{"id":"eea388ee-4ce3-46b3-912c-3ab9409f4696","arxiv_id":"2508.07986","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Using a hard-wall boundary, Coulomb wave functions, and a QPU-measured seed energy, the authors reproduce the known low-energy pp s-wave phase shift, with the short-range coupling tuned to the analytic answer.","lead":"The authors reproduce the low-energy proton-proton s-wave phase shift using a hybrid quantum-classical algorithm, with the ground-state energy measured on an IBM quantum processor. The quantum chip provides one noisy seed energy; classical relaxation iterations finish the calculation and match a known analytic curve.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"QPU-seeded relaxation convergence is asserted, not demonstrated; Table I seed errors of 16–46% leave the hybrid pipeline claim unsupported.","rationale":"Read in good faith, the paper is a benchmark of a specific hybrid scheme: a lattice EFT with a tuned contact coupling, a hard-wall phase-shift formula, and one QPU energy seed. For the central claim to hold, two conditions are needed: the regulated Hamiltonian reproduces the LO modified effective-range expansion, and the Gauss-Seidel iteration is stable against the QPU seed errors. The first is partially tested by the use of several lattice spacings and sizes and by the explicit c0 tuning to the scattering length. The second is only asserted. Table I provides direct evidence that the QPU seed errors are large, so the second condition is the least secure. This is not a claim that the authors are wrong; the classical solver may well be robust. The paper simply lacks the direct convergence and error-propagation evidence needed to support the hybrid-pipeline claim. The proposed test settles whether the concern lands. Since the reader's CONDITIONAL verdict already called for such a demonstration, I see no basis to move away from it.","tokens_in":10387,"tokens_out":15341,"duration_ms":196913,"concrete_test":"Take one or more Table I rows (e.g., L=15, b=1 fm and L=20, b=0.75 fm). Run the relaxation with three initial energies: the exact energy, the SVD QPU energy, and a deliberately wrong energy (±50%). For each, perform 200 iterations both (i) recomputing E from the current wave function classically and (ii) holding E fixed at the initial value. Record the final phase shift via Eq. (9). Also resample the 5000 QPU shots (bootstrap) to produce a distribution of initial energies and final phase shifts. If the three protocols give phase shifts within the stated accuracy (say <0.5°), the robustness claim is supported; if not, or if the fixed-E control fails to converge, the paper must either report a convergence study or weaken the hybrid-pipeline claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Table I shows the SVD QPU trial energies used for Fig. 1 are 1.16–1.46 times the exact values (16–46% high). The paper asserts that the Gauss-Seidel relaxation is 'sufficiently robust' and converges after about 30 iterations, but gives no convergence study, no final-energy error, and no phase-shift uncertainties. The description of the algorithm is ambiguous: Eq. (10) updates u using an energy E, and the text says the energy is measured on the QPU only for the initial trial state, with subsequent updates classical. If E is held fixed at the noisy QPU value, the iteration is solving (H−E)u=0 for a non-eigenvalue E, and convergence to the ground state is not guaranteed; if E is recomputed classically from the updated u, the QPU seed is eventually washed out and Fig. 1 tests the classical solver, not the hybrid pipeline. In either reading, the claimed link between the QPU measurement and the accurate phase shifts is not established. Without this link, the central demonstration—a noisy QPU energy seeding a relaxation that recovers the LO Coulomb-modified phase shift—is unsupported. The regulator-decoupling issue is real but secondary: varying b and L gives partial evidence, and a clean classical test would isolate it.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a hybrid quantum-classical computation of the low-energy proton-proton s-wave phase shift. The authors reduce the two-body problem to a 1D radial Schrödinger equation with a short-range regulated Coulomb potential, discretize it on a spatial lattice, and impose a hard spherical wall. The phase shift δ0(p) is obtained from Eq. (9) using the ground-state energy of the lattice Hamiltonian. The ground-state energy is measured on the IBMQ-Brisbane QPU for a particle-in-a-box trial state, using Schmidt decomposition to reduce measurements to one- and two-qubit circuits, and the energy is used as the seed for a classical Gauss-Seidel relaxation. The short-distance coupling c0 is tuned at each lattice spacing so that the classical lattice phase shift matches the leading-order Coulomb-modified effective range expansion Eq. (8). Results from noisy QPU measurements at b = 2, 1, 0.75 fm and several lattice sizes L are reported in Table I and Fig. 1, showing phase shifts close to the analytic curve.","tokens_in":10648,"tokens_out":4227,"duration_ms":47636,"significance":"If the pipeline performs as advertised, this is a useful step toward real-device quantum computation of nuclear scattering observables. The Schmidt-decomposition reduction to one- and two-qubit circuits is a practical error-reduction technique, and using a single QPU energy measurement to seed a classical relaxation is a plausible division of labor for near-term hardware. The manuscript also connects the lattice EFT wall method to a 1D radial formulation, which is convenient for quantum simulation. However, the central quantitative claim is currently underdetermined: the good agreement in Fig. 1 largely follows from tuning c0 to Eq. (8), and the specific role of the QPU measurement is not verified. With additional convergence and uncertainty analyses the method could be compelling, but the present evidence does not yet establish the hybrid pipeline as the source of the accurate phase shifts.","major_comments":[{"comment":"The calibration procedure removes most of the content from the headline agreement. Section III states that at each b, c0 is tuned so that the numerical phase shift from Eq. (9) reproduces Eq. (8); Eq. (8) is exactly the dashed curve in Fig. 1. Thus the classical part of the calculation is guaranteed to lie on the target curve at the tuned points. The QPU contributes only the energy entering p in Eq. (9). Table I shows the SVD QPU trial energies are 16–46% high. To support the hybrid claim, the authors must report the converged energies after relaxation, the corresponding phase shifts, and a comparison of QPU-seeded versus exact-seeded relaxation. Otherwise Fig. 1 tests the classical solver, not the hybrid pipeline.","section":"Section III, Fig. 1 and Table I"},{"comment":"The relaxation algorithm is not fully specified. Eq. (10) updates u using 'the energy E associated with the current wave function', but Section III says that after the initial QPU measurement 'the rest of the relaxation method iterations are done classically'. If E is held fixed at the noisy QPU value, the iteration is solving (H−E)u=0 for a non-eigenvalue E, and convergence to the ground state is not guaranteed. If E is recomputed classically, the QPU result is eventually washed out. The manuscript asserts convergence in 'about 30 iterations' without showing a convergence study, final energy errors, or phase-shift uncertainties. This is load-bearing because the central claim is that a noisy QPU measurement seeds a calculation that accurately reproduces the phase shift.","section":"Section I A, Eq. (10), Section III"},{"comment":"The claim that the uniformly charged sphere regulator 'changes nothing beyond r=2b' needs a quantitative demonstration. Retuning c0 removes the leading short-distance effect, but the finite shape of the potential can produce momentum-dependent (effective-range-like) distortions in the 10–70 MeV/c window. The b scan in Fig. 1 is suggestive, but b=1 fm at p≈60 MeV already shows a deviation that the text attributes to discretization. A clean classical test at varying b, L, and regulator shape, comparing against Eq. (8) and including the next-order effective-range term, would isolate regulator artifacts from QPU effects. Without this, the statement that the physics outside 2b is unchanged is an assumption rather than a demonstrated property.","section":"Section I, regulator prescription; Fig. 1"},{"comment":"The reported phase shifts have no error bars, even though the QPU energies in Table I carry statistical errors from 5000 shots and the relaxation seed has a systematic offset of 16–46%. Moreover, Eq. (8) is leading order only; the omitted effective-range term may be non-negligible at the upper end of the momentum range. The authors should provide an uncertainty budget for p and δ0(p), including shot noise, seed offset, lattice discretization, and the truncation of the effective-range expansion.","section":"Eq. (8), Eq. (9), Table I"}],"minor_comments":[{"comment":"The finite-difference expression contains a repeated u(r+b); presumably it should be u(r+b)+u(r-b).","section":"Eq. (10)"},{"comment":"The notation |2^l⟩ for computational basis states should be defined more carefully; as written it is easy to confuse with the decimal label.","section":"Eq. (15)"},{"comment":"The 'Exact (MeV)' column values are trial-state energies for a particle in a box of size 5b, but this is stated only in the text, not in the table caption.","section":"Table I caption"},{"comment":"The figure would benefit from a legend that distinguishes the classical 3D points (open squares) from the hybrid QPU points, and from error bars on the phase-shift data.","section":"Fig. 1"},{"comment":"The text says '10s of qubits' and 'about 30 iterations' — concrete numbers for the qubit counts and iteration counts should be given.","section":"Section III"},{"comment":"The scattering length a0 = -7.81 fm is taken from a chiral potential paper; the authors should specify whether this is the Coulomb-subtracted pp scattering length and which convention is used.","section":"Eq. (8), Ref. [30]"}],"recommendation":"major_revision","confidential_remarks":"The manuscript fits the journal's scope as an application of quantum computing to nuclear scattering. My main concern is the calibration circularity and the unspecified role of the QPU measurement in the relaxation. These issues are fixable with additional classical and quantum comparisons, so I recommend major revision rather than rejection. I see no indication of misconduct."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper is a genuine first step—Coulomb scattering phase shifts on a real QPU—but the thing that makes it a \"hybrid quantum-classical\" result rather than a classical calculation is asserted, not demonstrated. The reader's conditional verdict is fair, and the stress-test note points at the real soft spot.\n\nWhat's new and good: prior quantum-computing scattering benchmarks (Sharma et al., Wang et al., Turro et al.) treated neutral particles. This paper includes the Coulomb force in a hard-wall scattering calculation and runs the energy measurement on IBMQ-Brisbane. The SVD reduction to one- and two-qubit circuits is a concrete and transferable technical step. The paper is also honest in its setup: it states that c0 is tuned at each lattice spacing so the classical lattice phase shift matches the analytic modified effective range expansion, and it takes the scattering length a0 from the literature. That is standard EFT matching, not a hidden flaw—but it does mean Fig. 1 is a check of the discretization, not a new physics prediction.\n\nThe soft spots are real. First, the phase shifts in Fig. 1 are produced by a classical Gauss-Seidel relaxation seeded by one QPU energy measurement. Table I shows those seeds are 16–46% above the exact trial-state energies. The paper says the relaxation is \"sufficiently robust\" and converges in ~30 iterations, but gives no convergence study, no final-energy values, and no phase-shift uncertainties. More importantly, the algorithm is ambiguous: if the QPU value of E is held fixed during the relaxation, the iteration solves (H−E)u=0 for a non-eigenvalue E, and convergence is not guaranteed; if E is recomputed classically from the updated wave function, the QPU seed washes out and Fig. 1 tests the classical solver, not the hybrid pipeline. The paper needs to say which it is and show the relevant numbers.\n\nSecond, the regulator decoupling claim is plausible but under-supported. Tuning c0 at each b makes the b independence of the phase shift a weaker test; a direct comparison with a different regulator shape would have helped. The momentum range shown (10–70 MeV) is also an order of magnitude above the solar Gamow peak, which matters if the motivation is solar physics.\n\nBottom line: this is a serious, readable paper with a real technical contribution. It deserves a referee who will ask for a convergence study, error bars, and a clear statement of the QPU's role in the final result. If the QPU seed is irrelevant, the authors should say so; if it matters, they should prove it. Send it to review.","headline":"A serious first demonstration of Coulomb phase shifts on real QPU hardware, but the hybrid claim rests on an unshown convergence step and the figure is largely a re-fit of the input.","tokens_in":11161,"tokens_out":3940,"would_cite":false,"duration_ms":46827,"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":"A hybrid quantum-classical calculation on a noisy processor reproduces the low-energy proton-proton s-wave phase shift from a Coulomb-regulated lattice effective field theory, using one quantum energy measurement followed by classical relax","keywords":["proton-proton scattering","Coulomb phase shift","quantum computing","effective field theory","lattice EFT","hard-wall boundary condition","hybrid quantum-classical algorithm","Schmidt decomposition"],"falsifier":"Compare the phase shift from Eq. (9) obtained with exact classical ground-state energies to Eq. (8) for several $b$ values at fixed physical volume $(L-1)b$; if the residuals do not shrink as $b\\to 0$ or if they depend on $R_{\\mathrm{wall}}$ at fixed $b$, the uniformly-charged-sphere regulator is altering the momentum dependence and the central claim fails.","tokens_in":10191,"feed_emoji":"⚛️","tokens_out":7844,"duration_ms":87983,"temperature":0.7,"pith_summary":"This paper tries to establish that a near-term quantum computer can compute a charged-particle scattering observable, specifically the low-energy proton-proton s-wave phase shift, by a hybrid scheme in which only one energy expectation value is measured on the quantum device and all subsequent relaxation iterations run classically. The authors combine a leading-order effective field theory with a short-range contact interaction and the long-range Coulomb force, discretize the radial Schrödinger equation on a lattice, and convert the ground-state energy in a hard spherical wall into a phase shift through the ratio of regular and irregular Coulomb wave functions. They report that the resulting phase shifts track the analytical modified effective range expansion over momenta 10--70 MeV/c and across several lattice spacings and volumes. If this holds, quantum computation becomes a viable route to the proton-proton scattering input needed for solar fusion rates, extending earlier quantum-computer scattering calculations from neutral to charged particles.","feed_headline":"One noisy quantum measurement reproduces proton scattering phase shifts","feed_subtitle":"Hybrid quantum-classical relaxation recovers the Coulomb-modified s-wave phase shift at solar energies.","key_machinery":"The load-bearing identity is the hard-wall relation $\\delta_0(p)=\\tan^{-1}(-F_0(\\eta_p,R_{\\mathrm{wall}} p)/G_0(\\eta_p,R_{\\mathrm{wall}} p))$, which turns a single ground-state energy into a scattering phase shift: the wall fixes $u(R_{\\mathrm{wall}})=0$, so the ratio of regular to irregular Coulomb functions at the wall determines $\\delta_0$. Around this sit the regulator prescription $V(0)=c_0$, $V(b)=(c_0+\\alpha_{\\mathrm{EM}}/(2b))/2$, $V(r>b)=\\alpha_{\\mathrm{EM}}/r$, which renders the Coulomb singularity finite at the origin while leaving the exterior potential unchanged, and the Gauss-Seidel relaxation update $u^{(\\mathrm{new})}(r)=2t\\,\\bar{u}(r)/(2t+b^2[V(r)-E])$, with $E$ measured onc","core_discovery":"The central claim is that the Coulomb-modified s-wave phase shift $\\delta_0(p)$ for proton-proton scattering can be recovered from the ground-state energy of a two-proton lattice Hamiltonian with a hard wall, even when that energy comes from one noisy quantum computation. The phase shift is fixed by $\\delta_0(p)=\\tan^{-1}(-F_0(\\eta_p,R_{\\mathrm{wall}} p)/G_0(\\eta_p,R_{\\mathrm{wall}} p))$, where $F_0$ and $G_0$ are the regular and irregular Coulomb wave functions, and the momentum $p$ is obtained from the spectrum. The authors regulate the combined short-range and Coulomb potential as $V(0)=c_0$, $V(b)=(c_0+\\alpha_{\\mathrm{EM}}/(2b))/2$, $V(r>b)=\\alpha_{\\mathrm{EM}}/r$, tune $c_0$ at each lat","pith_inferences":["The paper uses only the leading-order modified effective range expansion, with the effective-range term omitted; a natural next test is to include the next-to-leading-order $r_0$ term and ask whether the same one-measurement relaxation loop still reproduces the phase shift, which would probe the method's sensitivity to momentum-dependent short-range physics.","Because the regulator is varied independently of lattice size, the residuals at fixed $b$ could be extrapolated to $b\\to 0$; the deviation near $p\\approx 60$ MeV at $b=1$ fm looks like a discretization artifact, so a quantitative continuum extrapolation would turn this demonstration into a precision statement.","The Gauss-Seidel variant requires only one quantum energy evaluation, but the Jacobi variant would need one per iteration; if gate errors continue to fall, a fully quantum iteration loop might become feasible and would remove the classical relaxation step entirely.","The same wall-plus-EFT pipeline could be applied to other charged-light systems where the classical wall method already works, such as proton-deuteron and alpha-alpha scattering, making the quantum resource cost a state-preparation question rather than a scattering-dynamics question."],"forward_implications":["Charged-particle scattering is no longer out of reach for near-term quantum hardware; only one noisy energy measurement is required, and the rest of the relaxation is classical.","Because the Schmidt decomposition reduces every Pauli-string measurement to one- or two-qubit circuits, the method sidesteps the deep state-preparation circuits that otherwise destroy the signal on current processors.","The agreement across $b=2$, 1, and 0.75 fm indicates the extracted phase shift is insensitive to the ultraviolet regulator once $c_0$ is retuned, so the effective field theory power counting is doing the work expected of it.","The same hard-wall phase-shift technique that has already been applied classically to proton fusion, proton-deuteron scattering, and alpha-alpha scattering is now demonstrated in a quantum-classical hybrid form for the two-proton case."],"supporting_citations":[{"why":"Derives the leading-order EFT phase shift formula (Eq. 8) that the lattice results are tuned to reproduce.","marker":"[11]"},{"why":"Supplies the 3D classical lattice EFT calculation whose regulator tuning and hard-wall spectrum method are adapted to the 1D radial problem.","marker":"[26]"},{"why":"Demonstrates spherical-wall phase shifts from a quantum computer for neutral particles, the approach this paper extends to charged particles.","marker":"[16]"},{"why":"Provides the Gauss-Seidel relaxation with a single quantum energy measurement and the Schmidt decomposition that reduces state preparation to one- and two-qubit circuits.","marker":"[21]"},{"why":"Introduces the hard outer wall condition that converts the ground-state energy into a phase shift.","marker":"[19]"},{"why":"Extends the wall method to two-particle lattice scattering and phase-shift extraction.","marker":"[20]"},{"why":"Supplies the proton-proton scattering length $a_0 = -7.81$ fm used in the analytic modified effective range expansion target.","marker":"[30]"},{"why":"Gives the variational-relaxation iteration for quantum bound-state energies used in the hybrid loop.","marker":"[33]"}],"fun_headline_variants":["Noisy quantum run recovers proton scattering phase","Hybrid quantum-classical method extracts proton phase shift","Proton phase shift from one noisy quantum measurement","Quantum computer reproduces proton scattering phase shift"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The regulated Coulomb potential (a uniformly charged sphere of radius $2b$ plus a retuned contact coupling) leaves the wave function unchanged outside $r=2b$; if its finite size shifts the momentum dependence of the phase shift in the 10--70 MeV/c window, the reproduced curve would deviate from Eq. (8) even with perfect energies.","fun_headline_variants_meta":{"raw":{"variants":["Noisy quantum run recovers proton scattering phase","Hybrid quantum-classical method extracts proton phase shift","Proton phase shift from one noisy quantum measurement","Quantum computer reproduces proton scattering phase shift"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000736,"raw_usage":{"total_tokens":3097,"prompt_tokens":683,"completion_tokens":2414,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":427,"completion_tokens_details":{"reasoning_tokens":2355}},"tokens_in":427,"tokens_out":2414,"duration_ms":19175,"temperature":1.0,"reasoning_tokens":2355,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T21:46:38.452016+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare the phase shift from Eq. (9) obtained with exact classical ground-state energies to Eq. (8) for several $b$ values at fixed physical volume $(L-1)b$; if the residuals do not shrink as $b\\to 0$ or if they depend on $R_{\\mathrm{wall}}$ at fixed $b$, the uniformly-charged-sphere regulator is altering the momentum dependence and the central claim fails.","supporting_citations":[{"cited_title":"Kong and F","cited_arxiv_id":null,"evidence_quote":"Derives the leading-order EFT phase shift formula (Eq. 8) that the lattice results are tuned to reproduce."},{"cited_title":"Rupak and P","cited_arxiv_id":null,"evidence_quote":"Supplies the 3D classical lattice EFT calculation whose regulator tuning and hard-wall spectrum method are adapted to the 1D radial problem."},{"cited_title":"Sharma, T","cited_arxiv_id":null,"evidence_quote":"Demonstrates spherical-wall phase shifts from a quantum computer for neutral particles, the approach this paper extends to charged particles."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Gauss-Seidel relaxation with a single quantum energy measurement and the Schmidt decomposition that reduces state preparation to one- and two-qubit circuits."},{"cited_title":"Carlson, V","cited_arxiv_id":null,"evidence_quote":"Introduces the hard outer wall condition that converts the ground-state energy into a phase shift."},{"cited_title":"Borasoy, E","cited_arxiv_id":null,"evidence_quote":"Extends the wall method to two-particle lattice scattering and phase-shift extraction."},{"cited_title":"Piarulli, L","cited_arxiv_id":null,"evidence_quote":"Supplies the proton-proton scattering length $a_0 = -7.81$ fm used in the analytic modified effective range expansion target."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the variational-relaxation iteration for quantum bound-state energies used in the hybrid loop."}],"review_version":1}