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A single pretrained Slater-Koster model can supply the Hamiltonian for variational quantum band-structure calculations on any crystal built from 65 elements, removing per-material DFT, Wannierization, or hand-fitting.

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2026-07-14 16:16 UTC pith:DVCVTTLN

load-bearing objection Solid methods paper: universal SlaKoNet Hamiltonian into VQD recovers bands to ~1.8 meV of exact diagonalization of the same matrix, with honest hardware and DMFT extensions. the 2 major comments →

arxiv 2607.09761 v1 pith:DVCVTTLN submitted 2026-07-06 cond-mat.mtrl-sci cond-mat.str-el

SlaKoNet-VQD: A universal Slater-Koster tight-binding Hamiltonian for variational quantum band-structure calculations on near-term hardware

Akshaya Ajith , Jaehyung Lee , Charles Rhys Campbell , Kamal Choudhary This is my paper
classification cond-mat.mtrl-sci cond-mat.str-el
keywords variational quantum eigensolvervariational quantum deflationSlater-Koster tight-bindingneural Hamiltonianband structuredynamical mean-field theorynear-term quantum hardwarematerials screening
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Variational quantum algorithms can compute electronic bands of solids on near-term hardware, but until now each material needed its own costly second-quantized Hamiltonian, usually from density-functional theory plus Wannierization or hand-tuned tight-binding parameters. This paper shows that a pretrained neural Slater-Koster model (SlaKoNet) can generate that Hamiltonian for any crystal made of its 65 trained elements in a single forward pass. The resulting SlaKoNet-VQD pipeline recovers the full eight-band silicon structure to 1.78 meV mean absolute deviation from exact diagonalization on a three-qubit simulator, matches that accuracy on five conventional superconductors without retraining, and runs a ground-state evaluation on real quantum hardware for aluminum. The same Hamiltonian can be promoted to a Hubbard model and solved with dynamical mean-field theory, recovering known correlation trends. A sympathetic reader cares because the bottleneck that limited quantum band-structure work to one material at a time is replaced by a structure-agnostic, differentiable generator suited to high-throughput screening and gradient-based co-optimization of ansatz and Hamiltonian.

Core claim

Coupling a universal, pretrained Slater-Koster tight-binding Hamiltonian generator to variational quantum deflation yields a structure-agnostic workflow that recovers full Brillouin-zone band structures for silicon and several superconductors to within about 1.8 meV of exact diagonalization of the same Hamiltonian on a few-qubit simulator, and that can be executed end-to-end on present quantum hardware for a representative ground-state point, without any per-material DFT, Wannierization, or empirical refitting.

What carries the argument

SlaKoNet: a neural parametrization of onsite energies and distance-dependent Slater-Koster hopping and overlap integrals across 65 elements; at runtime it builds H(k) and S(k) by polynomial interpolation, which is then Hermitized, Pauli-decomposed, and fed to a variational quantum deflation loop.

Load-bearing premise

The scientific usefulness of the whole pipeline rests on the claim that the pretrained tight-binding eigenvalues are faithful enough for screening, even though the model itself carries roughly three-quarters of an electron-volt mean absolute bandgap error versus experiment and lacks spin-orbit coupling.

What would settle it

Take a held-out crystal with Z at most 65, generate its SlaKoNet Hamiltonian, run the same VQD protocol along a standard high-symmetry path, and check whether mean absolute deviation from exact diagonalization of that Hamiltonian stays near 2 meV while the absolute bands still track a trusted TBmBJ or experimental reference within the model's stated bandgap error; a large VQD-versus-diagonalization gap or systematically wrong gap topology would falsify the central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • High-throughput benchmarking of variational quantum algorithms becomes possible across thousands of crystals without any Wannierization step per material.
  • Because the map from atomic coordinates to H(k) is differentiable, ansatz parameters and crystal geometry can be co-optimized under a quantum-evaluated objective.
  • The same neural Hamiltonian supplies a ready non-interacting bath for dynamical mean-field theory, making the impurity problem the natural target for a quantum solver without a per-material DFT front end.
  • A fixed, reproducible Hamiltonian format across compositions becomes a clean benchmark substrate for new excited-state variational algorithms.
  • Once fault-tolerant phase estimation is available for solids, the same universal generator can still supply the second-quantized input for any composition in the training domain.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the neural integrals can later be extended to dynamical matrices, the identical VQD loop would yield phonon bands without finite-difference force constants per material.
  • Hardware noise of several hundred meV currently swamps the meV-level simulator fidelity, so near-term value is more likely in algorithm and ansatz co-design than in production band maps.
  • Restricting the DMFT bath to a low-energy manifold for cuprates already recovers strong renormalization; a full orbital-projected downfolding of the same neural Hamiltonian would be a direct next quantitative test.
  • Compact log2(N) qubit encoding of the N-by-N matrix trades particle-number structure for qubit count; comparing it head-to-head with one-qubit-per-orbital encodings on the same SlaKoNet inputs would clarify which encoding scales first.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 9 minor

Summary. The manuscript presents SlaKoNet-VQD, a pipeline that feeds a pretrained universal Slater-Koster tight-binding Hamiltonian (SlaKoNet, trained on JARVIS-TBmBJ across 65 elements) into a Qiskit VQD solver for periodic solids, replacing per-material DFT+Wannierization or hand-fitted TB parameters. On silicon, sequential VQD on a 3-qubit EfficientSU2 ansatz recovers all eight bands along the Setyawan-Curtarolo path with 1.78 meV MAE relative to exact diagonalization of the same SlaKoNet H(k); comparable MAE (≤1.8 meV) is reported for Al, Ta, Nb, V, and ZrN with no retraining. A single-k ground-state VQE on aluminum is executed on ibm_boston (~0.37 eV error after mitigation). The same H(k) is promoted to a Hubbard model and solved with DMFT(IPT), recovering qualitative correlation trends across group-5 metals and strong quasiparticle renormalization in La2CuO4 when the bath is restricted to the low-energy manifold. The authors argue the pipeline enables high-throughput VQA benchmarking and, in principle, gradient-based ansatz-Hamiltonian co-optimization.

Significance. The work cleanly removes a real bottleneck in near-term quantum band-structure studies: per-material Hamiltonian construction. The central numerical claim—VQD eigenvalues match exact diagonalization of the identical SlaKoNet matrix to ~1–2 meV across multiple chemistries and qubit counts—is independent, non-circular, and well documented (ansatz/optimizer ablations, Hermitization, full k-path). Code, model weights, a web app, and an archived IBM workload support reproducibility. The DMFT sketch usefully identifies the impurity problem as the natural quantum target once interactions are restored. Absolute electronic-structure accuracy remains bounded by SlaKoNet itself (0.74 eV bandgap MAE vs experiment), which the authors state explicitly; the contribution is therefore best read as a methods and infrastructure paper for VQA benchmarking and transferable TB inputs, not as a new high-accuracy electronic-structure method. Within that scope it is a solid and timely step.

major comments (2)
  1. Abstract and Sec. IVA claim the workflow is "suited to high-throughput bandstructure screening" while Sec. IVB correctly states that absolute accuracy is bounded by SlaKoNet’s 0.74 eV mean absolute bandgap error (and ~2.3 eV on ultrawide-gap insulators). High-throughput VQA benchmarking is well supported by the reported numbers; materials screening for quantitative band features is not, at that error level. Please align the abstract and opening claims with the more careful distinction already present in Sec. IVA–B (benchmarking vs screening), so the central utility claim matches the accuracy bound the paper itself reports.
  2. Sec. IIID places SlaKoNet "on the same footing as prior quantum band-structure work" via a DFT+Wannier comparison, but then notes that bases do not match and defers a fully basis-matched, element-wise comparison to future work. The only quantitative anchors given (valence bandwidth 11.3 vs 11.7 eV; deep s-band at Γ within ~0.4 eV) are coarse. Either (i) provide a basis-matched comparison for at least Si, or (ii) reframe this subsection as a qualitative consistency check and remove language that implies a rigorous baseline equivalence. As written, the subsection does not yet support the "same footing" claim.
minor comments (9)
  1. Introduction: "descrepancy" should be "discrepancy" (hardware-execution paragraph).
  2. Sec. IIG / Eq. (6): state explicitly how β_i = 4 was chosen and whether any k-points required retuning; a one-sentence robustness check (e.g., β in {2,4,8}) would strengthen the claim that eigenvalues are "empirically robust."
  3. Table I reports relative error as |E_VQE − E_exact|/|E_VQE|; the more conventional |E_VQE − E_exact|/|E_exact| would be clearer, and the absolute error in eV should be listed alongside.
  4. Fig. 3 and Fig. 7: marker size and color contrast make it hard to see residual deviations on the highest bands; consider a small residual panel or a supplementary table of per-band MAE.
  5. Sec. IIIG: IPT is controlled near half-filling; the group-5 metals are not half-filled d shells. A brief note that Z(U) trends are qualitative (as already hinted) and that a CTQMC or quantum-impurity reference would be needed for quantitative Z would help non-DMFT readers.
  6. Sec. IIIG, La2CuO4: the low-energy-manifold restriction is described as a "proxy" that overestimates Z relative to full downfolding. Please cite the orbital character used to define that manifold (energy window or projection) so the procedure is reproducible.
  7. Hardware (Sec. IIIE): report the exact ground-state energy of the same SlaKoNet H(k) used as reference for the 0.37 eV figure, and clarify whether the ~0.37 eV is raw or TREX-mitigated (text says "error-mitigated" but Fig. 6 caption emphasizes shot-noise bars).
  8. Eq. (7)–(8): the lattice Green’s function is written with a local Σ(ω); state whether orbital off-diagonal self-energy components are neglected and how multi-orbital U is treated for V/Nb/Ta (density-density only?).
  9. Data availability: the reproducibility repo is promised "upon publication"; if the journal allows, provide a temporary anonymous archive or DOI so reviewers can check the notebooks that generate Figs. 3–8.

Circularity Check

0 steps flagged

No significant circularity: VQD is validated against exact diagonalization of the same fixed SlaKoNet H(k), an independent classical check.

full rationale

The load-bearing numerical claim is that sequential VQD recovers the eigenvalues of the SlaKoNet-generated H(k) to ~1.78 meV MAE (Si, full path) and ≤1.8 meV (Al, Ta, Nb, V, ZrN) relative to exact diagonalization of that same matrix on a statevector simulator. That comparison is independent of how H(k) was trained: the matrix is fixed input, NumPy/exact diagonalization is an external classical oracle, and the reported MAE measures only variational solver fidelity. SlaKoNet itself is pretrained prior work (slakonet_v0 weights, no fine-tuning here) trained on JARVIS-TBmBJ DOS/bandgaps; the present paper does not re-fit SK parameters to the VQD eigenvalues or call that training a prediction of the VQD results. Hyperparameters (β_i=4, EfficientSU2 reps=5, COBYLA) are fixed and ablated across circuits/optimizers rather than fitted to the headline MAE. Hardware (single-k Al, ~0.37 eV) and DMFT/IPT sections are scoped as limited demonstrations and do not feed back into the band-structure MAE. Self-citations to SlaKoNet [19] and prior Wannier-VQE work [6] supply the Hamiltonian source and context; they do not force the VQD-vs-exact numbers by construction. Absolute electronic-structure accuracy is bounded by SlaKoNet’s own ~0.74 eV bandgap MAE (Sec. IVB), which the authors state explicitly and which is a correctness/scope limit, not circularity. No self-definitional loop, fitted-input-as-prediction, uniqueness theorem, or renamed empirical pattern is load-bearing for the strongest claim.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central claim (universal neural SK Hamiltonian + VQD recovers bands to meV of exact diag) rests on the pretrained SlaKoNet model, the standard VQD cost with fixed overlap penalties, and the assumption that numerical Hermitization and Pauli decomposition preserve the spectrum. Free parameters are VQA hyperparameters and the DMFT U values; no new physical entities are invented. Upstream SlaKoNet training parameters are inherited from prior work and not re-fit here.

free parameters (4)
  • VQD overlap penalty β_i = 4
    Fixed at β_i=4 for all deflated states; stated to be empirically robust but is a hand-chosen scale that keeps the spectrum undistorted.
  • EfficientSU2 ansatz depth (reps) = 5
    Chosen as reps=5 (36 parameters) after ablation; controls expressivity and is not derived from first principles.
  • COBYLA max iterations = 400
    Set to 400 following prior TB-VQE work; optimizer budget is a free algorithmic choice.
  • Hubbard U values in DMFT = 2–6 eV (cRPA 3.2 eV)
    Scanned at 2, 4, 6 eV (and cRPA 3.2 eV for cuprate); interaction strengths are external inputs, not predicted by SlaKoNet.
axioms (4)
  • domain assumption Slater-Koster two-center approximation plus polynomial interpolation of distance-tabulated integrals yields a faithful non-orthogonal TB Hamiltonian for the 65-element domain.
    Inherited from SlaKoNet (Sec. IIA); the entire pipeline’s absolute accuracy is bounded by this model’s fidelity to TBmBJ/experiment.
  • domain assumption Sequential VQD with fixed overlap penalties recovers the ordered spectrum of an N×N Hermitian matrix when the ansatz is sufficiently expressive.
    Standard VQD premise (Eq. 6); validated empirically for N=8 but known to degrade for higher excited states (30× larger error on top band).
  • ad hoc to paper Symmetric projection H ← (H+H†)/2 removes only numerical noise and does not alter the physical spectrum at the reported precision.
    Introduced in Sec. IIB to fix 10^{-9} GPU asymmetry; verified to introduce <10^{-7} per-element deviation.
  • domain assumption Classical IPT impurity solver at half-filling captures correlation trends (Z(U)) sufficiently for the qualitative DMFT claims.
    Sec. IIIG; authors note IPT is controlled near particle-hole symmetry and that cuprate Z is an upper bound.

pith-pipeline@v1.1.0-grok45 · 20615 in / 3426 out tokens · 43481 ms · 2026-07-14T16:16:23.588833+00:00 · methodology

0 comments
read the original abstract

Variational quantum algorithms such as VQE and VQD are promising for near-term electronic structure calculations, but for periodic solids their reach is limited by the cost of building a faithful second-quantized Hamiltonian, typically via DFT plus Wannierization or hand-fit tight-binding parameters. SlaKoNet addresses this by combining deep learning with the Slater-Koster tight-binding formalism to fit hopping and overlap parameters across 65 elements, enabling deterministic Hamiltonian construction for any crystal built from these elements. Here we couple a SlaKoNet model trained on JARVIS-TBmBJ with a Qiskit-based VQD algorithm, replacing costly Hamiltonian construction with a universal neural Hamiltonian generator. The resulting SlaKoNet-VQD workflow is structure-agnostic, differentiable, and suited to high-throughput bandstructure screening. We benchmark on silicon, recovering the full eight-band structure along the standard k-path with mean absolute deviation of 1.78 meV from exact diagonalization on a 3-qubit simulator, and extend to five conventional superconductors (Al, Ta, Nb, V, ZrN) with similar accuracy. We demonstrate execution on IBM Quantum hardware for a k-point ground-state calculation on aluminum (MAE ~0.37 eV). We further promote the Hamiltonian to a correlated Hubbard model solved via dynamical mean-field theory, recovering weakening correlations across group-5 metals and strong quasiparticle renormalization in La2CuO4, identifying the impurity problem as a natural quantum solver target. This pipeline enables high-throughput VQA benchmarking across the periodic table and gradient-based ansatz-Hamiltonian co-optimization for materials discovery. Web app: https://atomgpt.org/quantum.

Figures

Figures reproduced from arXiv: 2607.09761 by Akshaya Ajith, Charles Rhys Campbell, Jaehyung Lee, Kamal Choudhary.

Figure 1
Figure 1. Figure 1: FIG. 1. End-to-end [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. EfficientSU2 ansatz circuit (reps=5) used for VQD band structure calculations on the 3-qubit [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Silicon band structure from [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Mean absolute error (MAE, meV) of VQD eigenvalues relative to exact diagonalization (NumPy) of the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. MAE (meV) for all six circuit ansatzes at reps=5 across three optimizers, for Si (JVASP-1002). The dashed red [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Aluminum [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

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