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REVIEW 4 major objections 4 minor 49 references

Simulating methylamine using symmetry adapted qubit-excitation-based variational quantum eigensolver

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Combining symmetry filtering with qubit-excitation circuits cuts the two-qubit gate budget for a methylamine VQE from roughly 600,000 to about 12,000 on 26 qubits.

desk verdict Useful resource data and an honest negative result, but the headline number is the wrong column of Table II and the full 26-qubit claim is an extrapolation, not a demonstrated simulation. read the letter →

arxiv 2501.17035 v3 pith:6H6WKRC3 submitted 2025-01-28 quant-ph

Konstantin M. Makushin , Aleksey K. Fedorov This is my paper · ORCID
classification quant-ph
keywords variationalquantumeigensolvermethylamineformicacidqubit-excitationcircuitssymmetryadaptationqubittaperingunitarycoupledclusterresourceestimation
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 four known VQE optimizations can be combined without losing chemical accuracy: filtering excitation operators by molecular point-group symmetry, replacing Pauli exponentials with compact qubit-excitation circuits, truncating the active space, and tapering away symmetry-redundant qubits. Applied to methylamine in the STO-3G basis, the best combination is said to cut the estimated two-qubit operations from about 600,000 for a naive UCCSD ansatz to roughly 12,000 on 26 qubits, a reduction of nearly two orders of magnitude. The claim is backed by noiseless simulations of LiH and BeH2, where the symmetry-filtered qubit-excitation ansatz (UCCSDQs) converges to FCI energy within chemical accuracy, and by a methylamine (6e,6o) active-space calculation that reaches the same accuracy. The authors then estimate that full active-space methylamine and formic acid simulations would need on the order of 10,000-15,000 two-qubit gates, a range that matters because two-qubit gate count is the dominant error bottleneck on near-term quantum hardware.

What carries the argument

The carrying object is the qubit-excitation circuit, a compact implementation of an excitation operator that uses a fixed, small number of CNOT gates by omitting the Pauli-Z strings that enforce fermionic anticommutation, combined with irreducible-representation filtering, which discards every excitation whose symmetry label differs from the Hartree-Fock state. Qubit tapering then removes qubits acting as conserved Z2 symmetries, and active-space truncation reduces the orbital count. The large-molecule estimates all flow through Eqs. (10)-(11), which multiply the numbers of single and double excitations by per-excitation gate-count coefficients supplied by the authors' in-house quantum chemistry library.

What would settle it

Recompile the UCCSDQs ansatz for full-active-space methylamine with any publicly available optimal qubit-excitation circuit decomposition and count the CNOTs; if the count is far from the paper's 4,130 or 12,000 figure, the reduction claim needs revision. Independently, run a noiseless VQE with UCCSDQs on the full methylamine active space and check whether the converged energy lands within 1.6 mHartree of the FCI energy.

Watch

Extended reading notes

Core claim

The central discovery is that a UCCSD ansatz built from qubit-excitation circuits and restricted to terms that preserve the irreducible-representation symmetry of the Hartree-Fock reference (UCCSDQs) can reproduce the correlation energy of small molecules with dramatically fewer gates than a naive implementation. For methylamine the authors estimate a reduction from roughly 600,000 to about 12,000 two-qubit operations using 26 qubits in the STO-3G basis, with circuit depth reduced by a similar factor. Converged noiseless VQE runs on LiH, BeH2, and methylamine in a (6e,6o) active space stay within chemical accuracy, which is the evidence that the gate savings do not come at the cost of the physics. For full active spaces the paper provides resource estimates, not converged energies, and it reports that the alternative k-UpGSDQ ansatz, though even cheaper, fails to converge for formic acid.

Load-bearing premise

The load-bearing premise is that the per-excitation gate-count coefficients underlying Table II are correct and representative, and that the qubit-excitation ansatz that converges on the (6e,6o) methylamine active space will also converge on the full active space; the formic acid result shows the same ansatz can fail on a comparable molecule.

Editorial extensions

If this is right

  • A 26-qubit STO-3G methylamine VQE calculation drops from roughly 600,000 to about 12,000 two-qubit operations, bringing it closer to the error budget of current high-fidelity devices.
  • Full active-space resource estimates for methylamine and formic acid fall near 10,000-15,000 two-qubit gates, with circuit depth reduced by nearly two orders of magnitude.
  • The UCCSDQs ansatz reaches chemical accuracy in noiseless simulations of LiH, BeH2, and the methylamine (6e,6o) active space, showing symmetry-filtered qubit excitations can retain the correlation energy.
  • Combining UCCSDQs with qubit tapering is identified as a further possible reduction, but the paper leaves it open because the interplay between Z2 symmetries and excitation circuit representations needs more analysis.
  • The cheaper k-UpGSDQ ansatz does not converge for formic acid, so the optimal strategy depends on the correlation structure of the target molecule.

Reading between the lines

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

  • An attentive reader will notice that the abstract's 'approximately 12,000' matches Table II's total-gate column, whereas the table's two-qubit column for the same ansatz is 4,130; the paper never reconciles the two presentations.
  • If the gate counts survive independent compilation, a small organic molecule's ground-state VQE enters the regime of few-dozen-qubit experiments, though error mitigation and measurement overhead would still apply.
  • The formic acid failure suggests a testable pattern: qubit-excitation circuits may lose accuracy exactly when static correlation is strong, so a practical recipe would switch to fermionic excitation circuits above some correlation-strength threshold.
  • Because the estimates depend on a proprietary library, a natural next step is a public benchmark that compiles the same excitation lists with published CNOT-optimal circuits and checks whether the two-orders-of-magnitude savings persist.
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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

4 major / 4 minor

Summary. The paper proposes combining symmetry-adapted excitation filtering, qubit-excitation-based ansatze, restricted excitation sets, and qubit tapering to reduce the quantum resources required for VQE simulations of small molecules. The authors validate the combined strategies on LiH and BeH2, reporting convergence to FCI reference energies, and on a (6e,6o) active-space model of methylamine on 12 qubits. They then present resource estimates in Table II for full-active-space methylamine and formic acid, claiming a reduction from roughly 600,000 to roughly 12,000 operations on 26 qubits for methylamine using a UCCSDQs ansatz.

Significance. If the central resource-reduction claim were stated correctly and supported by reproducible data, the paper would be a useful contribution to near-term VQE practice: it tests a concrete combination of optimization techniques on nontrivial molecules, benchmarks against independent FCI references, and provides resource tables for chemically interesting organic molecules. The LiH/BeH2 and methylamine active-space calculations are genuine and non-circular validations of convergence behavior. However, the headline claim is weakened by an internal inconsistency between the abstract and Table II, by the absence of a full-active-space convergence demonstration, and by reliance on undisclosed per-excitation gate-count coefficients from an in-house library. These issues affect the central quantitative claim and need to be resolved before the paper can be accepted.

major comments (4)
  1. [Abstract / Table II] The central resource-reduction claim conflates two-qubit gates with total gates and uses a baseline that does not match the table. The abstract states that the number of two-qubit operations is reduced from about 600,000 to about 12,000 on 26 qubits. In Table II, the methylamine UCCSD row (with tapering) lists 457,800 two-qubit gates and 631,022 total gates on 23 qubits, while the UCCSDQs row lists 4,130 two-qubit gates and 11,558 total gates on 26 qubits. The '600,000' figure is close to the UCCSD total gate count, and the '12,000' figure matches the UCCSDQs total gate count, not its two-qubit count. The Introduction's statement of 'around 10,000–15,000 two-qubit gates' is similarly inconsistent with Table II. Please correct the metric used in the abstract and Introduction, recompute the reduction factor accordingly, and state the baseline and optimized counts consistently (two-qubit vs total gates).
  2. [Sec. IV (methylamine and formic acid discussion)] The full-active-space resource estimate is not backed by a converged VQE calculation. The only methylamine VQE calculation shown is the (6e,6o) 12-qubit active space (Fig. 4). The 26-qubit UCCSDQs row in Table II is an estimate from Eqs. (10)-(11), not a demonstrated energy convergence. The paper itself reports in Sec. IV that qubit-excitation circuits 'do not show good convergence' for formic acid, and Sec. III explicitly notes that qubit excitations ignore fermionic anticommutation by excluding Pauli-Z products. Thus, the abstract's phrasing that the method reduces operations 'for simulating the methylamine molecule' overstates what is established. Please either present the full-active-space numbers as conditional resource estimates that require validation of convergence, or provide evidence that UCCSDQs converges on the full active space.
  3. [Eqs. (10)-(11) and Table II] The gate-count and depth estimates depend on the per-excitation coefficients alpha_S, alpha_D, beta_S, beta_D, gamma_S, gamma_D, which are introduced as average values but never given numerically. They also rely on the undisclosed in-house library of Ref. [47]. Without either the numerical values of these coefficients or a description/implementation of the circuit constructions, Table II cannot be independently checked. Please provide the coefficient values used for each qubit count (23/26 and 25/28), or make the circuit-construction code publicly available.
  4. [Table II] The resource comparison in Table II is not apples-to-apples because the ansatz and tapering choices are confounded: UCCSD and k-UpGSD are reported with qubit tapering (23 and 25 qubits), whereas UCCSDQs and k-UpGSDQ are reported without tapering (26 and 28 qubits). The claimed reduction factor therefore mixes the effect of the ansatz change with the effect of tapering. Please report the comparisons in a consistent setting (e.g., all ansatze with tapering, or all without tapering) or discuss how this inconsistency affects the advertised reduction.
minor comments (4)
  1. [Fig. 4 caption and Sec. IV text] The caption and text refer to 'UCCSQs', which should be 'UCCSDQs'.
  2. [Eq. (12)] The phrase 'irreducible irreducible representation' is a typo, and the condition is written informally; please rephrase it more precisely.
  3. [Reference [36]] Reference [36] gives only 'arXiv (2017), arXiv: Quantum Physics'; please provide the complete bibliographic information for the qubit-tapering result so readers can locate the method.
  4. [Sec. IV and Table II] The table states that k-UpGSD and k-UpGSDQ estimates use k=1, yet the text reports that k=4 repetitions were needed for convergence in BeH2. Please state explicitly how the k=1 assumption affects the methylamine and formic acid resource estimates and whether higher k would alter the advertised reduction factor.

Circularity Check

1 steps flagged · score 4.0 of 10

Resource-reduction headline depends on self-cited in-house library coefficients; energy benchmarks are independent.

  1. self citation load bearing [Section III (resource estimates), Eqs. (10)-(11) and Table II, with coefficients from Ref. [47]]
    "In all estimates, we use qubit-wise grouping of Pauli strings and an in-house quantum chemistry library specifically developed for the efficient implementation of variational quantum algorithms. [47]. ... The coefficients from Eqs. (10) and (11) depend on the actual definition of excitation sub-circuits in the ansatz, the fermionic transformation used, and the number of qubits."

    The headline reduction to approximately 12,000 two-qubit gates for methylamine is obtained by evaluating Eq. (10), N2-qubit = beta_S N_S + beta_D N_D, with the per-excitation gate coefficients beta_S, beta_D and the circuit model taken from Ref. [47], written by the present authors. The coefficient values are not given and no independent derivation is supplied, so the resource estimate is not a standalone prediction: it is the self-cited in-house library's gate-count model applied to the paper's excitation counts. The energy-convergence claims are benchmarked to FCI and are not affected, which is why this is partial rather than total circularity.

full rationale

The derivation chain for the convergence claims is self-contained: LiH, BeH2, and the (6e,6o) methylamine active-space VQE runs are compared to exact FCI energies, an external reference, so 'chemical accuracy' is not defined in terms of the ansatz or the optimization. The active-space choice in Fig. 3 is a classical scan, not a fit of VQE parameters, and the subsequent VQE result is checked against FCI. The only load-bearing step that reduces to the authors' own prior work is the gate-count model: the ~12,000 two-qubit number in the abstract is Eq. (10) evaluated with beta coefficients from the in-house library of Ref. [47] (authors overlap with this paper), with no coefficient values or independent reproduction provided. That makes the resource-reduction claim dependent on a self-citation, but not definitionally circular; if the library constants were disclosed and independently validated, it would be ordinary arithmetic. Hence score 4 rather than 0 or 6.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The resource estimates in Table II depend on undisclosed gate-count coefficients and a hand-picked active space, while the convergence claims depend on assumptions about ansatz expressibility and Trotter error that are only partly tested. These are the main hidden supports for the paper's quantitative conclusions.

free parameters (3)
  • Per-excitation gate-count coefficients (alpha_S, alpha_D, beta_S, beta_D, gamma_S, gamma_D) = not disclosed (in-house library [47])
    Eqs. (10)-(11) scale gate counts and circuit depth by these coefficients; the values come from an unpublished in-house library, so the central resource numbers in Table II rest on undisclosed constants.
  • Ansatz repetition count k = 1 for methylamine/formic acid estimates, 4 for BeH2
    The k-UpGSD variants use k repetitions; BeH2 required k=4 to converge, and Table II estimates use k=1. The choice changes circuit depth and gate counts.
  • Methylamine active space size = 6 electrons, 6 spin orbitals
    The (6e,6o) active space was selected based on the scan in Fig. 3; chemical accuracy is achieved only for that choice, making it a hand-picked modeling decision.
assumptions (6)
  • domain assumption Second-quantized molecular Hamiltonian under the Born-Oppenheimer approximation with the STO-3G basis set.
    Sec. II Eq. (4); the entire simulation is performed in this representation and basis.
  • domain assumption Frozen core approximation removes inner 1s orbitals without significantly changing the energies used.
    Sec. III 'frozen core approximation'; used to reduce qubit counts for methylamine and formic acid.
  • standard math Qubit tapering via Z2 symmetries preserves the spectrum of the Hamiltonian.
    Sec. III, Eq. (8) and surrounding text; relies on the known result from Bravyi et al. [36].
  • domain assumption Symmetry filtering in Eq. (12) keeps only excitations that preserve the irreducible representation of the Hartree-Fock reference.
    Sec. III, Eq. (12); if the reference has degenerate or broken symmetry, this filtering could discard relevant excitations.
  • domain assumption First-order Suzuki-Trotter decomposition of the UCC ansatz has negligible error for the reported energies.
    Sec. III 'employing the first-order Suzuki-Trotter decomposition'; the resource counts assume this decomposition, but Trotter error is not quantified.
  • ad hoc to paper Qubit-excitation operators, which exclude Pauli-Z products and ignore fermionic anticommutation, can recover the correlation energy.
    Sec. III states it remains unclear whether qubit excitations can adequately account for correlation; the paper's formic acid result shows this assumption fails for at least one molecule.

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Pith. "Pith review of Simulating methylamine using symmetry adapted qubit-excitation-based variational quantum eigensolver." pith.science (2026). https://pith.science/paper/6H6WKRC3

@misc{pith2026250117035,
  author       = {Pith},
  title        = {Pith review of: Simulating methylamine using symmetry adapted qubit-excitation-based variational quantum eigensolver},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6H6WKRC3}},
  note         = {Machine review of arXiv:2501.17035}
}
read the original abstract

In this work, we propose and analyze optimization strategies for the VQE algorithm that combine various methods, including molecular point group symmetries (symmetry adaptation), compact excitation circuits (qubit-excitation-based), different types of excitation sets, and qubit tapering. These strategies allow for a significant reduction in computational requirements while ensuring convergence to the correct energies. First, we apply these combinations to small molecules, such as LiH and BeH2, to evaluate their compatibility, accuracy, and potential applicability to larger problems. We then simulate the methylamine molecule within its restricted active space using the best-performing optimization strategies. Finally, we complete our analysis by estimating the resources required for full active-space simulations of the methylamine and formic acid molecules. Our best-performing optimization strategy reduces the number of two-qubit operations for simulating the methylamine molecule from 600,000 (in the STO-3G basis with a naive Unitary Coupled Cluster ansatz) to approximately 12,000, using 26 qubits. Thus, the proposed combination of optimization methods can reduce the number of two-qubit operations by nearly two orders of magnitude. Although, we present alternative approaches that are of interest in the context of the further optimization in the number of two-qubit operation, we note that these approaches do not perform well enough in terms of the convergence to required energies. While these challenges persist, our resource analysis represents a valuable step towards the practical use of quantum computers and the development of better methods for optimizing computing resources.

Figures

Figures reproduced from arXiv: 2501.17035 by the authors.

Figure 1
Figure 1. VQE calculation for the LiH molecule using various [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. VQE calculation for the BeH2 molecule using var￾ious types of ansatzes and optimization methods. The plot compares the convergence of energy values with the FCI en￾ergy as a reference and indicates the chemical accuracy thresh￾old, Ncx represents the number of two-qubit gates. ing them up to larger molecules is a whole different chal￾lenge. Indeed, as shown in Table II, which gives resource estimates for more comple… view at source ↗
Figure 3
Figure 3. The ground-state energy for different active spaces [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: VQE calculation for the CH3NH2 molecule in (6e, 6o) active space using UCCSDQ and UCCSQs ansatzes. The plot compares the convergence of energy values with the FCI en ergy as a reference and indicates the chemical accuracy threshold, Ncx represents the number of two-qub…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.