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REVIEW 3 major objections 5 minor 70 references

Approximate quantum circuit compilation for proton-transfer kinetics on quantum processors

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

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Pith's one-line read Two adaptive quantum-circuit stages, ADAPT-VQE plus approximate compiling, estimate the malonaldehyde proton-transfer barrier within 13% of a high-level reference while cutting two-qubit depth by up to 88%.

desk verdict Useful benchmark for early-FT quantum chemistry, but the text and tables disagree on several key numbers and the FNO truncation is unvalidated. read the letter →

arxiv 2507.08996 v1 pith:NFGTD67R submitted 2025-07-11 quant-ph physics.chem-ph

Arseny Kovyrshin , Dilhan Manawadu , Edoardo Altamura , George Pennington , Benjamin Jaderberg , Sebastian Brandhofer , Anton Nykänen , Aaron Miller
show 10 more authors
Walter Talarico Stefan Knecht Fabijan Pavošević Alberto Baiardi Francesco Tacchino Ivano Tavernelli Stefano Mensa Jason Crain Lars Tornberg Anders Broo
This is my paper · ORCID
classification quant-phphysics.chem-ph PACS 03.67.Ac
keywords protontransfernuclear-electronicorbitalquantumcomputingADAPT-VQEapproximatecompilingfrozennaturalorbitalsmalonaldehydezero-noiseextrapolation
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

The paper claims that proton-transfer kinetics — whose rate depends exponentially on the barrier height — can be brought within reach of quantum computers by a two-stage adaptive scheme. ADAPT-VQE first builds a compact ground-state ansatz in a nuclear-electronic orbital basis, treating the moving proton as a quantum particle, with the virtual orbital space truncated by the frozen natural orbital approximation. A second adaptive step, approximate quantum compiling (ADAPT-AQC), then recompiles that circuit by adding two-qubit gates one at a time, cutting the two-qubit depth from 411 to 51 layers (Left) and from 211 to 90 (Middle) while the noiseless barrier estimate lands at 13.4 mHa against the 11.9 mHa FNO-NEO-CASCI reference — within 13%, and bracketed by the semi-empirical (11.2 mHa) and experimental (13.5 mHa) estimates. The paper also reports that under a realistic device noise model, zero-noise extrapolation fails to recover absolute energies, though extrapolating the energy difference directly gives $18 \pm 3$ mHa, and concludes that the approach is practical for early fault-tolerant machines rather than today's noisy hardware.

What carries the argument

The object that carries the argument is the adaptive approximate quantum compiling (ADAPT-AQC) protocol applied to ADAPT-VQE target states built from a nuclear-electronic frozen natural orbital (NEO-FNO) operator pool. ADAPT-AQC is a variational compiler: it grows a new parameterized circuit $\hat{V}(\theta)$ from the vacuum by adding two-qubit unitaries on the qubit pair that most reduces the fidelity cost $C = 1 - |\langle \Psi_{\mathrm{ADAPT\text{-}VQE}} | \hat{V}(\theta)|0\rangle|^2$, where $\Psi_{\mathrm{ADAPT\text{-}VQE}}$ is the converged variational state it is approximating. The FNO truncation preceding it selects the active space — 6 protonic orbitals and 8 electronic orbitals per configuration, with 16 occupied orbitals frozen — by diagonalizing NEO-MP2 one-particle density matrices and keeping the highest-occupation eigenvectors, and this same truncated space defines the ground-truth FNO-NEO-CASCI reference. The division of labor is what carries the result: the FNO truncation keeps the simulation small, ADAPT-VQE supplies an accurate target, and ADAPT-AQC converts the deep target into hardware-scale circuits with controlled fidelity loss.

What would settle it

Recompute the malonaldehyde barrier with the FNO occupation-number cutoff relaxed, adding natural orbitals whose NEO-MP2 occupations lie just below the chosen threshold, or with a full NEO-CASCI in the untruncated virtual space, and compare against the 11.857 mHa reference; a shift of more than ~1 mHa would show the truncation is not converged and the 13% circuit-recovery figure measures internal consistency. Alternatively, execute the AQC-high circuits directly on the target hardware and measure the barrier, since the paper's noisy results are obtained from a model rather than the device.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that energy differences relevant to chemistry survive drastic circuit compression. Starting from ADAPT-VQE ansätze converged to within $10^{-2}$ Ha of the FNO-NEO-CASCI ground state, the ADAPT-AQC compiler produces 'high' fidelity circuits with two-qubit depths of 51 (Left) and 90 (Middle), reductions of 88% and 57% relative to the VQE-shallow circuits, and fidelities of 0.961 and 0.967 with respect to the reference wavefunction. Evaluating these compressed circuits without noise yields a barrier of 13.427 mHa, within approximately 13% of the 11.857 mHa FNO-NEO-CASCI value and in the interval between the semi-empirical and experimental estimates. Pushing compression further to 12 two-qubit layers for the Middle state makes the circuits executable on near-term hardware, but the barrier rises to 27.1 mHa, more than double the reference, which suppresses the computed rate constant by over two orders of magnitude at 120 K. The paper further shows that the compressed circuits reproduce the protonic density of the parent ansatz across all seven points of the transfer pathway, and that under the ibm_fez noise model with zero-noise extrapolation the 'difference first' barrier is $18 \pm 3$ mHa, placing the noiseless AQC-low value within $2\sigma$ of the error-mitigated estimate.

Load-bearing premise

The load-bearing premise is that the frozen-natural-orbital truncated active space — 6 protonic and 8 electronic orbitals per configuration, 16 frozen occupied orbitals — captures the proton-electron correlation that sets the barrier, because the ground-truth reference is computed in exactly that truncated space.

Editorial extensions

If this is right

  • AQC-high circuits (two-qubit depth 51 and 90) deliver a noiseless barrier of 13.4 mHa, within about 13% of the FNO-NEO-CASCI reference, showing that most of the circuit depth in an accurate ansatz can be discarded without destroying the chemistry.
  • The kinetic benchmark is stringent: to keep the rate-constant error under 20% at 120 K, the barrier must be accurate to roughly 0.08 mHa ($\approx$ 2 meV), a target the paper sets for quantum energy-estimation algorithms.
  • AQC-low circuits, with the Middle state compressed to 12 two-qubit layers, are the only ones small enough for current hardware, but their 27.1 mHa barrier suppresses the computed rate constant by more than two orders of magnitude at 120 K.
  • Under the ibm_fez noise model with zero-noise extrapolation, the 'difference first' protocol gives $18 \pm 3$ mHa, so error mitigation aimed directly at energy gaps performs better than mitigating each state separately.
  • The pipeline is modular and, the paper argues, transfers to the broader class of proton-coupled electron transfer problems where tunneling, delocalization, and zero-point motion set the kinetics.

Reading between the lines

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

  • The near-correct AQC-high barrier probably owes much to error cancellation: both compressed states sit tens of milli-Hartree above the CASCI energies in absolute terms, so the accurate 13.427 mHa barrier is a difference of two biased estimates rather than two individually accurate ones.
  • A direct test of that reading would be to run the same two-stage pipeline on molecules with exact or experimentally settled barriers of very different magnitudes and check whether the ~13% accuracy in energy differences is a general property of ADAPT-AQC or specific to malonaldehyde.
  • The 'difference first' ZNE result suggests a design principle for reaction kinetics on noisy hardware: fold gates and extrapolate on the barrier observable itself, since state-dependent noise bias partially cancels in the gap.
  • Scanning the FNO occupation-number cutoff would reveal whether the 11.857 mHa reference is converged; if the reference moves by more than about 1 mHa under that scan, the 13% recovery is internal consistency, not physical accuracy.
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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 develops a quantum-computing pipeline for proton-transfer kinetics in malonaldehyde within the nuclear-electronic orbital (NEO) framework. It combines ADAPT-VQE with a frozen natural orbital (FNO) truncated active space, compresses the resulting circuits with ADAPT-AQC, transpiles them for the ibm_fez device, and evaluates barriers and proton densities in noiseless and noisy (ZNE-mitigated) settings. The central quantitative claim is that AQC-high circuits reduce two-qubit depth substantially while keeping the noiseless barrier within about 13% of the FNO-NEO-CASCI reference: Table II reports AQC-high barriers of 13.427 mHa versus an 11.857 mHa CASCI barrier, with two-qubit depths 51 (Left) and 90 (Middle) compared with 411 and 211 for VQE-shallow. The paper also reports noisy ZNE barrier estimates of 24±12 mHa (fit-first) and 18±3 mHa (diff-first) and discusses the sensitivity of rate constants to barrier error.

Significance. If the central claim is correct, the paper provides a concrete demonstration that adaptive approximate quantum compiling can substantially reduce circuit depth for NEO-based proton-transfer simulations while preserving the truncated-space barrier estimate. The pipeline is clearly described, the resource tables are informative, and the use of a realistic device noise model with ZNE is a strength. The noiseless AQC-high result is benchmarked against an independent CASCI diagonalization in the same active space, and the 13% barrier agreement is a meaningful internal-consistency result. However, the physical accuracy of the barrier is not established by this agreement alone, because the FNO truncation that defines both the reference and the ansatz is not validated by a convergence study. Several quantitative statements in Section IV A are internally inconsistent with Table II and Eq. (6).

major comments (3)
  1. [§IV A, Eq. (6), Table II] The stated '60% underestimate' of the 120 K rate constant for AQC-high is not consistent with the paper's own data. With ΔE_AQC-high = 13.427 mHa and ΔE_CASCI = 11.857 mHa, the barrier error is δE = 1.57 mHa; at 120 K, k_B T ≈ 0.380 mHa, so Eq. (6) gives k_AQC-high/k_CASCI = exp(−1.57/0.380) ≈ 0.016, i.e., a ≈98% underestimate, not 60%. Even comparing to VQE-shallow (11.628 mHa) gives a ≈99% underestimate. In the same paragraph, 'within approximately 10%' conflicts with the actual relative error of 13.2% and with the abstract's 'within 13%'. These quantitative statements must be reconciled with Table II and Eq. (6).
  2. [§II B, §III B 1] The FNO truncation is load-bearing but unvalidated. The active spaces are fixed at 6 protonic orbitals and 3 HF + 5 FNO electronic orbitals with 16 frozen occupied orbitals, and the only justification given is that NEO-MP2 occupation numbers of discarded orbitals are small; no occupation numbers and no cutoff-convergence test are reported. Because FNO-NEO-CASCI and all quantum circuits live in this same truncated space, the AQC-high/CASCI agreement (13.427 vs 11.857 mHa) demonstrates that the compressed circuits approximate the truncated-space ground state, but it does not by itself establish that the truncation captures the physically relevant correlation. Please report the NEO-MP2 natural occupation spectra and show the CASCI barrier as a function of the number of retained FNOs (e.g., 0, 2, 5, 8) for at least the Left and Middle configurations.
  3. [§IV A, Table II] The fidelity statements do not match the reported table. Table II states that circuit fidelities are with respect to the FNO-NEO-CASCI wavefunction and lists AQC-high fidelities of 0.961 (Left) and 0.967 (Middle); the text says AQC-high circuits maintain 'fidelity 99%' and that AQC-low circuits have 'a minimum fidelity of 97% with respect to the VQE-shallow target.' Please state explicitly which reference state each fidelity number refers to, correct the 99% to the tabulated 96% if that is the intended value, and provide the fidelity-to-target values for the AQC-low circuits if they are being claimed.
minor comments (5)
  1. [Eq. (6), Fig. 3] Eq. (6) gives only a proportionality k(T) ∝ exp(−ΔE/k_B T), but Fig. 3 (right) plots absolute rate constants with units of s^-1. A pre-exponential factor must be specified (or the vertical axis relabeled as relative) for the plotted values and for statements such as '60% underestimate' to be well-defined.
  2. [§IV C, Table II] The text says the noiseless AQC-low result is placed '2σ away' from the diff-first ZNE zero-noise limit, but the quoted numbers give 27.140 − 18 = 9.14 mHa, which is about 3σ with the reported ±3 mHa uncertainty. Please verify whether the comparison uses the standard-error or bootstrap uncertainty and correct the σ statement.
  3. [§II B] The sentence 'we benchmark the combined effect combined methodological improvements' contains a duplicated word and should be rewritten.
  4. [Appendix D] The label 'Energy Diifference' in Fig. 9 is a typo and should read 'Energy difference'.
  5. [General] The paper does not include a data-availability statement or a link to the code used for the NEO-FNO and ADAPT-VQE calculations; adding a repository link or explicit statement that code is available on request would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the AQC barrier comes from a variational energy evaluation benchmarked against an independent CASCI diagonalization, and the self-citations are method attributions rather than load-bearing premises.

full rationale

The load-bearing numerical claim is that AQC-high circuits reduce two-qubit depth (e.g., Left 51 vs 411 for VQE-shallow) while giving a barrier of 13.427 mHa against the FNO-NEO-CASCI value of 11.857 mHa. These are distinct calculations: FNO-NEO-CASCI is an exact diagonalization of the truncated active-space Hamiltonian, while ADAPT-VQE minimizes the energy expectation with an incremental operator pool and ADAPT-AQC optimizes a compiled circuit against the ADAPT-VQE target through the fidelity cost C = 1 - |⟨Ψ_ADAPT-VQE|V(θ)|0⟩/N_n|^2. The resulting circuit energy is then evaluated, not set equal to the reference, and the variational parameters are not fitted to the barrier. The shared FNO truncation (6 protonic orbitals; 3 NEO-HF + 5 FNO electronic orbitals per setup) means the 13% agreement tests accuracy within the chosen model rather than validating the model against experiment; that is a modeling-assumption and correctness concern, not a circular reduction, because neither quantity is defined in terms of the other. Self-citations [26], [28], and [36] are used to attribute prior NEO dynamics, the NEO-ADAPT-VQE method, and the ADAPT-AQC compiling algorithm, respectively; none is invoked as an external uniqueness theorem or as evidence for the barrier. The paper's own caveats (ZNE does not recover absolute energies; the ZNE agreement 'may be partly coincidental') further show that the noiseless benchmarking, not a self-referential fit, carries the claim.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The pipeline rests on a set of domain assumptions inherited from NEO, FNO, ADAPT-VQE, ADAPT-AQC, and ZNE. No new particles or mediators are introduced. The main burden is that the truncated active space serves as its own reference, and the noise and extrapolation choices are user-selected; these assumptions should be tested against larger active spaces and real hardware.

free parameters (6)
  • ADAPT-VQE convergence thresholds = 10^-3 Ha (deep), 10^-2 Ha (shallow)
    Chosen to balance circuit depth and energy accuracy; not derived from the physics.
  • ADAPT-AQC compression settings = high and low fidelity targets, numeric values not reported
    The two compression levels are user-selected and directly determine circuit depth and barrier error.
  • ZNE polynomial degree = degree 2 (fit first), degree 1 (diff first)
    Selected by hold-out RMSE on the same noisy data, so the extrapolation model is fit to the measurements.
  • Active-space truncation = 16 frozen occupied electronic orbitals; 3 HF + 5 FNO electronic orbitals; 6 protonic orbitals
    Truncation chosen via FNO occupation numbers; the CASCI reference is exact only within this truncated space.
  • Noise model snapshot = ibm_fez calibration 2024-11-10 10:40:31 UTC, EPLG 0.003108
    The lowest-EPLG calibration among the sampled noise models was selected as representative, a favorable choice for feasibility.
  • ZNE sampling parameters = lambda in [1,4], 100 randomized foldings, 1000 shots per circuit
    Sampling and extrapolation parameters chosen by the authors; they affect the error bars and zero-noise estimates.
assumptions (7)
  • standard math Second-quantized fermionic operators obey normal anticommutation relations and the TDSE governs the coupled proton-electron system.
    Section II A: used without proof; standard quantum mechanics.
  • domain assumption NEO framework: selected proton treated quantum mechanically via multicomponent wavefunction, while scaffold nuclei are classical point charges under Born-Oppenheimer.
    Section II B, first step; if the classical scaffold assumption fails, the Hamiltonian is wrong.
  • domain assumption Adiabatic approximation: ground state of each instantaneous interpolated Hamiltonian H(t) captures proton transfer; non-adiabatic effects are neglected.
    Section II A: authors explicitly limit to the adiabatic regime; rate and densities rely on it.
  • domain assumption Frozen natural orbital truncation discards orbitals with small NEO-MP2 occupation numbers without significant accuracy loss.
    Section III B 1: this truncation defines both the reference and the circuit ansatz.
  • domain assumption Linear interpolation H(t)=alpha H_Left + beta H_Middle + gamma H_Right with seven points represents the adiabatic proton transfer pathway.
    Section II B, Eq. (5); the pathway and densities depend on this construction.
  • domain assumption Transition state theory expression Eq. (6) with effective quantum barrier is adequate for rate constants; thermal and entropic contributions are negligible.
    Section II C; used to translate barrier errors into rate-constant errors.
  • domain assumption The ibm_fez noise model (depolarizing, thermal relaxation, readout errors) and ZNE polynomial extrapolation recover the zero-noise limit.
    Section III D and Appendix D; no real hardware execution is performed.

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Cite this review

Pith. "Pith review of Approximate quantum circuit compilation for proton-transfer kinetics on quantum processors." pith.science (2026). https://pith.science/paper/NFGTD67R

@misc{pith2026250708996,
  author       = {Pith},
  title        = {Pith review of: Approximate quantum circuit compilation for proton-transfer kinetics on quantum processors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NFGTD67R}},
  note         = {Machine review of arXiv:2507.08996}
}
read the original abstract

Proton transfer reactions are fundamental to many chemical and biological systems, where quantum effects such as tunneling, delocalization, and zero-point motion play key kinetic control roles. However, classical methods capable of accurately capturing these phenomena scale prohibitively with system size. Here, we develop and demonstrate quantum computing algorithms based on the Nuclear-Electronic Orbital framework, treating the transferring proton quantum mechanically. We assess the potential of current quantum devices for simulating proton transfer kinetics with high accuracy. We first construct a deep initial ans\"atze within a truncated orbital space by employing the frozen natural orbital approximation. Then, to balance circuit depth against state fidelity, we implement an adaptive form of approximate quantum compiling. Using resulting circuits at varying compression levels transpiled for the ibm_fez device, we compute barrier heights and delocalised proton densities along the proton transfer pathway using a realistic hardware noise model. We find that, although current quantum hardware introduces significant noise relative to the demanding energy tolerances involved, our approach allows substantial circuit simplification while maintaining energy barrier estimates within 13% of the reference value. Despite present hardware limitations, these results offer a practical means of approximating key circuit segments in near-term devices and early fault-tolerant quantum computing systems.

Figures

Figures reproduced from arXiv: 2507.08996 by the authors.

Figure 1
Figure 1. FIG. 1. Proton density distribution for [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic of our multi-stage proton-transfer simulation workflow. We begin with the high-precision FNO-NEO-CASCI [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Proton density distributions obtained using the CASCI, VQE-shallow, and AQC-low methods. Each subplot [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Zero-noise extrapolation (ZNE) results for energy expectation values and proton transfer barrier heights across rep [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Energy profiles and relative barrier heights for the Left, Middle, Right and intermediate states of proton transfer in [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Error map of the [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. RMSE as a function of polynomial degree (left panel) and optimal fit to data (right panel) for the energies of the left [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. RMSE as a function of polynomial degree (left panel) and optimal fit to data (right panel) for the difference in energies [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Empirical bootstrap distributions for the intercept for the ‘Fit first’ (left panel) and ‘Diff first’ (right panel) extrapo [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

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Pith tools

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