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REVIEW 3 major objections 5 minor 75 references

On the Simulation of Conical Intersections in Water and Methanimine Molecules Via Variational Quantum Algorithms

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that variational quantum algorithms—VQE, VQD, and VQE-AC—can describe conical intersections in water and methanimine when the active space and molecular geometry are chosen appropriately, locating a CH2NH avoided crossing…

desk verdict The methanimine benchmark is clean and useful; the 'both molecules' claim overreaches because the water conical intersection rests on a classical SA-CASSCF calculation with no quantum simulation behind it. read the letter →

arxiv 2507.22670 v3 pith:2LSO33UJ submitted 2025-07-30 quant-ph physics.chem-ph

Samir Belaloui , Nacer Eddine Belaloui , Achour Benslama This is my paper · ORCID
classification quant-phphysics.chem-ph
keywords conicalintersectionsavoidedcrossingsvariationalquantumeigensolverexcitedstateschemistrystate-averageCASSCFmethaniminewatermolecule
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that near-term variational quantum algorithms can locate conical intersections and avoided crossings in small molecules, as long as the active space and nuclear geometry are chosen to make the crossing visible. VQE, VQD, and VQE-AC are run on water and methanimine, benchmarked against exact diagonalization, with classical state-average CASSCF used to scan for degenerate regions. The concrete findings are a methanimine avoided crossing at $\alpha = 94^\circ \pm 2^\circ$ at the (4,3) active space, and a water degeneracy at $G = 0.25$ Å in a deformed Jacobi geometry. This matters because nonadiabatic regions control photochemistry and photophysics, and if these variational methods can map them on near-term hardware, the experimental bottleneck for studying such processes is lowered.

What carries the argument

The load-bearing machinery is a set of variational cost functions plus one classical scanning tool. VQE minimizes the energy expectation value $\langle\Psi(\theta)|H|\Psi(\theta)\rangle$; VQD adds orthogonality penalties $\beta_i\,|\langle\Psi(\theta_k)|\Psi(\lambda_i)\rangle|^2$ to reach excited states; VQE-AC keeps the bare energy expectation value and enforces orthogonality externally as $|\langle\Psi(\theta)|\Psi_0\rangle|^2 \le 10^{-4}$; and state-average CASSCF averages a few electronic states together so that near-degeneracies become visible. The simulations use parity mapping to turn the fermionic Hamiltonian into qubit operators, the Efficient SU2 and UCCSD ansätze, and the SPSA, SLSQP, and COBYLA optimizers. The VQE-AC constraint, rather than a tuned penalty, is what the paper credits with stable behavior in the sensitive crossing region.

What would settle it

Recompute the water ground and first excited states in the same Jacobi coordinates with a slightly different basis set (for example cc-pVDZ instead of 6-31G) or a different active space and check whether the gap at $G = 0.25$ Å stays closed, and run VQD or VQE-AC at that geometry to see if the degeneracy reproduces. For methanimine, compute the two-state gap at the (12,9) level with a more expressive ansatz or a multireference method and see whether the avoided crossing at $\alpha \approx 94^\circ$ collapses to a true degeneracy or moves.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that variational quantum eigensolvers—VQE for ground states, VQD and VQE-AC for excited states—reproduce the exact-diagonalization energy surfaces closely enough to expose a conical-intersection signature in methanimine and, through a classical state-average CASSCF scan, in water. For CH2NH in the geometry with a $90^\circ$ dihedral angle, VQD and VQE-AC both place the avoided crossing at $\alpha = 94^\circ \pm 2^\circ$; enlarging the active space from (4,3) to (12,9) narrows the ground–excited gap near $\alpha \approx 90^\circ$ but shifts all energies upward because the ansatz struggles to express the larger space. For water, no crossing appears under symmetric O–H scaling; only the asymmetric Jacobi deformation with $\gamma = 0.00021^\circ$ produces an intersection, around $G = 0.25$ Å. The paper therefore concludes that the capability of the quantum algorithms to describe conical intersections is real but conditional on active-space and geometry choices.

Load-bearing premise

The claim that quantum variational algorithms can describe the water conical intersection rests on a classical state-average CASSCF calculation at one heavily deformed Jacobi geometry, and the paper never runs a quantum algorithm at that geometry; the paper admits the intersection can disappear if the basis set or active space changes.

Editorial extensions

If this is right

  • At the (4,3) active space, both VQD and VQE-AC put the CH2NH avoided crossing at $\alpha \approx 94^\circ$, and the two algorithms agree with each other and with exact diagonalization near the crossing.
  • VQE-AC can replace VQD in crossing regions without tuning a penalty weight $\beta$, because it enforces orthogonality as a hard constraint.
  • Symmetric water geometries never show a crossing, while the asymmetric Jacobi deformation does; geometry choice, not just method, determines whether a conical intersection is visible.
  • Larger active spaces improve the description of the crossing but raise computational cost and expose the limits of the chosen ansatz, as seen in the upward-shifted (12,9) CH2NH curves.
  • State-average CASSCF at the (4,3) active space reproduces the CH2NH near-degeneracy (around $\alpha \approx 100^\circ$) at lower cost than exact diagonalization, making it a practical scan tool for choosing where to run quantum algorithms.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test the paper leaves implicit: run VQD or VQE-AC at the water Jacobi geometry near $G = 0.25$ Å to see whether the quantum algorithms actually close the gap the way the classical SA-CASSCF scan does.
  • A true conical intersection requires degeneracy in a two-dimensional branching space; confirming the CH2NH feature would mean scanning a second coordinate, such as the dihedral angle, and showing the crossing survives.
  • Because the paper notes the water CI disappears under basis-set or active-space changes, practical NISQ implementations there would likely need error mitigation and a carefully chosen active space to keep the intersection from washing out.
  • The (12,9) VQD artifacts and energy shifts suggest active-space size alone is not the bottleneck; ansatz expressiveness and optimizer behavior matter, so adaptive ansätze are a natural next step.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper reports simulations of variational quantum algorithms (VQE, VQD, VQE-AC) and classical state-averaged CASSCF on the water and methanimine molecules, aiming to locate conical intersections. For CH2NH, VQD and VQE-AC calculations at a (4,3) active space reproduce an avoided crossing obtained by exact diagonalization near a bending angle of α≈94°, and a (12,9) active-space VQD run reproduces the qualitative trend with larger systematic errors. For H2O, VQE/VQD/VQE-AC are validated on symmetric O–H stretch deformations, and a conical intersection is claimed based solely on a classical SA-CASSCF calculation at a heavily deformed Jacobi geometry (G≈0.25 Å). The abstract and conclusion assert that the work 'confirms the quantum variational algorithms' capability of describing conical intersections in both molecules.'

Significance. If the claims were fully supported, this would be a useful benchmark of excited-state variational quantum algorithms against exact diagonalization, particularly the CH2NH avoided-crossing result at α=94°±2° and the comparison of VQD with VQE-AC. The explicit external benchmark, the clear experimental setup, and the demonstration of ansatz/optimizer sensitivity are strengths. However, the headline claim about 'both molecules' is not supported by the reported quantum simulations: the water conical intersection is identified only by classical SA-CASSCF, and the CH2NH results demonstrate an avoided crossing along a one-dimensional scan rather than a true conical intersection. The paper also lacks a data/code availability statement, limiting reproducibility. With a corrected scope, the study would be a modest but legitimate contribution to the VQA-for-excited-states literature.

major comments (3)
  1. [Abstract; Section IV.4; Fig. 12; Section VI] The abstract claims 'This work confirms the quantum variational algorithms' capability of describing conical intersections in both molecules,' but the only evidence for a conical intersection in water is a classical SA-CASSCF calculation at a (10,12) active space with the 6-31G basis set (Fig. 12). No VQE, VQD, or VQE-AC simulation is reported at the Jacobi geometry; the text explicitly states 'Simulations of quantum algorithms applied on these larger systems ... could be addressed in future works' and 'Changes to the basis set or the active space could make the CI disappear in the SA results.' The abstract and conclusion therefore overstate the support for the water half of the central claim. Please either report a variational quantum simulation at this geometry (or a reduced variant) or revise the abstract and conclusion to state that the water CI is identified by a classical state-averaged calculation and proposed as a target for future quantum-simulation studies.
  2. [Section V, Figs. 8–11; Section II.2; Section VI] For CH2NH, the variational quantum algorithms produce energy curves along the single bending coordinate α with a minimum gap near α≈94°; they do not locate a true degeneracy in a two-dimensional branching space. The paper itself defines a conical intersection as a degeneracy of adiabatic potential energy surfaces (Section II.2) and notes that an avoided crossing is 'often interpreted as evidence for an underlying conical intersection' but is not itself a conical intersection. Consequently, the abstract's wording 'capability of describing conical intersections' is too strong for the CH2NH results. Please either perform a two-dimensional scan (e.g., vary α and a second internal coordinate) to demonstrate an actual crossing point, or consistently use 'avoided crossing indicative of a conical intersection' for the quantum-algorithm results in the abstract, main text, and conclusion.
  3. [Fig. 10; Section V; Section VI] The (12,9) VQD results in Fig. 10 exhibit three distinct local minima, systematic upward energy shifts relative to exact diagonalization, and a gap at α≈90° that the authors describe as 'notably closer' but not closed. The conclusion nonetheless states that 'larger active spaces significantly improved the precision and expressiveness of quantum simulations in the vicinity of conical intersections.' This is not supported by the reported data: the (12,9) energies are less accurate in absolute terms than the (4,3) results, and no quantitative metric (e.g., minimum energy gap, state overlap, or gradient norm) is provided to demonstrate improvement near the crossing region. Please either quantify the claimed improvement or soften the conclusion to reflect the ansatz limitations and the absence of demonstrated improvement at the larger active space.
minor comments (5)
  1. [Section IV.4] The term 'Jacobbi' should be 'Jacobi' in the text and figure captions.
  2. [Eq. (9) and following text] The summation in Eq. (9) runs i=1 to k−1, but the text then refers to 'previously found k states (from the ground state, i=0, up to the (k−1)th excited state)'; please clarify the indexing convention for the previously computed states in the VQD penalty term.
  3. [Fig. 4 and Section V (H2O VQE)] The target value of −74.96742 Hartree is not tied to a specific basis set and active space in the text; please state the computational setup corresponding to this exact energy.
  4. [Section V, CH2NH VQD vs VQE-AC] The comparison between VQD (Efficient SU2) and VQE-AC (UCCSD) for CH2NH is not controlled with respect to the ansatz; please note this as a limitation or perform a same-ansatz comparison to isolate the effect of the orthogonality constraint.
  5. [General] No data or code availability statement is provided, and software versions, optimizer settings, and random seeds are not specified; adding these would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: quantum results are benchmarked against exact diagonalization, and no fitted parameter is renamed as a prediction.

full rationale

The paper's central numerical claims for CH2NH are validated against exact diagonalization (Figs. 9, 10, and 11), an external benchmark that does not depend on the variational algorithms being tested. The VQD hyperparameters (beta = 0.5 and 0.3) and the VQE-AC orthogonality threshold (10^-4) are adopted from the cited methods rather than fitted to the target energy curves, so the avoided-crossing location at alpha = 94 deg is not forced by construction. The water conical-intersection evidence is a classical state-average CASSCF calculation (Fig. 12) performed with PySCF, and no variational quantum algorithm is run at that geometry; the paper explicitly warns that 'Changes to the basis set or the active space could make the CI disappear in the SA results.' This is an unsupported extrapolation when the abstract credits quantum variational algorithms with describing conical intersections in 'both molecules,' but an untested extrapolation is not circular reasoning. The self-citations present (e.g., Belaloui et al. for the VQE figure and ansatz discussion) are contextual and not load-bearing for the main claim. No equation in the paper reduces to its own input, and no fitted parameter is relabeled as a prediction. Therefore, the paper contains no significant circularity, and the score is 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical entities, forces, or conserved quantities. It relies on standard electronic-structure approximations, fermion-to-qubit mappings (parity), and heuristic choices of active space, basis set, ansatz, and optimizer. The main hand-tuned numbers are the VQD penalty weight and the VQE-AC constraint threshold.

free parameters (2)
  • VQD penalty weight beta = 0.5 (Experiment 1), 0.3 (Experiment 2)
    Hand-chosen hyperparameter controlling orthogonality enforcement in the VQD cost function; affects excited-state energies and whether the optimizer finds the correct root.
  • VQE-AC orthogonality constraint threshold = 10^-4
    Hand-chosen threshold in Eq. (11); determines how strictly the excited state is orthogonal to the ground state and influences the quality of the excited-state solution.
assumptions (3)
  • domain assumption Born-Oppenheimer approximation is valid for the studied geometries except at the conical intersection point
    The paper constructs the electronic Hamiltonian under BO (Section II.1) and uses adiabatic surfaces; near the CI the coupling diverges, which is exactly the effect they seek to detect.
  • domain assumption The chosen active space and basis set adequately represent the low-lying states of interest
    The paper uses (4,3) and (12,9) active spaces with STO-3G or 6-31G bases; for (12,9) VQD results are visibly shifted, and the water CI only appears at (10,12)/6-31G, so this assumption is fragile.
  • domain assumption The ansatz (Efficient SU2 or UCCSD) is expressive enough to approximate the target eigenstates
    The paper itself notes the (12,9) VQD energies are higher than exact due to 'limited expressiveness of the chosen ansatz', so the central claim depends on choosing an ansatz that is sufficient, which is not guaranteed.

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Cite this review

Pith. "Pith review of On the Simulation of Conical Intersections in Water and Methanimine Molecules Via Variational Quantum Algorithms." pith.science (2026). https://pith.science/paper/2LSO33UJ

@misc{pith2026250722670,
  author       = {Pith},
  title        = {Pith review of: On the Simulation of Conical Intersections in Water and Methanimine Molecules Via Variational Quantum Algorithms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2LSO33UJ}},
  note         = {Machine review of arXiv:2507.22670}
}
read the original abstract

We investigate the electronic structure of methanimine (CH2NH) and water (H2O) molecules in an effort to locate conical intersections (CIs) using variational quantum algorithms. Our approach implements and compares a range of hybrid quantum-classical methods, including the Variational Quantum Eigensolver (VQE), Variational Quantum Deflation (VQD), VQE with Automatically-Adjusted Constraints (VQE-AC), and we explore molecular configurations of interest using a State-Average (SA) approach. Exact Diagonalization is employed as the classical benchmark to evaluate the accuracy of the quantum algorithms. We perform simulations across a range of molecular geometries, basis sets, and active spaces to compare each algorithm's performance and accuracy, and to enhance the detectability of CIs. This work confirms the quantum variational algorithms' capability of describing conical intersections in both molecules, as long as appropriate active spaces and geometries of the molecule are chosen. We also compare the accuracy and reliability of VQE-based methods for computing excited states with classical benchmark methods, and we demonstrate good agreement within desired regions.

Figures

Figures reproduced from arXiv: 2507.22670 by the authors.

Figure 1
Figure 1. FIG. 1: VQE algorithm: the Quantum Processing Unit [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Geometrical representations of the H [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The used geometry of the Methanimine [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Energy convergence of the VQE algorithm for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Convergence graph of the VQE algorithm for [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Comparison between the exact diagonalization [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Comparison between the exact [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 12
Figure 12. Figure 12: FIG. 12: State-average simulation for a (10, 12) active [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: State-average results for CH [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.