{"id":"18428dc8-67ce-4849-8488-bf931e0ad3cf","arxiv_id":"2510.18869","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A quantum-simulation framework based on discretized light-front QCD extracts the c→J/ψ fragmentation function from a truncated four-particle Hilbert space, finding rough agreement with the 1993 NRQCD calculation.","lead":"This paper shows how to compute quark-to-hadron fragmentation functions by simulating light-front QCD on a quantum computer, and demonstrates it with a simplified calculation of charm quarks fragmenting into J/ψ mesons. If the method scales, it would give a first-principles route to quantities that are currently obtained by fitting data.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed broad agreement with NRQCD is not robust because the extracted D(z) is defined by projection onto a hand-input model J/ψ wavefunction (Eqs. 7–8) whose overlap with the actual light-front eigenstate is never quantified.","rationale":"The paper is an honest proof-of-concept: it gives the full LFQCD Hamiltonian, encoding details, Trotter/time-step convergence, Fock-truncation sensitivity, and an internal analytic benchmark (Eq. 19). The central claim, however, is stronger than a demonstration of a pipeline. To claim an ab-initio-style FF and a meaningful comparison with NRQCD, the detection operator must correspond to the physical J/ψ. The authors use a two-parameter model wavefunction that is not obtained from their own Hamiltonian and is not assigned an uncertainty. This is precisely the reader's weakest_assumption. I do not find a more severe internal inconsistency: the Trotter and momentum truncations are acknowledged and partially quantified; the no-code issue affects reproducibility but not the physical reasoning; the 'first time' overclaim affects novelty but is a wording issue rather than a load-bearing technical flaw. The dimensional mismatch in Eq. (8) strengthens the concern about the ansatz but is fixable. Therefore the verdict should remain CONDITIONAL: the method is promising, but the crucial hadron-state input must be validated before the agreement with NRQCD can be taken as evidence of an ab-initio FF calculation.","tokens_in":18518,"tokens_out":13489,"duration_ms":127835,"concrete_test":"Replace the model χ0 in Eqs. (7)–(8) by the ground state of the same truncated light-front Hamiltonian: solve the two-body (qqbar, color-singlet, J^PC = 1^--) light-front Schrödinger equation H_P^- |χ⟩ = E|χ⟩ on the N=4 and N=8 longitudinal grids with p⊥ = 0 (using the same P^-, α_s, m_c, κ conventions, with the dimensional fix κ→κ^2 if needed). Compute O = |⟨χ0|χ_gs⟩|^2 and re-run the fragmentation extraction with |χ_gs⟩ as the detection state. If D(z) at the z-points in Table XIV changes by more than ~50% or the scatter against [15] worsens, the claimed agreement is not robust. Alternatively, vary m_c and κ by ±20% and check whether the Fig. 2 symbols remain inside the NRQCD band.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative claim is the 'broad agreement' with BCY NRQCD [15] in Fig. 2. That curve is obtained by projecting the time-evolved Fock state onto the model |J/ψ⟩ of Eq. (7) with χ0(x) ∝ x^(β/2)(z−x)^(α/2), α = 4m_q^2/κ, β = m_qbar^2/κ (m_q = 1.27 GeV, κ = 1.34 GeV). This χ0 is not an eigenstate (or even a variational minimum) of the truncated P^- used for the evolution; the authors concede 'Eq. (8) has to be seen as a variational approximation.' Since D(z) is essentially |⟨ψ(t)|J/ψ_model(z)⟩|^2, every symbol in Fig. 2 inherits the ansatz. If χ0 is a poor approximation to the qqbar component of the J/ψ in this Hamiltonian — wrong endpoint behavior, missing the physical node structure, or far from the ground state in overlap — the extracted D(z) can shift point-by-point and the 'agreement' with NRQCD becomes a model-dependent coincidence. Additionally, as printed Eq. (8) has dimensionally inconsistent exponents: m_q^2/κ has units of GeV if κ is taken from Table IV (GeV), while exponents of dimensionless x must be dimensionless; a missing κ^2 (or different κ convention) is not discussed. This is an internal inconsistency in the central detection state, not merely a stylistic point.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a quantum-computing framework for computing parton-to-hadron fragmentation functions directly from the light-front QCD Hamiltonian. The authors encode a truncated, discretized LFQCD Hamiltonian in a particle-register qubit architecture, evolve an initial charm quark on a classical simulator, and extract c→J/ψ fragmentation by projecting the time-evolved state onto a model J/ψ longitudinal wavefunction. The extracted D(z) is compared with the 1993 NRQCD calculation of Braaten–Cheung–Yuan, with error bars reflecting the choice of extraction time. The paper includes a full re-derivation of the LFQCD interaction Hamiltonian, a detailed gate-resource scaling analysis, and an analytic check (Eq. 19 of the Supplementary Material) of the simulation for the λ=0 case. The central claim is that this is the first ab-initio-style calculation of fragmentation functions, with the J/ψ result broadly agreeing with NRQCD.","tokens_in":18907,"tokens_out":5532,"duration_ms":50274,"significance":"If the systematic uncertainties were controlled, this would be an important first step toward nonperturbative, real-time calculations of fragmentation functions from light-front QCD, complementing lattice methods and global fits. The paper's strengths are concrete: a complete LF Hamiltonian in light-front gauge, a working qubit encoding for fermions and bosons, a validation of the simulation against an analytic expression, and a resource analysis showing polynomial scaling with the momentum-grid size. However, the central quantitative result — the agreement with NRQCD shown in Fig. 2 — is defined through a hand-input J/ψ wavefunction and a heuristic stop-time criterion, and the paper does not quantify how the result depends on either. The work is therefore best read as a proof-of-principle; the 'ab initio' claim in the abstract is not yet supported by the evidence presented.","major_comments":[{"comment":"The exponents in Eq. (8) are α = 4 m_q^2/κ and β = m_qbar^2/κ. With m_q = 1.27 GeV and κ = 1.34 GeV, m_q^2/κ has mass dimension GeV, so the exponents of the dimensionless ratios x/z and (z−x)/z are dimensionally inconsistent. If the intended convention uses κ^2 in the denominator, or κ in GeV^2, the shape of χ0 changes and the curves in Fig. 2 are not uniquely defined. Since the extracted D(z) is defined by projection onto this state, this inconsistency must be fixed and the resulting sensitivity assessed.","section":"Simulating Fragmentation Functions, Eq. (8) and Table IV"},{"comment":"The J/ψ detection state is a hand-input ansatz, not obtained from the truncated P^−. The authors acknowledge this ('Eq. (8) has to be seen as a variational approximation'), but the overlap of χ0 with the actual ground state of the truncated Hamiltonian is never quantified, and no variation of (m_c, κ) or alternative longitudinal wavefunctions is shown. Because D(z) is essentially |⟨ψ(t)|J/ψ_model(z)⟩|^2, the 'broad agreement' with NRQCD in Fig. 2 could be dominated by the choice of χ0 rather than by the Hamiltonian evolution. Please report the overlap ⟨χ0|χ_gs⟩ for the truncated Hamiltonian and show the sensitivity of Fig. 2 to reasonable variations of the ansatz parameters.","section":"Eqs. (7)–(8) and Fig. 2"},{"comment":"The stop-time criterion identifies a Shannon-entropy plateau in the truncated unitary system with the x^+→∞ limit of the fragmentation function. This identification is asserted rather than demonstrated, and a finite unitary system will recur. There is also an internal inconsistency in the extraction time: the main text says the FF is extracted at times 'up to 1 GeV^{−1}', while Supplementary Sec. V.B says the values are extracted 'around t∼4 GeV^{−1}' (the first minimum of the no-gluon probability). This discrepancy must be resolved, and the dependence of D(z) on the plateau window should be quantified beyond the two times used to set the error bars.","section":"Simulating Fragmentation Functions; Supplementary Sec. V.B"},{"comment":"The abstract claims 'for the first time how to calculate fragmentation functions, a problem heretofore untractable in general from ab-initio approaches.' The presented calculation uses a Fock-space truncation to at most four particles, zero transverse momentum, a fixed α_s with no renormalization, and a model wavefunction; none of these cutoffs is controlled by an extrapolation. This is an interesting proof-of-concept, but the 'ab initio' claim is not supported by the evidence in the manuscript. The claim should be softened or the dominant truncations should be controlled.","section":"Abstract and Computational Scaling section"}],"minor_comments":[{"comment":"Typo: 'untractable' should be 'intractable'.","section":"Abstract"},{"comment":"The caption spells the NRQCD authors as 'Braaten, Cheung and Yan' while the reference gives 'Braaten, Cheung and Yuan' (E. Braaten, K. Cheung, T. C. Yuan). The spelling should be consistent.","section":"Fig. 2 caption / Ref. [15]"},{"comment":"The entry 'M. G´omez-Rocha and S. D. G/suppress lazek' contains a LaTeX error; it should read 'S. D. Głazek'.","section":"Ref. [8]"},{"comment":"The table refers to 'Fig.(3) of the main text', but the fragmentation function is shown in Fig. 2 of the main text. The cross-reference should be corrected.","section":"Supplementary Table XIV"},{"comment":"The J/ψ state notation uses a spin factor σ⃗_ij without an explicit color-singlet projector. Please clarify the normalization and color structure of the state.","section":"Eq. (7)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for an hep-ph journal and reports a genuinely novel computational framework. The main risk is overclaiming: the 'ab initio' statement and the 'broad agreement' with NRQCD both rest on a model wavefunction and an unvalidated entropy-plateau criterion. I believe these can be fixed within the manuscript's scope by adding overlap calculations, parameter-variation studies, and a more careful framing. I see no grounds for concern about the authors' integrity; the issues are technical and presentational."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here’s my read: this is a genuine proof-of-concept for computing a fragmentation function from a truncated light-front QCD Hamiltonian on a quantum simulator. The new pieces are the application of the particle-register encoding to FFs, the entropy-plateau stopping criterion, and a transparent discussion of Trotter, Fock-space, and momentum-cutoff uncertainties. The analytical check of Eq. (19) against the λ=0 simulation is a nice validation of the encoding and evolution. I also appreciate the scaling analysis of CNOT counts; that will be useful for future work.\n\nBut the headline result — “broad agreement” with NRQCD — does not survive close reading. The extracted D(z) is defined by projecting the time-evolved state onto a hand-input model J/ψ wavefunction (Eqs. 7–8). The authors admit this state should come from minimizing the Hamiltonian but don’t do it, and they don’t quantify how the result changes under reasonable variations of m_q and κ. That alone makes the agreement with NRQCD a statement about the ansatz as much as about QCD. Worse, Eq. (8) as printed has a dimensional inconsistency: α = 4m_q^2/κ has units of GeV if κ is in GeV, while the exponent of a dimensionless variable x must be dimensionless. That’s an internal inconsistency in the central detection state, not a stylistic point.\n\nThe abstract also overclaims: “for the first time” ignores the NJL-model quantum simulation in ref. [6], and lattice-based FF programs are not discussed. The Fock-space truncation (2 quarks + 1 antiquark + 1 gluon) and a 4-node momentum grid are severe, no renormalization is applied, and no code or data are shipped, so the numbers cannot be independently reproduced. The supplementary table shows an unexplained and very large difference between SU(2) and SU(3) results (e.g., z=4/8: 7.7 vs 125 in arbitrary units), which makes the comparison to NRQCD hard to interpret as more than suggestive.\n\nIn sum: the paper deserves a serious referee because the method is novel and the authors are unusually candid about many limitations. But the central claim is not supported as stated. I’d recommend a revise-and-resubmit: tone down the abstract, quantify sensitivity to the model wavefunction (at least by varying its parameters and, ideally, comparing to a Hamiltonian-extracted state), fix the dimensional issue, and address the SU(2)/SU(3) discrepancy. If those are addressed, this could be a useful contribution to the quantum-simulation/LFQCD literature.","headline":"A real proof-of-concept for quantum-simulated fragmentation functions, but the claimed NRQCD agreement is not yet established and the model wavefunction has a dimensional inconsistency.","tokens_in":19425,"tokens_out":4422,"would_cite":false,"duration_ms":38542,"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":"This paper claims the first calculation of hadron fragmentation functions from QCD itself, by evolving a charm quark under a truncated light-front Hamiltonian on a simulated quantum computer and projecting onto a model J/psi state.","keywords":["fragmentation functions","light-front quantization","quantum simulation","QCD","charmonium","NRQCD","Fock-space truncation","Trotter evolution"],"falsifier":"Recompute the same fragmentation function after replacing the model ansatz with the lowest eigenstate of the truncated light-front Hamiltonian, obtained by minimizing P^- in the available Fock space. If D(z) shifts by more than the quoted error bands, the central result is dominated by the input wavefunction rather than the Hamiltonian dynamics. Alternatively, evolve the same truncated system by exact diagonalization and compare plateau-extracted D(z) against the true long-time projection to test the stopping rule.","tokens_in":18349,"feed_emoji":"⚛️","tokens_out":7512,"duration_ms":63814,"temperature":0.7,"pith_summary":"Fragmentation functions — the probabilities that a quark or gluon turns into a particular hadron carrying a fraction z of its momentum — are usually fitted to data rather than derived from QCD, because lattice QCD cannot evolve along a lightlike direction. This paper claims the first direct computation of one from the QCD Hamiltonian: it evolves a charm quark under a discretized, Fock-truncated light-front Hamiltonian on a classical simulator of a quantum computer, stops at a plateau of Shannon entropy, and projects the evolved state onto a model J/psi wavefunction. The extracted D(z) broadly agrees with the 1993 NRQCD calculation of charm-to-J/psi fragmentation. If the method holds up, it opens a route to calculating fragmentation functions ab initio for hadrons that experiments can reach only through hadronization.","feed_headline":"Simulated quantum computer computes charm-to-J/psi fragmentation","feed_subtitle":"Evolving a charm quark under the light-front QCD Hamiltonian reproduces the 1993 NRQCD curve.","key_machinery":"The load-bearing object is the light-front QCD Hamiltonian P^- in light-front gauge, expanded in momentum-space creation and annihilation operators and truncated to at most two quarks, one antiquark and one gluon with N=4 or N=8 longitudinal momentum fractions. It is implemented as Trotterized unitary rotations on a particle-register encoding: each register carries a presence/absence qubit that controls the gate, plus qubits for momentum, spin, color and flavor, with symmetrizer/antisymmetrizer operations enforcing boson/fermion statistics. The extraction protocol has two novel pieces: the entropy-plateau stopping rule, which identifies when the probability spread over active modes has satur","core_discovery":"The central claim is that the c→J/psi fragmentation function can be obtained from real-time light-front QCD: start from a charm quark, apply Trotterized unitary gates built from the light-front Hamiltonian P^- in A+=0 gauge, use the saturation plateau of Shannon entropy as a proxy for infinite light-front time, and read off D(z) through an annihilation gate that maps the model J/psi state to the vacuum, so an empty quark-antiquark register signals fragmentation. With the Fock space truncated to two quarks, one antiquark and one gluon, and longitudinal momentum on a 4- or 8-point grid, the extracted D(z) broadly agrees with the 1993 NRQCD result. The authors present this as a proof of princip","pith_inferences":["My inference: replacing the hand-built J/psi ansatz with the ground state of the truncated Hamiltonian is the natural decisive test; if D(z) moves outside the quoted bands, the agreement with NRQCD is largely inherited from the input wavefunction rather than from QCD dynamics.","My inference: the entropy-plateau rule should be validated against exact diagonalization of the same truncated Hamiltonian, since a finite system under unitary evolution can recur; the plateau may be a practical proxy rather than the true infinite-time limit.","My inference: comparing at more than one value of alpha_s, or with a running coupling, would test whether the match to NRQCD is stable or an accident of the single scale chosen.","My inference: because the annihilation-gate construction is state-agnostic, gluon-initiated and light-quark fragmentation could be computed with the same machinery once the corresponding hadron model states are supplied."],"forward_implications":["Fragmentation functions become targetable from the same light-front Hamiltonian that describes bound states, closing the gap left by Euclidean lattice methods.","The particle-register encoding gives a concrete, gate-level blueprint for scaling to larger Fock sectors and finer momentum grids as quantum hardware improves.","The entropy-plateau criterion gives a practical stopping rule for extracting light-front-time quantities before decoherence and truncation effects take over.","Agreement with the 1993 NRQCD curve at intermediate z provides a quantitative calibration point for a theory that presently has no renormalization scheme.","The same pipeline, with a few hundred qubits, could lower the reach in z and eventually include transverse-momentum dependence needed for full collinear fragmentation functions."],"fun_headline_variants":["Quantum computing computes charm-to-J/psi fragmentation","First ab-initio fragmentation via light-front QCD","Charm quark to charmonium via quantum gates","Simulated quantum computer reproduces 1993 NRQCD curve","Fragmentation functions from light-front QCD simulation"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The extraction relies on a fixed hand-built J/psi wavefunction, with parameters chosen from the charm mass and a spring constant, standing in for the physical J/psi component of the evolved state; if that ansatz is not a good approximation, the extracted D(z) — and the agreement with NRQCD — would change.","fun_headline_variants_meta":{"raw":{"variants":["Quantum computing computes charm-to-J/psi fragmentation","First ab-initio fragmentation via light-front QCD","Charm quark to charmonium via quantum gates","Simulated quantum computer reproduces 1993 NRQCD curve","Fragmentation functions from light-front QCD simulation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000228,"raw_usage":{"total_tokens":1265,"prompt_tokens":651,"completion_tokens":614,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":395,"completion_tokens_details":{"reasoning_tokens":536}},"tokens_in":395,"tokens_out":614,"duration_ms":5837,"temperature":1.0,"reasoning_tokens":536,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T08:45:33.202519+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the same fragmentation function after replacing the model ansatz with the lowest eigenstate of the truncated light-front Hamiltonian, obtained by minimizing P^- in the available Fock space. If D(z) shifts by more than the quoted error bands, the central result is dominated by the input wavefunction rather than the Hamiltonian dynamics. Alternatively, evolve the same truncated system by exact diagonalization and compare plateau-extracted D(z) against the true long-time projection to test the stopping rule.","supporting_citations":[],"review_version":1}