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REVIEW 4 major objections 4 minor 65 references

Learning to Prepare Molecular Ground States with Transformer Models

T0 review · 4 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read A transformer trained on ADAPT-VQE reference circuits can generate molecule-specific ground-state preparation circuits in one forward pass, cutting circuit generation time by up to four orders of magnitude while matching or beating the refe

desk verdict A genuine, honestly-reported proof-of-concept for amortized circuit synthesis, but the abstract overclaims accuracy and the headline speedup numbers omit the dominant offline data-generation cost. read the letter →

arxiv 2607.22468 v1 pith:GQXUJO4M submitted 2026-07-24 quant-ph cs.AI

Alex Koziell-Pipe , Jasmine Brewer , Jem Guhit , Marwa H. Farag , Kripa Panchagnula , Gabriel Laude , Fabian Finger , Carlo Gaggioli
show 9 more authors
Ludmila Szulakowska Oliver J. Backhouse Christos Papalitsas Jason G. Mustakis Thomas Soini David Munoz Ramo Stephen Clark Elica Kyoseva Enrico Rinaldi
This is my paper
classification quant-phcs.AI
keywords quantumstatepreparationADAPT-VQEgenerativetransformerreinforcementlearningchemistrycircuitsynthesismolecularconformersground-stateenergy
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 sets out to show that ground-state preparation circuits for a molecular Hamiltonian are learnable structure rather than the output of an expensive per-geometry search. Its pipeline, ADAPT-GQE, first generates thousands of reference circuits with the iterative algorithm ADAPT-VQE, trains a transformer to reproduce those circuits as token sequences, and then fine-tunes the small model with reinforcement learning, scoring its own proposed circuits by energy. The central claim: after post-training, the model's circuits beat the accuracy of the reference data, and end-to-end circuit generation plus energy evaluation is 930–8,800 times faster than running ADAPT-VQE on the 12-to-16-qubit systems tested (14–86 times for the larger pretrained model). If true, the variational search is amortized: once the offline data is paid for, hundreds of conformers of the same molecule can be served in seconds each. The paper further claims the generated circuits compile down to a few hundred two-qubit gates and run on current trapped-ion hardware, with noiseless energies close to reference.

What carries the argument

The load-bearing object is the transformer used as a sequence model over operator-coefficient pairs, conditioned on molecular structure through a vector of canonically ordered Hamiltonian coefficients injected as a multimodal token. The training pipeline has two phases: pretraining by next-token prediction on ADAPT-VQE circuits, then post-training in which the model proposes 16 candidate circuits, scores them with an energy reward, and is updated with group-relative policy optimization and self-distillation on its own best-scoring sequences. This mechanism converts circuit synthesis from iterative variational search into amortized sequence generation, and it is the reason the paper can claim

What would settle it

Measure total wall-clock cost for a previously unseen molecule, including ADAPT-VQE data generation (13,000–15,700 reference circuits), model training, and inference for the same number of conformers, and compare with ADAPT-VQE run from scratch; the amortization claim fails if the fixed cost dominates. A second check: evaluate generated circuits on a strictly structure-disjoint conformer test set, as the paper's out-of-distribution split does, and ask whether the accuracy gain over the random-split numbers survives; panel (a) of Figure 9 shows noticeable degradation on the out-of-distribution

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that a generative transformer conditioned on the molecular Hamiltonian can synthesize complete ADAPT-VQE-quality circuits in one autoregressive pass, and that reinforcement learning on an energy reward lets the small model exceed its training labels: median errors fall to 2.53 and 3.61 milliHartrees on the two 12-qubit benchmarks versus ADAPT-VQE convergence tolerances of 5 and 10 mHa. The speedup, defined as ADAPT-VQE wall time divided by generation plus evaluation time, is 930–8,800× for the small model and 14–86× for the large pretrained model on the same 12-, 14-, and 16-qubit conformer, and the advantage widens with system size because ADAPT-VQ

Load-bearing premise

The reported 930–8,800× speedup counts only inference and evaluation time and assumes the cost of producing and training on thousands of ADAPT-VQE reference circuits is amortized over a large number of conformers of the same molecule; if the offline investment must be re-paid molecule-by-molecule, the practical advantage narrows or disappears.

Editorial extensions

If this is right

  • For a molecule whose conformers will be sampled many times—common in drug-stability screening—the per-conformer cost of state preparation drops from hours of variational iteration to seconds of model inference, making the quantum part of the workflow affordable.
  • Because post-training optimizes energy rather than imitation, generated circuits can be more accurate than the ADAPT-VQE circuits used for training, so the approach is not permanently capped by the training tolerance.
  • The strong pretraining degradation on long operator sequences—and its removal after reinforcement learning—shows that long-sequence generation, not fundamental expressivity, is the current bottleneck to generalizing the method to deeper circuits.
  • Best-of-16 sampling plus symmetry-verified measurement gives noiseless energies within about a milliHartree of the reference on the hardware-executed example, suggesting that modest sampling overhead buys much of the accuracy.
  • The scaling of the speedup with system size implies the advantage should grow further if the same architecture extends to larger active spaces.

Reading between the lines

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

  • If the amortization story holds, the economic sweet spot is many-conformer, single-molecule workflows; for one-off calculations the headline speedup overstates the gain because the offline data generation and training are excluded.
  • The relative failure of geometric embeddings compared to Hamiltonian coefficients hints that the model is learning operator-selection rules tied to the energy landscape rather than to three-dimensional structure; testing on a second molecule would reveal which representation carries the transferable knowledge.
  • A natural stress test is cross-molecule transfer with the no-reference-energy reward variant; the paper's appendix shows it is nearly as good, so scaling to active spaces without expensive reference energies looks plausible.
  • If long-sequence errors are the core barrier, replacing the sparse terminal reward with per-operator reward models or tree search over operator choices is a concrete next step with testable accuracy gains.
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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 introduces ADAPT-GQE, a generative-AI framework in which transformer language models are trained to produce ADAPT-VQE-style ground-state preparation circuits for molecular conformers. Two models are considered: a 325M-parameter Gemma model trained from scratch and a 12B Nemotron model adapted by continual pretraining and supervised fine-tuning. Using imipramine as a test case with 12-, 14-, and 16-qubit active spaces, the authors report that pretrained models match ADAPT-VQE quality on easier datasets, while GRPO-based reinforcement learning plus self-distillation improves the Gemma model's accuracy beyond the ADAPT-VQE training-data tolerance on most datasets. The paper claims 14-8,800x speedups over ADAPT-VQE, defined in Table 13 as T_ADAPT-VQE/(T_generation + T_evaluation), and demonstrates execution of generated circuits on Quantinuum Helios-1 hardware.

Significance. The work is significant if the speedup claim survives full accounting. The energy targets (CASCI/CCSD) are genuinely external, and the RL improvement over ADAPT-VQE training data is not circular. The authors report failures honestly: out-of-distribution degradation (Fig. 9), poor MACE-based encodings (Fig. 10), and large hardware errors (Table 1). The main concern is that the headline computational-advantage claim excludes offline data generation and training costs, making the end-to-end speedup unverifiable. If a total-cost analysis is added and claims tempered, the framework would be a useful amortization of variational circuit search for conformer ensembles.

major comments (4)
  1. [§4.2, Table 13] The speedup is defined as T_ADAPT-VQE/(T_generation + T_evaluation), which excludes the offline ADAPT-VQE data-generation (13,000-15,700 circuits per dataset, Table 2) and model training (CPT/SFT/RL). The abstract claims order-of-magnitude reductions for the 'pipeline', and §4.2 calls this 'end-to-end speedup'. As written, the comparison is not end-to-end. Please add a total-cost-to-serve accounting: data-generation GPU-hours using per-conformer ADAPT-VQE times in Table 13, training compute, and inference; then state the break-even number of downstream conformers. Without this, the headline speedup is not evaluable.
  2. [§4.2, Discussion] The text states that 'Applied at the scale of hundreds of conformers per molecule, this translates to a reduction in total dataset generation time from weeks to minutes.' Using Table 2 and Table 13, generating the 12q ε=5 mHa dataset costs ~14,332 × 2,333 s ≈ 9,300 GPU-hours; for 16q it is ~15,498 × 23,404 s ≈ 100,800 GPU-hours. At Gemma inference of ~2-4 s per conformer, break-even is on the order of thousands to tens of thousands of conformers, far beyond 'hundreds.' Please provide a realistic amortization scenario or revise the claim.
  3. [§4.1 / Appendix A.1.1] Main-text accuracy results use a random 80/18/2 split (Section 4.1) that the authors concede can leak near-duplicate MD conformers into the test set (Appendix A.1.1). The stricter out-of-distribution split in Fig. 9 shows noticeably degraded accuracy. Because the central contribution includes conformer generalization, the main-text accuracy claims should either use the OoD split or include a clear leakage diagnostic quantifying similarity between training and test conformers.
  4. [§4.1.4, Table 10] The text states that after post-training 'the fraction of high-quality circuits saturates near 100% across all datasets.' Table 10 reports fractions of only 17.2% for 14q ε=5 mHa and 22.2% for 16q ε=15 mHa. This contradicts the claim and overstates the benefit of RL on the harder datasets. Please correct the sentence and temper the claim.
minor comments (4)
  1. [Abstract / §4.2] The abstract says 'order-of-magnitude reductions in circuit generation time' without specifying that this is inference-only. Consider adding 'after amortization' or 'per-conformer inference' for precision.
  2. [§4.2] The Discussion states '1k- to 8k-fold speedups' but Table 13 lists 929.5x as the lowest Gemma speedup; '930-8,800x' is more accurate. Adjust the text to match the table.
  3. [Table 7] The 'Epochs' row for 12 qubits lists '[2,3,4]' while 14 and 16 qubits list '2' and '2'; clarify whether these are per-stage values and format consistently.
  4. [References] Reference [26] lists 'Team, G.' as the first author; use the standard 'Gemma Team' citation format. Also ensure reference [51] includes the full author list or a consistent abbreviation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; central accuracy claims are benchmarked against external CASCI/CCSD references and genuine out-of-distribution splits.

full rationale

The derivation chain is: (1) ADAPT-VQE generates reference circuits at a stated tolerance relative to external CASCI/CCSD energies; (2) transformers are trained by next-token prediction to imitate those circuits; (3) RL optimizes a reward (Eq. 1) that depends on E_HF, E_ref (CASCI/CCSD), and E_circuit, not on any ADAPT-VQE label; (4) generated circuits are evaluated by statevector energy against the same external references. Each stage is empirically measured rather than forced by construction: the model is not defined to output the ADAPT-VQE circuit, and the RL target is an external energy, so 'beyond ADAPT-VQE' is a real optimization claim. The '1 mHa relative to ADAPT-VQE' imitation metric is transparently a fit-quality metric, not an independent prediction, and is supplemented by E-E_CASCI values. The speedup definition (Table 13: T_ADAPT-VQE/(Tgen+Teval)) excludes offline data generation and training; this is a cost-attribution and amortization limitation, acknowledged in the Discussion ('reduced reliance on the (expensive) training data'), but it does not make the speedup equivalent to an input by construction. Self-citations (PMSV, InQuanto, Helios) are tool/hardware references, not load-bearing mathematical premises. No uniqueness theorem, ansatz-smuggling citation, or renamed empirical law was found.

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

The method introduces no new physics, so the ledger is about comparison choices and engineering hyperparameters. The two items that matter most are the excluded offline data-generation cost (the true price of the speedup) and the leakage-prone random split underneath the headline accuracy numbers. The reference energies and operator pools are honest, external anchors; the RL is not fitting to a self-authored target.

free parameters (6)
  • ADAPT-VQE energy convergence tolerance ε per dataset = 5/10 mHa (12q), 5/16 mHa (14q), 15 mHa (16q)
    Section 3.1. Chosen by hand per dataset; defines the training-data quality ceiling and the yardstick for 'beyond ADAPT-VQE' claims.
  • Reward clip R_max in Eq. 1 = 30
    Section 3.2.3. Cap on the RL reward designed to stabilize training against rare very-low-energy circuits.
  • GRPO KL penalty β = 0.28
    Table 7. Conservatism hyperparameter on policy updates; chosen by hand.
  • Distillation selection thresholds and top-k per RL stage = e.g. [5,3.4,1.6]e-3 with top-n [8,4,2] for 12q
    Table 7. Hand-set energy thresholds and counts that filter model-generated sequences for self-distillation; tightened each round.
  • Best-of-16 candidate sampling = 16
    Section 4. All reported accuracies use the lowest-energy of 16 generated circuits per conformer; ADAPT-VQE baselines are single runs.
  • tanh reward steepness α (Eq. 2, alternative reward) = computed dynamically
    Appendix A.1.4. Tunable steepness for the reference-free reward; adjusted during fine-tuning so most circuits stay in the linear regime.
assumptions (6)
  • domain assumption CASCI (12q/14q) and CCSD (16q) energies are accurate references for benchmarking circuit quality.
    Section 3.1; the paper itself flags interpretation care for the 16q CCSD reference (footnote 3).
  • domain assumption The UCCGSD/UCCSD operator pool bounds the reachable ansatz space, and ADAPT-VQE's solutions within it are appropriate training targets.
    Section 3.1; pool choice is an input, not derived. The model can never propose circuits outside this ansatz family, so 'beyond ADAPT-VQE' is bounded by its expressivity.
  • domain assumption The random 80/18/2 split does not materially leak near-duplicate MD conformers into the test set.
    Section 4.1 and Appendix A.1.1, where the authors acknowledge that MD-trajectory redundancy can cause leakage; the stricter OoD split shows degraded accuracy (Fig. 9).
  • standard math Jordan-Wigner mapping of PySCF 6-31G integrals gives a faithful qubit Hamiltonian for each active space.
    Section 3.1; standard quantum-chemistry pipeline, not derived in this paper.
  • domain assumption MACE-OFF MD, NEB and CREST/ETKDG sampling covers the imipramine conformational space relevant to the drug-stability use case.
    Section 3.1 and Appendix A.2; coverage is heuristic and the reference conformer labeling is admitted to be ambiguous (A.1.1).
  • domain assumption Noiseless statevector energy is the correct reward/ranking signal for generated circuits.
    Sections 3.2.3 and 4.3; the hardware run diverges 200-400 mHa from statevector, so the RL ranking only reflects ideal-circuit quality.

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Cite this review

Pith. "Pith review of Learning to Prepare Molecular Ground States with Transformer Models." pith.science (2026). https://pith.science/paper/GQXUJO4M

@misc{pith2026260722468,
  author       = {Pith},
  title        = {Pith review of: Learning to Prepare Molecular Ground States with Transformer Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GQXUJO4M}},
  note         = {Machine review of arXiv:2607.22468}
}
read the original abstract

Quantum state preparation is a key component of many quantum algorithms. Performing this step efficiently is essential for realizing practical quantum advantage in quantum chemistry applications. Iterative algorithms like ADAPT-VQE can produce shallow ground-state preparation circuits, but become computationally prohibitive for the larger molecules relevant to materials science and pharmaceutical development. Here, we introduce ADAPT-GQE, a generative AI framework that learns to synthesize ground-state preparation circuits for electronic structure calculations. We first use ADAPT-VQE to generate high-quality reference circuits, which are then used as targets for training models for circuit generation. Once trained, the model can efficiently propose and score circuits, enabling reinforcement learning (RL) to drive circuit generation accuracy beyond the accuracy of the ADAPT-VQE training data. This pipeline achieves order-of-magnitude reductions in circuit generation time relative to ADAPT-VQE while maintaining comparable or improved state-preparation accuracy. We demonstrate ADAPT-GQE on imipramine, a well-established tricyclic antidepressant that serves as a representative, challenging target for computational modelling in drug stability protocols. We execute generated circuits on Quantinuum Helios-1, representing a milestone for AI-generated quantum chemistry circuits on state-of-the-art quantum hardware. These results establish a pathway toward automated quantum circuit synthesis for utility-scale quantum computational chemistry.

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Works this paper leans on

65 extracted references · 3 canonical work pages

  1. [1]

    https://arxiv.org/abs/1411.4028

    Farhi, E., Goldstone, J., Gutmann, S.: A Quantum Approximate Optimization Algorithm (2014). https://arxiv.org/abs/1411.4028

    arXiv 2014

  2. [2]

    SIAM Journal on Computing26(5), 1484–1509 (1997) https://doi.org/10.1137/S0097539795293172

    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete log- arithms on a quantum computer. SIAM Journal on Computing26(5), 1484–1509 (1997) https://doi.org/10.1137/S0097539795293172

    doi:10.1137/s0097539795293172 1997

  3. [3]

    Chem- ical Reviews119(19), 10856–10915 (2019) https://doi.org/10.1021/acs.chemrev

    Cao, Y., Romero, J., Olson, J.P., Degroote, M., Johnson, P.D., Kieferov´ a, M., Kivlichan, I.D., Menke, T., Peropadre, B., Sawaya, N.P.D., Sim, S., Veis, L., Aspuru-Guzik, A.: Quantum chemistry in the age of quantum computing. Chem- ical Reviews119(19), 10856–10915 (2019) https://doi.org/10.1021/acs.chemrev. 8b00803

    doi:10.1021/acs.chemrev 2019

  4. [4]

    John Wiley & Sons, LTD, Chichester (2000)

    Helgaker, T., Jørgensen, P., Olsen, J.: Molecular Electronic Structure Theory. John Wiley & Sons, LTD, Chichester (2000)

    2000

  5. [5]

    Science309(5741), 1704–1707 (2005)

    Aspuru-Guzik, A., Dutoi, A.D., Love, P.J., Head-Gordon, M.: Simulated quantum computation of molecular energies. Science309(5741), 1704–1707 (2005)

    2005

  6. [6]

    McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S.C., Yuan, X.: Quantum computational chemistry. Rev. Mod. Phys.92(1), 015003 (2020) https://doi.org/ 10.1103/revmodphys.92.015003 arXiv:1808.10402 [quant-ph] 29

    arXiv 2020

  7. [7]

    Quantum2, 79 (2018) https://doi.org/10.22331/q-2018-08-06-79

    Preskill, J.: Quantum Computing in the NISQ era and beyond. Quantum2, 79 (2018) https://doi.org/10.22331/q-2018-08-06-79

    doi:10.22331/q-2018-08-06-79 2018

  8. [8]

    Nature Communications5, 4213 (2014) https://doi.org/10

    Peruzzo, A., McClean, J.R., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P.J., Aspuru-Guzik, A., O’Brien, J.L.: A variational eigenvalue solver on a photonic quantum processor. Nature Communications5, 4213 (2014) https://doi.org/10. 1038/ncomms5213

    2014

Show all 65 references
  1. [9]

    New Journal of Physics18(2), 023023 (2016) https://doi.org/10.1088/1367-2630/18/2/023023

    McClean, J.R., Romero, J., Babbush, R., Aspuru-Guzik, A.: The theory of varia- tional hybrid quantum–classical algorithms. New Journal of Physics18(2), 023023 (2016) https://doi.org/10.1088/1367-2630/18/2/023023

    2016 doi

  2. [10]

    Nature Reviews Physics3, 625–644 (2021) https://doi.org/10.1038/ s42254-021-00348-9

    Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S.C., Endo, S., Fujii, K., McClean, J.R., Mitarai, K., Yuan, X., Cincio, L., Coles, P.J.: Variational quantum algorithms. Nature Reviews Physics3, 625–644 (2021) https://doi.org/10.1038/ s42254-021-00348-9

    2021

  3. [11]

    Nature Communications 9, 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4

    McClean, J.R., Boixo, S., Smelyanskiy, V.N., Babbush, R., Neven, H.: Barren plateaus in quantum neural network training landscapes. Nature Communications 9, 4812 (2018) https://doi.org/10.1038/s41467-018-07090-4

    2018 doi

  4. [12]

    Nature Communications10, 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2

    Grimsley, H.R., Economou, S.E., Barnes, E., Mayhall, N.J.: An adaptive varia- tional algorithm for exact molecular simulations on a quantum computer. Nature Communications10, 3007 (2019) https://doi.org/10.1038/s41467-019-10988-2

    2019 doi

  5. [13]

    https://arxiv.org/abs/2511.16559

    Krumt¨ unger, M., Wilms, A., Faehrmann, P.K., Eisert, J., Kottmann, J., Erdman, P.A., Khatri, S.: Reinforcement Learning of Quantum Circuit Architectures for Molecular Potential Energy Curves (2025). https://arxiv.org/abs/2511.16559

    2025

  6. [14]

    https: //arxiv.org/abs/2511.08096

    Rieckmann, T.R., Scheel, S., Plato, A.D.K.: Gate Sequence Optimization for Parameterized Quantum Circuits using Reinforcement Learning (2025). https: //arxiv.org/abs/2511.08096

    2025

  7. [15]

    https://arxiv.org/abs/2501.16986

    Minami, S., Nakaji, K., Suzuki, Y., Aspuru-Guzik, A., Kadowaki, T.: Gener- ative Quantum Combinatorial Optimization by Means of a Novel Conditional Generative Quantum Eigensolver (2025). https://arxiv.org/abs/2501.16986

    2025 arXiv

  8. [16]

    https://arxiv.org/abs/2510

    Dai, J., Rizvi-Martel, M., Rabusseau, G.: FlowQ-Net: A Generative Frame- work for Automated Quantum Circuit Design (2025). https://arxiv.org/abs/2510. 26688

    2025

  9. [17]

    https://arxiv.org/abs/2504.16350

    Tyagin, I., Farag, M.H., Sherbert, K., Shirali, K., Alexeev, Y., Safro, I.: QAOA- GPT: Efficient Generation of Adaptive and Regular Quantum Approximate Optimization Algorithm Circuits (2025). https://arxiv.org/abs/2504.16350

    2025 arXiv

  10. [18]

    https: //developer.nvidia.com/cuda-q

    NVIDIA: CUDA-Q: A Platform for Hybrid Quantum-Classical Computing. https: //developer.nvidia.com/cuda-q. Accessed 2026-05-28 (2026) 30

    2026

  11. [19]

    https://github.com/NVIDIA/cuda-quantum (2023)

    NVIDIA: CUDA Quantum. https://github.com/NVIDIA/cuda-quantum (2023)

    2023

  12. [20]

    https://arxiv

    Xu, H., Liu, X., Pothen, A., Safro, I.: QAOA Parameter Transferability for Max- imum Independent Set using Graph Attention Networks (2025). https://arxiv. org/abs/2504.21135

    2025 arXiv

  13. [21]

    https://arxiv.org/abs/2511.03726

    Bincoletto, D., Stein, K., Motyl, J., Kottmann, J.S.: A Transferable Machine Learning Approach to Predict Quantum Circuit Parameters for Electronic Structure Problems (2025). https://arxiv.org/abs/2511.03726

    2025

  14. [22]

    https://arxiv.org/abs/ 2505.01236

    Zhang, C., Jiang, L., Chen, F.: Qracle: A Graph-Neural-Network-based Parameter Initializer for Variational Quantum Eigensolvers (2025). https://arxiv.org/abs/ 2505.01236

    2025 arXiv

  15. [23]

    Frank C., Wood, G.P.F., Zelesky, T., Sluggett, G.W., Mustakis, J., Green, W.H.: Kinetic modeling of api oxidation: (2) imipramine stress testing

    Wu, H., Grinberg-Dana, A., Ranasinghe, D.S., Pickard, I. Frank C., Wood, G.P.F., Zelesky, T., Sluggett, G.W., Mustakis, J., Green, W.H.: Kinetic modeling of api oxidation: (2) imipramine stress testing. Molecular Pharmaceutics19(5), 1526– 1539 (2022) https://doi.org/10.1021/ac...

    2022 doi

  16. [24]

    Frank C., Wood, G.P.F., Zelesky, T., Sluggett, G.W., Mustakis, J., Green, W.H.: Kinetic modeling of api oxidation: (1) the aibn/h 2o/ch3oh radical “soup”

    Grinberg-Dana, A., Wu, H., Ranasinghe, D.S., Pickard, I. Frank C., Wood, G.P.F., Zelesky, T., Sluggett, G.W., Mustakis, J., Green, W.H.: Kinetic modeling of api oxidation: (1) the aibn/h 2o/ch3oh radical “soup”. Molecular Pharmaceutics 18(8), 3037–3049 (2021) https://doi.org/1...

    2021 doi

  17. [25]

    Frank C., Wood, G.P.F., Zelesky, T., Sluggett, G.W., Mustakis, J., Green, W.H.: An in silico tool for quantitative kinetic predictions of api degradation

    Wu, H., Grinberg-Dana, A., Ranasinghe, D.S., Pickard, I. Frank C., Wood, G.P.F., Zelesky, T., Sluggett, G.W., Mustakis, J., Green, W.H.: An in silico tool for quantitative kinetic predictions of api degradation. In: AIChE Annual Meeting Proceedings (2021). Abstract 463e

    2021

  18. [26]

    https://arxiv.org/abs/2503.19786

    Team, G., Kamath, A., Ferret, J., Pathak, S., Vieillard, N., Merhej, R., Perrin, S., Matejovicova, T., Ram´ e, A., Rivi` ere, M., Rouillard, L., Mesnard, T., Cideron, G., Grill, J.-b., Ramos, S., Yvinec, E., Casbon, M., Pot, E., Penchev, I., Liu, G., Visin, F., Kenealy, K., Be...

    2025 arXiv

  19. [27]

    https://arxiv.org/abs/2508.14444

    NVIDIA: NVIDIA Nemotron Nano 2: An Accurate and Efficient Hybrid Mamba- Transformer Reasoning Model (2025). https://arxiv.org/abs/2508.14444

    2025 arXiv

  20. [28]

    The Journal of Physical Chemistry B128(1), 109–116 (2024) https://doi.org/10.1021/acs.jpcb.3c06662 https://doi.org/10.1021/acs.jpcb.3c06662

    Eastman, P., Galvelis, R., Pel´ aez, R.P., Abreu, C.R.A., Farr, S.E., Gal- licchio, E., Gorenko, A., Henry, M.M., Hu, F., Huang, J., Kr¨ amer, A., Michel, J., Mitchell, J.A., Pande, V.S., Rodrigues, J.P., Rodriguez-Guerra, J., Simmonett, A.C., Singh, S., Swails, J., Turner, P....

    2024

  21. [29]

    Journal of the American Chemical Society147(21), 17598–17611 (2025) https://doi.org/10

    Kov´ acs, D.P., Moore, J.H., Browning, N.J., Batatia, I., Horton, J.T., Pu, Y., Kapil, V., Witt, W.C., Magd˘ au, I.-B., Cole, D.J., Cs´ anyi, G.: Mace-off: Short- range transferable machine learning force fields for organic molecules. Journal of the American Chemical Society14...

    2025 doi

  22. [30]

    Zenodo (2006)

    Landrum, G., et al.: RDKit: Open-source cheminformatics. Zenodo (2006)

    2006

  23. [31]

    Journal of Physics: Condensed Matter29(27), 273002 (2017) 32

    Larsen, A.H., Mortensen, J.J., Blomqvist, J., Castelli, I.E., Christensen, R., Du lak, M., Friis, J., Groves, M.N., Hammer, B., Hargus, C., Hermes, E.D., Jen- nings, P.C., Jensen, P.B., Kermode, J., Kitchin, J.R., Kolsbjerg, E.L., Kubal, J., Kaasbjerg, K., Lysgaard, S., Marons...

    2017

  24. [32]

    WIREs Computational Molecular Science8(1), 1340 (2018) https://doi.org/10.1002/wcms.1340

    Sun, Q., Berkelbach, T.C., Blunt, N.S., Booth, G.H., Guo, S., Li, Z., Liu, J., McClain, J., Sayfutyarova, E.R., Sharma, S., Wouters, S., Chan, G.K.-L.: PySCF: The python-based simulations of chemistry framework. WIREs Computational Molecular Science8(1), 1340 (2018) https://do...

    2018 doi

  25. [33]

    Journal of Chemical Physics153(2), 024109 (2020) https://doi.org/10.1063/5.0006074

    Sun, Q., Zhang, X., Banerjee, S., Bao, P., Barbry, M., Blunt, N.S., Bogdanov, N.A., Booth, G.H., Chen, J., Cui, Z.-H., Eriksen, J.J., Gao, Y., Guo, S., Hermann, J., Hermes, M.R., Koh, K., Koval, P., Lehtola, S., Li, Z., Liu, J., Mardirossian, N., McClain, J.D., Motta, M., Muss...

    2020

  26. [34]

    Hehre, W.J., Ditchfield, R., Pople, J.A.: Self-consistent molecular orbital meth- ods. xii. further extensions of gaussian-type basis sets for use in molecular orbital studies of organic molecules. Journal of Chemical Physics56(5), 2257–2261 (1972) https://doi.org/10.1063/1.1677527

    1972 doi

  27. [35]

    Zeitschrift f¨ ur Physik47, 631–651 (1928) https://doi.org/10.1007/BF01331938

    Jordan, P., Wigner, E.: ¨Uber das paulische ¨ aquivalenzverbot. Zeitschrift f¨ ur Physik47, 631–651 (1928) https://doi.org/10.1007/BF01331938

    1928 doi

  28. [36]

    https://arxiv.org/abs/1812.02233

    Tranter, A., Sofia, S., Seeley, J., Kaicher, M., McClean, J., Babbush, R., Coveney, P.V., Mintert, F., Wilhelm, F., Love, P.J.: A Comparison of the Bravyi–Kitaev and Jordan–Wigner Transformations for the Quantum Simulation of Quantum Chemistry (2018). https://arxiv.org/abs/1812.02233

    2018 arXiv

  29. [37]

    Journal of Chemical Theory and Computation15(1), 311–324 (2019) https://doi.org/10.1021/acs.jctc

    Lee, J., Huggins, W.J., Head-Gordon, M., Whaley, K.B.: Generalized unitary coupled cluster wave functions for quantum computation. Journal of Chemical Theory and Computation15(1), 311–324 (2019) https://doi.org/10.1021/acs.jctc. 8b01004

    2019 doi

  30. [38]

    https://arxiv.org/abs/2302.03241

    Ke, Z., Shao, Y., Lin, H., Konishi, T., Kim, G., Liu, B.: Continual Pre-training of Language Models (2023). https://arxiv.org/abs/2302.03241

    2023 arXiv

  31. [39]

    https://arxiv.org/abs/2305.13245

    Ainslie, J., Lee-Thorp, J., Jong, M., Zemlyanskiy, Y., Lebr´ on, F., Sanghai, S.: GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints (2023). https://arxiv.org/abs/2305.13245

    2023 arXiv

  32. [40]

    https://arxiv.org/abs/2004.05150

    Beltagy, I., Peters, M.E., Cohan, A.: Longformer: The Long-Document Trans- former (2020). https://arxiv.org/abs/2004.05150

    2020 arXiv

  33. [41]

    Advances in neural information processing systems32(2019) 33

    Zhang, B., Sennrich, R.: Root mean square layer normalization. Advances in neural information processing systems32(2019) 33

    2019

  34. [42]

    Neurocomputing568, 127063 (2024)

    Su, J., Ahmed, M., Lu, Y., Pan, S., Bo, W., Liu, Y.: Roformer: Enhanced transformer with rotary position embedding. Neurocomputing568, 127063 (2024)

    2024

  35. [43]

    https://arxiv.org/abs/2402.03300

    Shao, Z., Wang, P., Zhu, Q., Xu, R., Song, J., Bi, X., Zhang, H., Zhang, M., Li, Y.K., Wu, Y., Guo, D.: DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models (2024). https://arxiv.org/abs/2402.03300

    2024 arXiv

  36. [44]

    https://arxiv.org/abs/2503.14476

    Yu, Q., Zhang, Z., Zhu, R., Yuan, Y., Zuo, X., Yue, Y., Dai, W., Fan, T., Liu, G., Liu, L., Liu, X., Lin, H., Lin, Z., Ma, B., Sheng, G., Tong, Y., Zhang, C., Zhang, M., Zhang, W., Zhu, H., Zhu, J., Chen, J., Chen, J., Wang, C., Yu, H., Song, Y., Wei, X., Zhou, H., Liu, J., Ma...

    2025 arXiv

  37. [45]

    https://doi.org/10.1038/s41586-025-09422-z

    DeepSeek-AI, Guo, D., Yang, D., Zhang, H., Song, J., Wang, P., Zhu, Q., Xu, R., Zhang, R., Ma, S., Bi, X., Zhang, X., Yu, X., Wu, Y., Wu, Z.F., Gou, Z., Shao, Z., Li, Z., Gao, Z., Liu, A., Xue, B., Wang, B., Wu, B., Feng, B., Lu, C., Zhao, C., Deng, C., Zhang, C., Ruan, C., Da...

    2026 arXiv

  38. [46]

    https://arxiv.org/abs/2402.13669 34

    Yang, Z., Pang, T., Feng, H., Wang, H., Chen, W., Zhu, M., Liu, Q.: Self- Distillation Bridges Distribution Gap in Language Model Fine-Tuning (2024). https://arxiv.org/abs/2402.13669 34

    2024 arXiv

  39. [47]

    https://arxiv.org/abs/ 2405.21060

    Dao, T., Gu, A.: Transformers are SSMs: Generalized Models and Efficient Algo- rithms Through Structured State Space Duality (2024). https://arxiv.org/abs/ 2405.21060

    2024 arXiv

  40. [48]

    https://github.com/huggingface/trl

    Werra, L., Belkada, Y., Tunstall, L., Beeching, E., Thrush, T., Lambert, N., Huang, S., Rasul, K., Gallou´ edec, Q.: TRL: Transformers Reinforcement Learning (2020). https://github.com/huggingface/trl

    2020

  41. [49]

    https://arxiv.org/abs/2309.06180

    Kwon, W., Li, Z., Zhuang, S., Sheng, Y., Zheng, L., Yu, C.H., Gonzalez, J.E., Zhang, H., Stoica, I.: Efficient Memory Management for Large Language Model Serving with PagedAttention (2023). https://arxiv.org/abs/2309.06180

    2023 arXiv

  42. [50]

    Yordanov, Y.S., Arvidsson-Shukur, D.R.M., Barnes, C.H.W.: Efficient quantum circuits for quantum computational chemistry. Phys. Rev. A102, 062612 (2020) https://doi.org/10.1103/PhysRevA.102.062612

    2020 doi

  43. [51]

    https://arxiv.org/abs/2511.05465

    Ransford, A., Allman, M.S., Arkinstall, J., III, J.P.C., Cooper, S.F., Delaney, R.D., Dreiling, J.M., Estey, B., Figgatt, C., Hall, A., Husain, A.A., Isanaka, A., Kennedy, C.J., Kotibhaskar, N., Madjarov, I.S., Mayer, K., Milne, A.R., Park, A.J., Reed, A.P., Ancona, R., Anders...

    2025 arXiv

  44. [52]

    Quantum Science and Technology6(1), 014003 (2020) https://doi.org/10.1088/2058-9565/ab8e92

    Sivarajah, S., Dilkes, S., Cowtan, A., Simmons, W., Edgington, A., Duncan, R.: t—ket〉: a retargetable compiler for nisq devices. Quantum Science and Technology6(1), 014003 (2020) https://doi.org/10.1088/2058-9565/ab8e92

    2020 doi

  45. [53]

    Electronic Proceedings in Theoretical Computer Science318, 213–228 (2020) https://doi.org/10.4204/eptcs.318.13

    Cowtan, A., Dilkes, S., Duncan, R., Simmons, W., Sivarajah, S.: Phase gadget synthesis for shallow circuits. Electronic Proceedings in Theoretical Computer Science318, 213–228 (2020) https://doi.org/10.4204/eptcs.318.13

    2020 doi

  46. [54]

    Yamamoto, K., Manrique, D.Z., Khan, I.T., Sawada, H., Ramo, D.M.n.: Quantum hardware calculations of periodic systems with partition-measurement symmetry verification: Simplified models of hydrogen chain and iron crystals. Phys. Rev. Res.4, 033110 (2022) https://doi.org/10.110...

    2022 doi

  47. [55]

    https://www.quantinuum.com/ products-solutions/inquanto

    Tranter, A., Ward, C., Di Paola, C., Ramo, D., Manrique, D.Z., Gowland, D., Plekhanov, E., Greene-Diniz, G., Christopoulou, G., Prokopiou, G., Keen, H.D.J., Polyak, I., Khan, I.T., Pilipczuk, J., Kirsopp, J.J.M., Yamamoto, K., Panchag- nula, K., Szulakowska, L., Tudorovskaya, ...

    2022

  48. [56]

    https://nexus.quantinuum.com/

    Quantinuum Nexus (2024). https://nexus.quantinuum.com/

    2024

  49. [57]

    The MIT Press, ??? (2018).http://incompleteideas.net/book/the-book-2nd.html

    Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction, 2nd edn. The MIT Press, ??? (2018).http://incompleteideas.net/book/the-book-2nd.html

    2018

  50. [58]

    arXiv preprint arXiv:2312.01072 (2023)

    Pignatelli, E., Ferret, J., Geist, M., Mesnard, T., Hasselt, H., Pietquin, O., Toni, L.: A survey of temporal credit assignment in deep reinforcement learning. arXiv preprint arXiv:2312.01072 (2023)

    2023 arXiv

  51. [59]

    In: International Conference on Learning Representations (2024)

    Lightman, H., Kosaraju, V., Burda, Y., Edwards, H., Baker, B., Lee, T., Leike, J., Schulman, J., Sutskever, I., Cobbe, K.: Let’s verify step by step. In: International Conference on Learning Representations (2024). https://openreview.net/forum?id=v8L0pN6EOi

    2024

  52. [60]

    https://arxiv.org/abs/2312.08935

    Wang, P., Li, L., Shao, Z., Xu, R.X., Dai, D., Li, Y., Chen, D., Wu, Y., Sui, Z.: Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations (2023). https://arxiv.org/abs/2312.08935

    2023 arXiv

  53. [61]

    https://doi.org/10.48550/arXiv

    Batatia, I., Batzner, S., Kov´ acs, D.P., Musaelian, A., Simm, G.N.C., Drautz, R., Ortner, C., Kozinsky, B., Cs´ anyi, G.: The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials (2022). https://doi.org/10.48550/arXiv. 2205.06643 36

    2022 doi arXiv

  54. [62]

    In: Oh, A.H., Agarwal, A., Belgrave, D., Cho, K

    Batatia, I., Kovacs, D.P., Simm, G.N.C., Ortner, C., Csanyi, G.: MACE: Higher order equivariant message passing neural networks for fast and accurate force fields. In: Oh, A.H., Agarwal, A., Belgrave, D., Cho, K. (eds.) Advances in Neural Information Processing Systems (2022)....

    2022

  55. [63]

    Pracht, P., Bohle, F., Grimme, S.: Automated exploration of the low-energy chem- ical space with fast quantum chemical methods. Phys. Chem. Chem. Phys.22, 7169–7192 (2020) https://doi.org/10.1039/C9CP06869D

    2020 doi

  56. [64]

    https: //arxiv.org/abs/1711.05101

    Loshchilov, I., Hutter, F.: Decoupled Weight Decay Regularization (2019). https: //arxiv.org/abs/1711.05101

    2019 arXiv

  57. [65]

    standard

    Rajbhandari, S., Rasley, J., Ruwase, O., He, Y.: ZeRO: Memory Optimizations Toward Training Trillion Parameter Models (2020). https://arxiv.org/abs/1910. 02054 A Supplementary Material A.1 Supporting Results In this section we provide a set of auxiliary results that support cl...

    2020

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.