained shots lie in the zero-mode manifold. However, the bound on manifold-breaking weight is inferred from the circuit's ideal exactness and the noise model rather than measured independently. The manuscript should state more explicitly that the per-shot exactness is conditional on the symmetry-filtered sample being representative of the ideal zero-mode ensemble, and should indicate what would falsify this interpretation.","section":"§III C and Table II"}],"minor_comments":[{"comment":"The Haffnian is grouped with the constant-depth ladders although its plotted depth rises to 16 at larger sizes; the caption should clarify that the algorithmic depth is size-independent while the transpiled/routed depth reflects circuit anatomy and heavy-hex routing.","section":"Fig. 1(a) and §II E"},{"comment":"The phrase 'root recovered at every electron' is used repeatedly without a formal definition; please specify whether this means every root peak is present in the ensemble-averaged density or that the exact root pattern appears in individual postselected shots.","section":"§II E"},{"comment":"The chained families have no F(MPS) entry; a short note explaining why the transfer-matrix contraction is not reported for those rows would improve the table's self-containedness.","section":"Table I"},{"comment":"The abstract says 'all 156 qubits of an IBM Heron processor,' while Table I shows that only Halperin 331 reaches 156 qubits; the body's phrasing 'catalog circuits reach all 156 qubits' is more precise and should be used consistently.","section":"Abstract and §III D"}],"recommendation":"major_revision","confidential_remarks":"This is a strong experimental-theoretical paper with exemplary data availability, and the constant-depth clustered-state construction is likely to be influential. The main concern is the abstract's overclaim about the Laughlin linear-depth requirement, which the authors themselves concede in the text; this is readily fixable by rephrasing. The circularity of the parent-Hamiltonian certification and the thin-torus adiabatic assumption should also be stated more carefully to avoid overstating the FQH interpretation. I would support publication after these revisions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Key thing to know: this is a substantial hardware-plus-theory paper, and the core constant-depth construction for clustered states looks solid. The 18-family catalog, the closed-form squeezing amplitudes, and the per-shot quantized charge measurements are the most convincing parts. But the headline 'clustering dichotomy' is oversold: the linear-depth Laughlin claim is proven only for the specific sequential thin-torus circuit family, and the paper itself concedes constant depth is not excluded for chained states. Don't let that framing make you discount the actual result.\n\nWhat's new: a systematic parent-Hamiltonian-to-circuit pipeline based on pattern-of-zeros data, with constant-depth circuits for Moore–Read, Read–Rezayi Z3/Z4, Gaffnian, Haffnian, and multicomponent families. The hardware scale is impressive: up to 154 qubits for Z4, a 156-qubit Halperin root family, root recovery at every electron, cross-device replication, and exact e/4 and e/5 charges in every symmetry-selected shot. The verification culture is genuinely careful: zero-mode kernel counts, signed overlaps with exact diagonalization in small windows, MPS contraction at larger sizes, postselection, and honest error budgets. That is real evidence and deserves credit.\n\nSoft spots, in order of importance. First, the Laughlin 'requires linear depth' is not a theorem. The paper's Sec. VI says constant depth is not excluded for chained states in principle, and the cited no-go theorems apply to two-dimensional local circuits in the thermodynamic limit, not to these quasi-1D thin-torus circuits. The abstract's first sentence still states the stronger claim, and that should be fixed. Second, there is some circularity in the parent-Hamiltonian certification: the Hamiltonians are built from the same pattern-of-zeros data used to check kernel counts. It is a self-consistency check, not an independent derivation. The closed-form amplitudes are admitted fits to the numerical kernel, then verified; acceptable, but weaker than a from-scratch derivation. Third, all hardware runs sit in the thin-torus regime, and the adiabatic connection to isotropic FQH states is assumed rather than shown—most doubtful for the non-unitary Gaffnian and Haffnian. If that connection fails, the circuits prepare CDW-like states, though the depth result would survive. Fourth, the data availability statement gives no repository handle or URL in the preprint, so referees currently cannot check the raw counts and scripts.\n\nWho is it for: anyone working on quantum simulation of topological matter, fractional charge or braiding on processors, or thin-torus FQH circuit constructions. It definitely deserves serious refereeing. My recommendation: send it out, and ask for an honest revision of the abstract plus a working repository link. The scientific content is strong enough that those fixes matter more than the length.","headline":"A real, large hardware-plus-theory paper whose constant-depth clustered-state construction holds up, but the advertised Laughlin linear-depth 'requirement' is not proven and the abstract overstates it.","tokens_in":28916,"tokens_out":3043,"would_cite":true,"duration_ms":37846,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["73.43.-f","73.43.Cd"],"model":"deepseek-v4-flash","headline":"The paper claims that clustered non-Abelian fractional quantum Hall states—the exotic ones—prepare at constant circuit depth while the common Abelian Laughlin state needs linear depth, demonstrated on up to 156 qubits.","keywords":["fractional quantum Hall states","non-Abelian anyons","Read–Rezayi states","constant-depth quantum circuits","pattern of zeros","parent Hamiltonians","thin-torus limit","quantum simulation"],"falsifier":"A decisive check would be to compute the exact overlap between the constant-depth circuit output and the zero mode of $H=\\sum_M B_M^\\dagger B_M$ at circumferences beyond the verification window ($L_y \\gtrsim 8$): if the overlap collapses while the root pattern is still recovered, the circuit is preparing only the root state, not the FQH representative. For the non-unitary families, exact diagonalization at larger sizes that finds a gap closing or extra zero modes in the Gaffnian or Haffnian parent would break the claimed adiabatic connection.","tokens_in":28005,"feed_emoji":"⚛️","tokens_out":8750,"duration_ms":98004,"temperature":0.7,"pith_summary":"This paper claims that the more exotic fractional quantum Hall states—the clustered non-Abelian ones—are fundamentally cheaper to prepare on a programmable quantum processor than the everyday Abelian Laughlin state. It shows this through a clustering dichotomy: clustered roots admit parallel circuits whose two-qubit depth stays constant as the system grows, while the Laughlin root forces a sequential chain whose depth grows linearly. The demonstration spans an 18-family catalog on up to 156 qubits, including a Read–Rezayi Z3 state at algorithmic depth 3 from 8 to 118 qubits and a full root sample of a 104-electron Read–Rezayi Z4 state at 154 qubits. If the claim holds, the usual intuition that exotic topological matter is harder to reach is inverted, and non-Abelian physics becomes accessible to scalable preparation and interferometric probing.","feed_headline":"Exotic quantum Hall states prepare at constant depth","feed_subtitle":"Read–Rezayi Z3 runs at two-qubit depth 3 from 8 to 118 qubits, while Laughlin needs linear depth.","key_machinery":"The central object is the pseudopotential parent Hamiltonian $H=\\sum_M B_M^\\dagger B_M$, built from each family's pattern-of-zeros polynomial $P_\\lambda$, whose kernel is the target trial wavefunction and whose conserved $(N,K)$ quantum numbers provide error-heralding postselection. The certification is the kernel-counting identity: the number of $(k,r)$-admissible occupation strings (at most $k$ particles in any $r$ consecutive orbitals) must match the pattern-of-zeros count, verified at more than 70 flux and size points. The circuits are built from thin-torus root patterns plus local squeezing operators with closed-form amplitudes, e.g. $\\tau_\\ell=(-1)^\\ell\\binom{q}{\\ell}e^{-\\kappa^2\\ell(q-\\ell)}$ for the Laughlin series, so every preparation angle is analytic. The dichotomy enters through circuit structure: clustered roots factor into disjoint junction blocks that can be rotated in a single layer of flag gates and expanded in parallel, while the Laughlin roots share electrons between adjacent squeezes and compile to a chained recursion.","core_discovery":"The paper establishes the clustering dichotomy as a structural principle of fractional quantum Hall trial-state preparation. Near the thin-torus limit, each state is generated from a root configuration by local squeezing operations; when the root clusters into disjoint blocks of k≥2 particles, the junction squeezes act on disjoint electrons and execute in parallel at constant depth, whereas the k=1 Laughlin root squeezes at every pair, so the flag rotations form a blocking chain and the depth grows with cell count. Concretely, the Read–Rezayi Z3 parafermion state is prepared at algorithmic two-qubit depth three from 8 to 118 qubits, full root sampling reaches a 154-qubit, 104-electron Read–Rezayi Z4 state, and the entire 18-family catalog fits on all 156 qubits of a superconducting processor. For the clustered states the e/4 and e/5 quasihole charges are exact in every symmetry-selected shot, and interferometric measurements of Moore–Read e/4 quasiholes recover flux slope 0.2500(17)/0.2503(12) against the exact 1/4 with fusion splitting near the Ising monodromy π.","pith_inferences":["A testable screening rule follows: any FQH trial state whose pattern-of-zeros root factorizes into disjoint cell-local junction blocks should admit a constant-depth static circuit, so the dichotomy could rank candidate states for preparability before a parent Hamiltonian is built.","If the adiabatic connection to the isotropic phase fails for the non-unitary Gaffnian and Haffnian, the depth result would still stand as a claim about thin-torus root states but would no longer be a claim about fractional quantum Hall phases; a numerical check of that connection at larger circumferences would settle which reading is right.","The per-shot exactness suggests symmetry-selected sampling can act as an error-heralding primitive for topological observables: shots that pass the zero-mode sector filters carry quantized observables exactly, turning estimators into counters.","On future lower-noise processors, the scaling bottleneck for clustered-state experiments is likely to shift from gate depth to readout retention, since retention rather than depth limits the largest registers in this work."],"forward_implications":["The depth of a static preparation circuit is fixed by the factorization of the thin-torus root, not by the anyon statistics: the non-Abelian $\\nu=1/4$ Pfaffian compiles to the same sequential chain as the Laughlin series because its parent includes a two-body channel that reintroduces squeezing at every pair.","Constant-depth preparation persists across the catalog to chip scale, including non-unitary boundary states such as the Gaffnian and Haffnian and multicomponent Abelian states, so a broad family of trial wavefunctions is now preparable at low logical depth.","For clustered states, fractional quasihole charge is a per-shot counting observable: every symmetry-selected shot returns exactly $e/4$ or $e/5$, bounding manifold-breaking weight below $1.5\\times10^{-4}$ at 95% confidence.","The fixed thin-torus circuits outperform the variational route at the isotropic crossover on current hardware because representative bias is smaller than the noise penalty of deep circuits; adding one bond qubit at a time carries the construction toward the isotropic limit at cost linear in particle number."],"supporting_citations":[{"why":"Supplies the parent-Hamiltonian pseudopotential construction from which every family's zero-mode kernel and circuit amplitudes are derived.","marker":"[3]"},{"why":"Establishes the exact Hamiltonian framework for general interactions in the quantum Hall regime that the certification tests rely on.","marker":"[4]"},{"why":"Provides the geometric construction of clustering Hamiltonians and the channel catalogue the paper extends to 18 families.","marker":"[46]"},{"why":"Gives the sequential Laughlin linear-depth circuit that serves as the baseline for the depth dichotomy.","marker":"[47]"},{"why":"Defines the Moore–Read paired wavefunction, the first clustered non-Abelian family the constant-depth construction generalizes.","marker":"[9]"},{"why":"Defines the Read–Rezayi parafermion series whose Z3 and Z4 states anchor the constant-depth ladders.","marker":"[11]"},{"why":"Supplies multiparticle pseudopotentials for the three- and four-body cluster channels used in the parents.","marker":"[56]"},{"why":"Establishes the multiple thin-torus vacua and domain-wall structure that carry the e/4 charge for Moore–Read.","marker":"[61]"},{"why":"Matched domain-wall counting to conformal-field-theory fusion rules for Read–Rezayi states, backing the kernel-count identity.","marker":"[62]"},{"why":"Provides the (k,r)-clustering rule used as the kernel-counting identity certifying each parent Hamiltonian.","marker":"[69]"}],"fun_headline_variants":["More exotic Hall states are the easier ones to prepare on quantum chips","Constant-depth circuits: non-Abelian Hall states cheaper than Laughlin","Quantum Hall factory: constant-depth prep for clustered non-Abelian states","Read-Rezayi Z3 at depth 3: the exotic Hall state that prepares easily","Quantum processors flip FQH cost: exotic states win over Laughlin"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the states prepared on hardware are the actual thin-torus representatives of their fractional quantum Hall phases: the parent Hamiltonian built from pattern-of-zeros data must have the target wavefunction as a unique zero mode, and the zero-mode manifold at the hardware circumferences must connect adiabatically to the isotropic fractional quantum Hall state; if that connection fails, especially for the non-unitary Gaffnian and Haffnian, the constant-depth circuits produce charge-density-wave-like root states instead of fractional quantum Hall states.","fun_headline_variants_meta":{"raw":{"variants":["More exotic Hall states are the easier ones to prepare on quantum chips","Constant-depth circuits: non-Abelian Hall states cheaper than Laughlin","Quantum Hall factory: constant-depth prep for clustered non-Abelian states","Read-Rezayi Z3 at depth 3: the exotic Hall state that prepares easily","Quantum processors flip FQH cost: exotic states win over Laughlin"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001389,"raw_usage":{"total_tokens":5698,"prompt_tokens":1096,"completion_tokens":4602,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":712,"completion_tokens_details":{"reasoning_tokens":4503}},"tokens_in":712,"tokens_out":4602,"duration_ms":39848,"temperature":1.0,"reasoning_tokens":4503,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T04:23:31.281534+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check would be to compute the exact overlap between the constant-depth circuit output and the zero mode of $H=\\sum_M B_M^\\dagger B_M$ at circumferences beyond the verification window ($L_y \\gtrsim 8$): if the overlap collapses while the root pattern is still recovered, the circuit is preparing only the root state, not the FQH representative. For the non-unitary families, exact diagonalization at larger sizes that finds a gap closing or extra zero modes in the Gaffnian or Haffnian parent would break the claimed adiabatic connection.","supporting_citations":[{"cited_title":"Lee and J","cited_arxiv_id":null,"evidence_quote":"Provides the geometric construction of clustering Hamiltonians and the channel catalogue the paper extends to 18 families."},{"cited_title":"Rahmani, K","cited_arxiv_id":null,"evidence_quote":"Gives the sequential Laughlin linear-depth circuit that serves as the baseline for the depth dichotomy."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies multiparticle pseudopotentials for the three- and four-body cluster channels used in the parents."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the multiple thin-torus vacua and domain-wall structure that carry the e/4 charge for Moore–Read."},{"cited_title":"Ardonne, E","cited_arxiv_id":null,"evidence_quote":"Matched domain-wall counting to conformal-field-theory fusion rules for Read–Rezayi states, backing the kernel-count identity."}],"review_version":1}