{"id":"d20bb6f8-ca49-45ce-9244-4731c09d70b5","arxiv_id":"2507.06361","paper_version":3,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A 103-qubit IBM experiment yields a kagome antiferromagnet energy per site of -0.417J, boundary-corrected to -0.4386J, but the Hamiltonian was engineered and the couplings were fitted to exact small-system energies.","lead":"This paper reports a 103-qubit experiment on IBM quantum processors estimating the ground-state energy of the kagome antiferromagnet, a benchmark frustrated magnet. If valid, it would show near-term quantum hardware can handle frustrated two-dimensional spin systems at utility scale, but the couplings were tuned and corrections were applied to reach the known answer.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported energy is produced by an ODR rescaling that compares H and Hpert observables and by post hoc selection of the lowest run; without a justified correction the benchmark match is an artifact.","rationale":"The reader's weakest assumption targets the Hamiltonian-engineering premise (J' ≈ 2). That is a real concern, but the paper's own small-lattice calibrations (Tables I and II) give it some support: J' ≈ 1.9 reproduces ED energies on 6-23 site patches. The more decisive weakness is the step that actually produces the headline number. The raw hardware energies in Table III are -113 to -133J; the ODR formula rescales them by a factor of 1.3-1.5 to -166 to -172J. Equation (2) is written with the reference expectation on H (⟨ϕ|H|ϕ⟩ = -147) but the target on Hpert. In a proper ODR or any ratio-based noise extrapolation, the reference and target observables must match; otherwise the correction factor is arbitrary. The reference Clifford state is a static dimer cover; if any reference dimer lies on a modified bond, the ideal value under Hpert differs from -147, changing the factor. Additionally, the parameters are not optimized for Hpert; the global VQE minimizes the truncated HSEL, and the final 'best' parameter set is chosen by minimizing the noise-mitigated Tr(ρHpert) across processors and runs. This is post hoc selection on the very quantity being reported. A noiseless simulation of the final ansatz at the selected parameters would settle this directly. Our recommendation is to keep the reader's REJECT verdict; the load-bearing defect is that the central number is a product of an inconsistent noise rescaling and post hoc selection, not a measured or variationally bounded energy.","tokens_in":14080,"tokens_out":8257,"duration_ms":88664,"concrete_test":"Recompute the ODR-corrected values in Table III with the reference expectation evaluated on Hpert instead of H: i.e., replace ⟨ϕ|H|ϕ⟩/Tr(σH) by ⟨ϕ|Hpert|ϕ⟩/Tr(σHpert) in Eq. (2), using the same reference circuit. If the corrected per-site energy shifts by more than 5% from -0.417J (or no longer brackets -0.4386J after the OBC), the headline match is an artifact of the observable mismatch. As a cross-check, run the selected Table V parameters on a noiseless statevector simulator and compute Tr(ρHpert); if the noiseless value is above -172.4, the ODR rescaling is the sole source of the benchmark match.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (Section VI: per-site energy -0.417J, matching -0.4386J after OBC) rests on the noise-mitigated value -172.4J for Tr(ρHpert). That value is obtained from a raw hardware measurement near -113.7J (Table III, ibm fez) multiplied by the ODR factor ⟨ϕ|H|ϕ⟩/Tr(σH) from Eq. (2). Two problems make this factor unreliable. First, the reference expectation is evaluated with the original Hamiltonian H (⟨ϕ|H|ϕ⟩ = -147, Tr(σH) measured on H), while the target is the engineered Hamiltonian Hpert. Because Hpert changes 13 defect bonds to J' ≈ 1.9-2.0, the ideal reference value should be ⟨ϕ|Hpert|ϕ⟩, which is not -147 whenever the Clifford dimer cover includes a modified bond. The scalar ratio is therefore not a controlled correction for Tr(ρHpert). Second, the factor is applied after the parameters are selected post hoc: Table V lists many runs; the authors choose the parameter set and processor that minimize the noise-mitigated Tr(ρHpert) itself (Table III, Figure 5). Taking the minimum of many noisy trials biases the estimate downward, and the claim that two values are 'statistically significant' ignores the multiple-comparison problem. The raw values are 30-40% above the classical benchmark; the ODR factor supplies the entire downward shift. Even granting the Hamiltonian-engineering premise, the reported number is not a controlled estimate of any Hamiltonian's ground-state energy.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports a hybrid local/global VQE estimate of the ground-state energy per site of a 103-site kagome antiferromagnetic Heisenberg (KAFH) model, using IBM Heron processors. The method splits a hardware-efficient ansatz into classically optimized local segments, recombines them on quantum hardware with six junction angles optimized by global VQE on a truncated Hamiltonian, and applies an ODR noise-mitigation rescaling. The headline result is a per-site energy of -0.417J, which, after an open-boundary correction for a 125-site lattice containing 25 edge sites, is claimed to match the DMRG thermodynamic-limit value -0.4386J. The paper also advertises the approach as a scalable route to utility-scale quantum simulation of frustrated 2D magnets.","tokens_in":14440,"tokens_out":8064,"duration_ms":88258,"significance":"If the central claim were established, this would be a notable experimental milestone: a variational ground-state energy estimate on a 100+ qubit two-dimensional frustrated spin system, with open-source code, measurements on five IBM processors, and a systematic comparison against classical MPS and exact diagonalization. The hybrid local/global decomposition and the bond-strength engineering idea are potentially interesting. However, the headline numerical result depends on several load-bearing elements that are not justified in the manuscript, including an unexplained -36J correction term, an inconsistent site-counting and arithmetic conversion, an ODR reference that is not matched to the target observable, and post hoc selection of the best hardware result. As written, the paper does not provide a controlled estimate of the KAFH ground-state energy.","major_comments":[{"comment":"The reported per-site value -0.417J does not follow from the stated arithmetic. The text gives '-172.4J/4 = -52.1J' and '-521.J/103 = -0.417J', but -172.4/4 = -43.1J and -43.1/103 ≈ -0.418J, while -52.1/103 ≈ -0.506J. The value -0.417J emerges only if one first subtracts the unexplained -36J term (in 4x units) and divides by 125 sites: (-172.4 - 36)/4/125 ≈ -0.417J. The -36J term for the 22 sites excluded from the quantum circuit (Figure 2) is never derived or referenced, and the denominator is used inconsistently (103 vs 125 sites). This correction changes the per-site energy by roughly 0.07J, which is comparable to the claimed agreement with -0.4386J, so the central estimate is currently unsupported.","section":"Section VI, Eq. (3)"},{"comment":"The ODR rescaling is not a controlled correction for the target observable. The reference expectation values used in Eq. (2) are ⟨ϕ|H|ϕ⟩ = -147 and Tr(σH), both for the original Hamiltonian H, while the quantity to be mitigated is Tr(ρHpert), where Hpert differs from H on the 13 defect bonds (Eq. (1)). If any enhanced bond overlaps the dimer cover defining |ϕ⟩, as is the case for the engineered defect triangles, then ⟨ϕ|Hpert|ϕ⟩ ≠ ⟨ϕ|H|ϕ⟩ and the scalar ratio is not an anchor for the noise affecting Tr(ρHpert). A valid ODR application would require ⟨ϕ|Hpert|ϕ⟩ and Tr(σHpert). Furthermore, the noise-mitigated values in Table III are reported without error bars, so the statement in Section V.B that -172.4 is 'statistically significant' is not supported.","section":"Section IV.C, Eq. (2)"},{"comment":"The best value -172.32 is selected post hoc as the minimum over multiple processors and multiple parameter sets. The text states that among several minima found during global VQE, parameter sets achieving minimal objective values were selected, and Table V lists many candidate parameter sets. Table III then reports, for each processor, the parameter set yielding the minimum noise-mitigated Tr(ρHpert). Taking the minimum of many noisy estimates introduces a downward selection bias, and the comparison to the classical MPS value -167.95 in Section V.B and Figure 5 is a multiple-comparison claim rather than a single pre-specified measurement. The paper should report all runs, state the selection rule before data analysis, or apply a proper multiple-testing correction.","section":"Section V, Tables III and V"},{"comment":"The extension of the calibrated coupling J' ≈ 2 from small patches to the 103-site system is not quantitatively supported. J' is tuned so that local VQE matches exact diagonalization on subregions of 6-23 sites (Table I), and Section III.B justifies the extrapolation by locality and self-similarity. However, the final energy is an expectation value of Hpert, not of H, and the paper provides no numerical evidence (e.g., comparison of low-lying spectra of H and Hpert on intermediate-size clusters, or DMRG checks on larger patches) that the low-energy sector of Hpert faithfully represents the KAFH ground state at the target size. Without such evidence, the comparison of the measured value to the DMRG benchmark -0.4386J is not physically meaningful.","section":"Section III.B"}],"minor_comments":[{"comment":"There are arithmetic and sign errors: '-172.4J/4 = -52.1J' should be '-43.1J', and 'Etotal = 52.1J' is missing a minus sign.","section":"Section VI"},{"comment":"The definition of HSEL contains a duplicate pair (47,48) and the listed set may be missing some intended junction bonds; please check the edge list against the circuit in Figure 3.","section":"Section IV.B.2"},{"comment":"The statistical comparison is unclear: noise-mitigated values are plotted without error bars, while unmitigated values are binned, and the text says '7 out of 10 bars have a mean value lower than -167.95' but does not define the test used.","section":"Figure 5"},{"comment":"Reference [25] is a competition blog rather than a peer-reviewed publication; please cite the formal version if one exists.","section":"References"},{"comment":"The phrase 'Javg =≈ 4/3' is ambiguous and should be rewritten to state the average coupling on defect triangles unambiguously.","section":"Section III.C"}],"recommendation":"reject","confidential_remarks":"The central numerical claim is constructed from a chain of adjustments, each of which is either unexplained (-36J), internally inconsistent (103 vs 125 sites), mismatched to the target observable (ODR reference H instead of Hpert), or selected post hoc (minimum over processors and parameter sets). None of these issues is a presentation-only problem; they all bear directly on whether the reported -0.417J is a controlled estimate of the KAFH ground-state energy. A revision that derives the omitted-site energy, fixes the ODR reference, and pre-specifies the selection rule would be needed to assess whether the approach actually produces the claimed benchmark match."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is scale: a 103-qubit VQE experiment on a planar Kagome lattice, run on IBM hardware, with the ansatz split into classically optimized local segments and a few tunable junction gates. That is a real engineering achievement, and the open-source code is a plus. The local/global decomposition and the idea of strengthening defect-triangle bonds to mimic loop-flip physics are worth discussing, even if the physical motivation is hand-wavy.\n\nThe problem is the central number. The per-site energy -0.417J is not an independent estimate. The J' values are fitted so that small-patch VQE matches exact diagonalization, so the local energies are trained to the answer. The ODR correction in Eq. (2) is applied to Tr(ρHpert), but the reference expectation uses the original H, not Hpert. When Hpert changes 13 bonds, the reference value is not −147 for the engineered Hamiltonian. The ratio is therefore not a controlled rescaling for the quantity being measured. On top of that, the -36 adjustment for the 22 omitted sites appears without derivation, and the final result is the best among many processors and parameter sets, so there is a clear multiple-comparisons bias. The raw hardware values sit 30–40% above the classical benchmark; the ODR factor supplies the entire downward shift. Given all that, the close match to -0.4386J after an open-boundary correction that uses edge energies from the same small fitted systems is exactly what you would expect from a post hoc assembly, not from a measured ground state.\n\nThe soft spots are load-bearing, not cosmetic. But the paper is not worthless: it demonstrates that current hardware can run a 100+ qubit variational circuit for a 2D frustrated system and that careful noise mitigation can produce stable, reproducible expectation values for a reduced Hamiltonian. That is useful for the NISQ community, and the authors are transparent about their procedures.\n\nWho should read it? People working on large-scale VQE experiments and error mitigation will get value from the experimental details, but readers should treat the physics claim as unproven. I would send it to peer review because the scale and the method are significant enough to warrant referee time, but the reviewers should push for a major reframing: present it as a hardware demonstration of hybrid local/global VQE, and remove the claim that the DMRG benchmark has been reproduced.","headline":"A real 103-qubit VQE run on a Kagome lattice, but the headline energy is stitched together from fitted couplings, a mismatched ODR reference, and post hoc selection—so the benchmark match is not evidence.","tokens_in":14930,"tokens_out":1811,"would_cite":false,"duration_ms":22705,"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 that a 103-site kagome antiferromagnet ground-state energy can be estimated on current superconducting quantum processors, and that the per-site estimate $-0.417J$ matches the thermodynamic-limit benchmark after…","keywords":["kagome antiferromagnet","variational quantum eigensolver","Hamiltonian engineering","ground-state energy","quantum spin liquid","noise mitigation","frustrated magnetism","superconducting quantum processor"],"falsifier":"Compute the exact ground-state energy, via a high-accuracy tensor-network calculation, of the engineered Hamiltonian $H_{\\rm pert}$ with $J'=2$ on a 36- or 48-site planar kagome patch and compare it to the true KAFH ground-state energy on the same patch; if the per-site difference grows with system size, or if dimer correlations change qualitatively, the engineered Hamiltonian is not representing the original model.","tokens_in":13895,"feed_emoji":"🧲","tokens_out":8810,"duration_ms":88202,"temperature":0.7,"pith_summary":"This paper claims that a 103-site planar kagome antiferromagnetic Heisenberg lattice is within reach of current superconducting quantum processors, and that the measured per-site ground-state energy of $-0.417J$ is consistent with the thermodynamic-limit value $-0.4386J$ once open-boundary effects are removed. The route is a hybrid VQE: small overlapping patches are optimized classically, then stitched into a 103-qubit ansatz whose only trainable parameters are six junction rotations tuned on hardware. The central trick is Hamiltonian engineering: raising one exchange bond on each defect triangle to about twice the natural coupling, which mimics the loop-flip dimer resonances of a spin liquid and lets a shallow single-layer circuit reach accurate energies. If the claim holds, frustrated two-dimensional magnetism becomes a realistic target for near-term quantum simulation despite shallow circuits and limited connectivity.","feed_headline":"Quantum processor estimates 103-site kagome ground-state energy","feed_subtitle":"Per-site energy -0.417J lands on the -0.4386J thermodynamic-limit benchmark once edge sites are subtracted.","key_machinery":"The load-bearing object is the engineered Heisenberg Hamiltonian $H_{\\rm pert}$ of Eq. (1): on each 'defect triangle' selected by an initial static valence-bond (dimer) covering, one exchange bond is strengthened from $J=1$ to $J'\\approx 2$, while all other bonds stay at $J$. The calibration is done on small patches of 6 to 23 sites by matching VQE energies to exact diagonalization, and the same $J'\\approx 1.9$ to $2.0$ transfers across patches. Physically, the enhanced bond makes a loop-flip around the defect triangle energetically accessible, so the shallow single-repetition real-amplitude circuit, a chain of $R_y$ rotations and nearest-neighbor CNOT gates, can form a superposition of dimer covers instead of freezing into the static dimer configuration. Around this sits a two-stage scheme: local VQE optimizes 15- to 19-qubit subcircuits classically, stitch junctions add six $R_y(\\theta)$ gates, global VQE on hardware optimizes only those six parameters using a truncated cost Hamiltonian $H_{\\rm SEL}$ of junction-neighbor terms, and the final noisy expectation is post-processed with the ODR rescaling $\\text{noise-mitified}\\,\\mathrm{Tr}(\\rho H_{\\rm pert}) = \\langle\\phi|H|\\phi\\rangle / \\mathrm{Tr}(\\sigma H) \\cdot \\mathrm{Tr}(\\rho H_{\\rm pert})$, where $|\\phi\\rangle$ is a Clifford-reachable static dimer state.","core_discovery":"The paper's central claim is that a spin-1/2 kagome antiferromagnetic Heisenberg model on 103 sites can be treated as a utility-scale quantum-computation target. Using a single-repetition hardware-efficient ansatz on superconducting processors, the paper reports a total energy of $-172.4J$ in its four-times convention, or $-0.417J$ per site. After an open-boundary correction that removes the contribution of the 25 edge sites, the bulk per-site energy becomes $-0.4386J$, the published DMRG thermodynamic-limit value. The paper also reports that quantum-optimized junction parameters produce lower raw energies than parameters from a classical matrix-product-state simulation with circuit cutting on every processor tested, and that two noise-mitigated values, $-168.62J$ and $-172.4J$, lie below the classical baseline $-167.95J$ even after accounting for error bars. Stated on its own terms, the discovery is that a shallow 1D-entanglement ansatz, guided by locally calibrated Hamiltonian engineering, can estimate the KAFH ground-state energy at a size far beyond exact classical treatment.","pith_inferences":["The paper leaves implicit that the same $J'\\approx 2$ prescription could be tested directly on the engineered Hamiltonian itself: a tensor-network ground state of $H_{\\rm pert}$ on a 36-site patch would separate 'does the ansatz reach the ground state of the modified model' from 'is the modified model the right physics.'","A natural extension is to apply defect-triangle tuning as a general-purpose variational-error-mitigation tool for frustrated lattices beyond kagome, since the mechanism only needs a local reference configuration whose loop-flip resonances a shallow ansatz cannot express.","The quoted open-boundary correction propagates edge-site energies estimated from 12- to 23-site benchmarks; repeating Eq. (3) with edge energies taken from the 103-site geometry itself would reveal how much of the match to $-0.4386J$ is built into the correction.","The ODR rescaling assumes a depolarizing noise channel; testing whether the ratio $\\langle\\phi|H|\\phi\\rangle/\\mathrm{Tr}(\\sigma H)$ is stable across several Clifford reference states on the same processor would indicate how much of the final estimate inherits that assumption."],"forward_implications":["If the central claim is correct, a single-repetition hardware-efficient ansatz with only six global parameters can reach the KAFH ground-state estimate on a 103-site open-boundary lattice, so circuit depth is not the bottleneck for this class of frustrated magnets.","The same calibrated value $J'\\approx 1.9$ to $2.0$ worked on patches from 6 to 23 sites, which implies the defect-triangle engineering recipe transfers to larger lattices without per-geometry retuning.","Because the quantum-optimized junction parameters gave consistently lower raw energies than the classical MPS-optimized set on every processor tested, hardware-in-the-loop parameter optimization can capture correlations that approximate classical simulations miss.","The noise-mitigated values $-168.62J$ and $-172.4J$ sitting below the classical baseline $-167.95J$ mean the quantum result is not merely reproducing a classically computable answer; it is adding information beyond the tensor-network approximation.","At larger lattice sizes the fraction of boundary sites shrinks, so the paper's own scaling argument implies future per-site estimates should approach the thermodynamic-limit value without needing an open-boundary correction."],"supporting_citations":[{"why":"supplies the thermodynamic-limit per-site energy $-0.4386(5)J$ that the open-boundary-corrected result is benchmarked against","marker":"[13]"},{"why":"established high-precision DMRG studies of the kagome model on strips and cylinders that motivate the full-2D geometry","marker":"[7]"},{"why":"provides independent DMRG evidence for the Z2 spin-liquid ground state and the $-0.436$ to $-0.438J$ energy range","marker":"[12]"},{"why":"introduces the ODR noise-mitigation protocol used to correct the final energy expectation values","marker":"[30]"},{"why":"supplies the hardware-efficient ansatz framework that the single-repetition circuit is based on","marker":"[3]"},{"why":"provides the hardware-efficient circuit library and classical simulator used in the experiments and baselines","marker":"[31]"},{"why":"supplies the circuit-cutting and matrix-product-state classical benchmark energy $-167.95J$ that the quantum results are compared against","marker":"[36]"},{"why":"provides the finite-size and open-boundary correction approach used in the benchmarking section","marker":"[28]"}],"fun_headline_variants":["103-qubit kagome energy reaches thermodynamic limit after edge correction","Quantum hardware estimates 103-site kagome ground-state energy","Hamiltonian engineering guides 103-qubit kagome energy calculation","Shallow circuit matches kagome ground-state energy at 103 sites","Utility quantum processor hits kagome energy benchmark on 103 sites"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands or falls on the assumption that raising one exchange bond on each defect triangle to $J'\\approx 2$ yields an engineered Hamiltonian whose low-energy sector faithfully represents the original kagome ground state at 103 sites, even though the calibration is verified only on patches of 6 to 23 sites.","fun_headline_variants_meta":{"raw":{"variants":["103-qubit kagome energy reaches thermodynamic limit after edge correction","Quantum hardware estimates 103-site kagome ground-state energy","Hamiltonian engineering guides 103-qubit kagome energy calculation","Shallow circuit matches kagome ground-state energy at 103 sites","Utility quantum processor hits kagome energy benchmark on 103 sites"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001148,"raw_usage":{"total_tokens":4792,"prompt_tokens":1009,"completion_tokens":3783,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":625,"completion_tokens_details":{"reasoning_tokens":3692}},"tokens_in":625,"tokens_out":3783,"duration_ms":25093,"temperature":1.0,"reasoning_tokens":3692,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:06:56.308342+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the exact ground-state energy, via a high-accuracy tensor-network calculation, of the engineered Hamiltonian $H_{\\rm pert}$ with $J'=2$ on a 36- or 48-site planar kagome patch and compare it to the true KAFH ground-state energy on the same patch; if the per-site difference grows with system size, or if dimer correlations change qualitatively, the engineered Hamiltonian is not representing the original model.","supporting_citations":[{"cited_title":"Sachdev, Phys","cited_arxiv_id":null,"evidence_quote":"supplies the thermodynamic-limit per-site energy $-0.4386(5)J$ that the open-boundary-corrected result is benchmarked against"},{"cited_title":"Kandala et al., Nature 549, 242 (2017)","cited_arxiv_id":null,"evidence_quote":"established high-precision DMRG studies of the kagome model on strips and cylinders that motivate the full-2D geometry"},{"cited_title":"Local VQE produces pre-optimized ansatz segments for each subregion of the Kagome lattice","cited_arxiv_id":null,"evidence_quote":"supplies the hardware-efficient ansatz framework that the single-repetition circuit is based on"},{"cited_title":"Ahsan, S","cited_arxiv_id":null,"evidence_quote":"supplies the circuit-cutting and matrix-product-state classical benchmark energy $-167.95J$ that the quantum results are compared against"},{"cited_title":"Javanmard, U","cited_arxiv_id":null,"evidence_quote":"provides the finite-size and open-boundary correction approach used in the benchmarking section"}],"review_version":1}