Pith. sign in

REVIEW 3 major objections 48 references

Graph-VQE: A CUDA-Q Multi-QPU Simulation Framework for Hamiltonian-Aware Protein-Folding VQE

T0 review · 3 major / 0 minor · reviewed 2026-07-12 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Partitioning a protein Hamiltonian by its interaction graph lets multi-GPU VQE reach lower folding energies than standard methods.

desk verdict Clean multi-QPU VQE engineering that reliably beats baselines on lattice-peptide energies; structure comparisons are secondary and the systems remain tiny. read the letter →

arxiv 2607.02749 v1 pith:HVOJVBDB submitted 2026-07-02 cs.ET

Yujun Feng , Yuqi Zhang , Jingyi Huang , Bo Fang , Shuai Xu , Qiang Guan , Yang Zhang This is my paper
classification cs.ET
keywords VariationalQuantumEigensolverproteinfoldingHamiltonianpartitioningLouvaincommunitydetectionmulti-QPUparallelizationCUDA-Qhybridquantum-classicalcomputing
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

Graph-VQE claims that protein-folding VQE can be made both more accurate and more parallel by building a weighted qubit interaction graph from the Hamiltonian, detecting weakly coupled communities with Louvain, and optimizing each community’s parameters on the full energy while other parameters stay fixed, then finishing with a short global refinement that batches Hamiltonian terms across GPUs. The authors argue this biologically informed split overcomes the sequential bottleneck of classical optimizers and the barren landscapes that appear when every parameter is updated together. On ten short lattice peptides the method reports the lowest energy in the large majority of settings against SeqVQE, Hamiltonian batching, EQC, CVaR-VQE and ADAPT-VQE, and the reconstructed backbones yield RMSD and docking affinities competitive with AlphaFold3 and IBM hardware baselines. The practical payoff is a Qiskit-compatible, multi-GPU path that isolates algorithmic performance from device noise and scales wall-clock time without degrading solution quality.

What carries the argument

Hamiltonian-aware Louvain partitioning of the weighted qubit interaction graph (edges weighted by absolute Pauli coefficients derived from Miyazawa–Jernigan contacts), followed by concurrent restricted full-objective block updates and a short global refinement stage that reuses CUDA-Q multi-QPU Hamiltonian batching.

What would settle it

Run the same Graph-VQE pipeline on a larger or all-atom peptide set where the ground-state energy and crystallographic structure are known; if the method no longer reaches lower energy than the listed baselines or yields systematically worse RMSD/affinity than AlphaFold3 under identical shot budgets, the central claim fails.

Watch

Extended reading notes

Core claim

When the protein Hamiltonian’s interaction graph is partitioned into Louvain communities and each community’s variational parameters are updated under the full Hamiltonian objective while the rest remain frozen, followed by a brief joint refinement with Hamiltonian batching, the optimizer reaches substantially lower final energies than global VQE baselines on the same lattice protein-folding instances, while reconstructed structures remain competitive with AlphaFold3 and hardware baselines.

Load-bearing premise

That a coarse tetrahedral-lattice model with fixed contact energies and uniform geometric penalties, once split by community detection on absolute Pauli weights, still produces blocks whose restricted optimization recovers physically meaningful low-energy folds comparable to all-atom and hardware results.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 0 minor

Summary. Graph-VQE extends NVIDIA CUDA-Q with optimization-level parallelism for lattice protein-folding VQE. From the tetrahedral-lattice Hamiltonian (MJ contacts plus uniform geometric penalties), the authors build a weighted qubit interaction graph, partition it by Louvain modularity into weakly coupled blocks, optimize each block by restricted updates on the full-Hamiltonian objective while other parameters are frozen, then perform a short global refinement with CUDA-Q Hamiltonian batching. A Qiskit-to-CUDA-Q translation layer maps EfficientSU2 and operators onto JIT kernels. On ten 5–6-residue peptides, under six entanglement patterns, Graph-VQE (and its no-global ablation) reports the lowest energy in 54/60 settings versus SeqVQE, HBatch, EQC, CVaR-VQE and ADAPT-VQE; multi-GPU scaling preserves energy quality; reconstructed structures yield competitive Kabsch RMSD and AutoDock Vina affinities versus AlphaFold3 and IBM hardware baselines.

Significance. If the energy gains and structure metrics hold under tighter validation, the work supplies a practical, Hamiltonian-aware route to optimization-level multi-QPU parallelism that CUDA-Q currently lacks, together with a usable Qiskit bridge. Strengths that should be credited include the systematic multi-entanglement evaluation (Table I), the no-global ablation isolating the refinement stage, the shot-sensitivity study (Fig. 6), the GPU scaling that preserves accuracy (Fig. 8), and the explicit hierarchical schedule (block-restricted full-H updates + batched global refinement). These are concrete engineering contributions for hybrid biomolecular simulation on multi-QPU platforms, even though the present instances remain small lattice peptides.

major comments (3)
  1. §IV-A / Eqs. (1)–(3) and Tables II–III: The central claim equates lower lattice energies (Table I) with physically meaningful conformations competitive with AlphaFold3 and IBM hardware VQE. Under uniform penalties λ=10 a single geometric violation produces large positive energy, so large negative energies can be obtained by merely avoiding penalties without recovering native packing. The manuscript never reports the fraction of sampled bitstrings that remain penalty-free, nor the gap of the reported minima to the true lattice ground state. Without those diagnostics the RMSD/affinity numbers (which further rely on Modeller relaxation of a Cα trace) cannot be taken as evidence that the partitioned VQE recovered native contacts rather than post-hoc reconstruction of any valid lattice fold.
  2. §V-A and Table I: All results are exact state-vector simulations on 5–6-residue peptides (N=8–10 qubits). The abstract and conclusion present Graph-VQE as a path to high-fidelity biomolecular simulations and multi-QPU scaling. The energy advantage is real under the stated protocol, but the load-bearing claim that the Louvain + restricted-update schedule will continue to help once circuit depth, shot noise, and inter-block correlations grow with system size is not yet supported. At minimum the paper should either (i) demonstrate a larger instance or (ii) clearly bound the claim to the lattice-peptide regime and relegate the drug-discovery framing to future work.
  3. §IV-C / Eqs. (9)–(10) and the free-parameter list: Louvain modularity on absolute Pauli coefficients is presented as biologically informed, yet the only free parameters that control block quality (resolution, S_min merge threshold) and the early-stopping / epoch-patience schedule are fixed without sensitivity analysis. Because the no-global ablation already wins 9/60 cases and loses under certain entanglement topologies, it is unclear how robust the hierarchical schedule is to these choices. A short ablation on S_min / resolution (or an explicit statement that defaults were used throughout) is needed before the partitioning strategy can be treated as a reliable contribution.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: Graph-VQE is an empirical optimization heuristic whose energy/RMSD/affinity claims are measured against external baselines rather than forced by construction or self-citation.

full rationale

The paper's derivation chain is: (1) encode lattice protein Hamiltonian from amino-acid sequence via fixed Miyazawa-Jernigan contacts plus uniform geometric penalties (Eqs. 1-6); (2) build weighted qubit interaction graph from absolute Pauli coefficients (Eq. 9); (3) Louvain-partition into blocks (Eq. 10); (4) perform concurrent restricted full-Hamiltonian block updates followed by short global refinement with Hamiltonian batching; (5) report final energies, decode bitstrings to structures, and compute Kabsch RMSD plus AutoDock Vina affinities. None of these steps defines a quantity in terms of itself, fits a free parameter to the target data and then re-predicts it, or imports a uniqueness theorem from overlapping authors that forces the result. Energies are obtained by ordinary VQE evaluation of the same Hamiltonian used by all baselines; RMSD and affinity are post-hoc comparisons to crystallographic segments and AlphaFold3/IBM structures. The sole self-reference is the SeqVQE baseline drawn from the authors' prior work [27]; it is used only as one of several empirical competitors and does not underwrite the partitioning or refinement claims. The method is therefore self-contained against external benchmarks, warranting a near-zero circularity score.

Assumptions & free parameters 5 free parameters · 4 assumptions · 1 invented entities

The central performance claims rest on standard lattice-protein modeling choices, fixed numerical hyper-parameters, and the unproved but conventional assumption that modularity of the absolute-coefficient interaction graph yields useful VQE blocks. No new physical entities are postulated; free parameters are the usual algorithmic knobs.

free parameters (5)
  • penalty coefficients λ_chiral = λ_back = λ_overlap = 10.0
    Set uniformly to 10.0 by hand to create a high barrier against invalid lattice configurations; magnitude directly controls whether energies are negative (valid) or positive (invalid).
  • measurement shots = 8192
    Chosen as 8192 after a sensitivity sweep; directly affects estimator variance and reported energies.
  • ansatz depth (reps) = 4
    Fixed at 4 for main experiments; trades expressibility against barren-plateau risk and runtime.
  • early-stopping tolerance / patience / window / epoch patience = 10^{-4}/12/40/3
    10^{-4}, 12, 40, 3; control when block, global and epoch loops terminate and therefore final energies.
  • S_min block-size merge threshold
    Configurable minimum community size after Louvain; affects number and balance of parallel blocks.
assumptions (4)
  • domain assumption Thermodynamic hypothesis: native fold is the global free-energy minimum of the chosen lattice Hamiltonian.
    Invoked in Section II-A to justify energy minimization as structure prediction.
  • domain assumption Miyazawa-Jernigan statistical contact potentials plus geometric penalties adequately encode folding energetics for the evaluated peptides.
    Hamiltonian construction (Eqs. 1–3) and all numerical results rest on this model.
  • ad hoc to paper Louvain modularity on absolute Pauli coefficients identifies weakly coupled qubit blocks useful for restricted full-objective VQE.
    Core methodological claim of Section IV-C; not derived from first principles but justified by protein community-structure literature.
  • domain assumption Exact multi-QPU state-vector simulation with finite shots is a faithful proxy for future multi-QPU hardware behavior under the proposed schedule.
    Stated motivation in Introduction and Discussion; isolates algorithmic performance from device noise.
invented entities (1)
  • Graph-VQE hierarchical schedule (block-restricted full-H updates + global refinement + CUDA-Q multi-QPU dispatch)
    purpose: Enable optimization-level parallelism for protein-folding VQE while preserving cross-block correlations.
    The schedule itself is the paper’s main technical object; it is an algorithmic construction, not a physical entity, and is evaluated empirically.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Graph-VQE: A CUDA-Q Multi-QPU Simulation Framework for Hamiltonian-Aware Protein-Folding VQE." pith.science (2026). https://pith.science/paper/HVOJVBDB

@misc{pith2026260702749,
  author       = {Pith},
  title        = {Pith review of: Graph-VQE: A CUDA-Q Multi-QPU Simulation Framework for Hamiltonian-Aware Protein-Folding VQE},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HVOJVBDB}},
  note         = {Machine review of arXiv:2607.02749}
}
read the original abstract

The Variational Quantum Eigensolver (VQE) is essential for molecular simulation in drug discovery, but hardware noise and algorithmic limits restrict its precision. While the NVIDIA CUDA-Q platform mitigates some hardware issues via exact simulation, it lacks Qiskit support and restricts parallelization. To solve this, we introduce Graph-VQE, a novel framework that extends CUDA-Q with optimization-level parallelism. Graph-VQE leverages amino acid sequence structures by partitioning Hamiltonian interaction graphs into weakly coupled clusters using Louvain community detection. These clusters undergo restricted updates on the full-Hamiltonian objective, followed by a global refinement stage utilizing Hamiltonian batching. Furthermore, a custom Qiskit-CUDA-Q integration layer enables standard workflows with GPU acceleration. Evaluations on protein folding tasks prove that Graph-VQE outperforms baselines, achieving lower final energies. It delivers competitive RMSD and binding affinity compared to AlphaFold3 and IBM quantum processors while maintaining stable quality across multi-GPU environments, thereby providing a highly practical path toward high-fidelity biomolecular simulations.

Figures

Figures reproduced from arXiv: 2607.02749 by the authors.

Figure 1
Figure 1. Binding Affinity Comparison (kcal/mol, lower is better.) [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Hamiltonian Construction Pipeline for Lattice Protein Folding [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Hardware-Efficient EfficientSU2 Ansatz Structure [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Graph-VQE Optimization Workflow. A weighted qubit interaction [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Bitstring Decoding and 3D Structure Reconstruction [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 7
Figure 7. Figure 7: ADAPT-VQE vs Graph-VQE (Circular Entanglement). Lower energy [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: GPU Scaling and Accuracy Preservation for Graph-VQE (Circular [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Lowest Energy vs Execution Time, averaged over all evaluated [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: Comparison of CUDA-Q backends: multi-GPU memory pooling [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

48 extracted references · 17 canonical work pages

  1. [1]

    A variational eigenvalue solver on a photonic quantum processor,

    A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, “A variational eigenvalue solver on a photonic quantum processor,”Nature communications, vol. 5, no. 1, p. 4213, 2014. [Online]. Available: https://doi.org/10.1038/ncomms5213

    doi:10.1038/ncomms5213 2014

  2. [2]

    The theory of variational hybrid quantum-classical algorithms,

    J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms,”New Journal of Physics, vol. 18, no. 2, p. 023023, 2016. [Online]. Available: http://dx.doi.org/10.1088/1367-2630/18/2/023023

    doi:10.1088/1367-2630/18/2/023023 2016

  3. [4]

    Scalable quantum simulation of molecular energies,

    P. J. O’Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding et al., “Scalable quantum simulation of molecular energies,”Physical Review X, vol. 6, no. 3, p. 031007, 2016. [Online]. Available: https://doi.org/10.1103/PhysRevX.6.031007

    doi:10.1103/physrevx.6.031007 2016

  4. [5]

    Helgaker, P

    T. Helgaker, P. Jorgensen, and J. Olsen,Molecular electronic- structure theory. John Wiley & Sons, 2013. [Online]. Available: https://doi.org/10.1002/9781119019572

    doi:10.1002/9781119019572 2013

  5. [6]

    The variational quantum eigensolver: a review of methods and best practices,

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y . Li, E. Grant, L. Wossnig, I. Rungger, G. H. Boothet al., “The variational quantum eigensolver: a review of methods and best practices,” Physics Reports, vol. 986, pp. 1–128, 2022. [Online]. Available: https://doi.org/10.1016/j.physrep.2022.08.003

    doi:10.1016/j.physrep.2022.08.003 2022

  6. [7]

    Barren plateaus in quantum neural network training landscapes,

    J. R. McClean, S. Boixo, V . N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,”Nature communications, vol. 9, no. 1, p. 4812, 2018. [Online]. Available: https://doi.org/10.1038/s41467-018-07090-4

    doi:10.1038/s41467-018-07090-4 2018

  7. [8]

    The protein-folding problem, 50 years on,

    K. A. Dill and J. L. MacCallum, “The protein-folding problem, 50 years on,”science, vol. 338, no. 6110, pp. 1042–1046, 2012. [Online]. Available: https://doi.org/10.1126/science.1219021

    doi:10.1126/science.1219021 2012

  8. [9]

    Quantum computing at the frontiers of biological sciences,

    P. S. Emani, J. Warrell, A. Anticevic, S. Bekiranov, M. Gandal, M. J. McConnell, G. Sapiro, A. Aspuru-Guzik, J. T. Baker, M. Bastiani et al., “Quantum computing at the frontiers of biological sciences,” Nature Methods, vol. 18, no. 7, pp. 701–709, 2021. [Online]. Available: https://doi.org/10.1038/s41592-020-01004-3

    work page doi:10.1038/s41592-020-01004-3 2021

Show all 48 references
  1. [10]

    Community detection in graphs,

    S. Fortunato, “Community detection in graphs,”Physics reports, vol. 486, no. 3-5, pp. 75–174, 2010. [Online]. Available: https://doi.org/10.1016/j.physrep.2009.11.002

    2010 doi

  2. [11]

    Graph partitioning methods for fast parallel quantum molecular dynamics,

    H. N. Djidjev, G. Hahn, S. M. Mniszewski, C. F. Negre, A. M. Niklasson, and V . B. Sardeshmukh, “Graph partitioning methods for fast parallel quantum molecular dynamics,” in2016 Proceedings of the Seventh SIAM Workshop on Combinatorial Scientific Computing. SIAM, 2016, pp. 42–...

    2016 doi

  3. [12]

    Doubling the size of quantum simulators by entanglement forging,

    A. Eddins, M. Motta, T. P. Gujarati, S. Bravyi, A. Mezzacapo, C. Hadfield, and S. Sheldon, “Doubling the size of quantum simulators by entanglement forging,”PRX Quantum, vol. 3, no. 1, p. 010309, 2022. [Online]. Available: https://doi.org/10.1103/PRXQuantum.3.010309

    2022 doi

  4. [13]

    Cutting quantum circuits to run on quantum and classical platforms,

    W. Tang and M. Martonosi, “Cutting quantum circuits to run on quantum and classical platforms,”arXiv preprint arXiv:2205.05836,

    arXiv

  5. [14]

    Available: https://doi.org/10.48550/arXiv.2205.05836

    [Online]. Available: https://doi.org/10.48550/arXiv.2205.05836

    doi arXiv

  6. [15]

    Variational quantum eigensolver with reduced circuit complexity,

    Y . Zhang, L. Cincio, C. F. Negre, P. Czarnik, P. J. Coles, P. M. Anisimov, S. M. Mniszewski, S. Tretiak, and P. A. Dub, “Variational quantum eigensolver with reduced circuit complexity,”npj Quantum Information, vol. 8, no. 1, p. 96, 2022. [Online]. Available: https://doi.org/...

    2022 doi

  7. [16]

    Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation,

    S. Miyazawa and R. L. Jernigan, “Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation,”Macromolecules, vol. 18, no. 3, pp. 534–552, 1985. [Online]. Available: https://doi.org/10.1021/ma00145a039

    1985 doi

  8. [17]

    Residue–residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading,

    ——, “Residue–residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading,”Journal of molecular biology, vol. 256, no. 3, pp. 623–644,

  9. [18]

    Available: https://doi.org/10.1006/jmbi.1996.0114

    [Online]. Available: https://doi.org/10.1006/jmbi.1996.0114

    1996 doi

  10. [19]

    Contact order, transition state placement and the refolding rates of single domain proteins,

    K. W. Plaxco, K. T. Simons, and D. Baker, “Contact order, transition state placement and the refolding rates of single domain proteins,” Journal of molecular biology, vol. 277, no. 4, pp. 985–994, 1998. [Online]. Available: https://doi.org/10.1006/jmbi.1998.1645

    1998 doi

  11. [20]

    Contact order revisited: influence of protein size on the folding rate,

    D. N. Ivankov, S. O. Garbuzynskiy, E. Alm, K. W. Plaxco, D. Baker, and A. V . Finkelstein, “Contact order revisited: influence of protein size on the folding rate,”Protein science, vol. 12, no. 9, pp. 2057–2062,

  12. [21]

    Available: https://doi.org/10.1110/ps.0302503

    [Online]. Available: https://doi.org/10.1110/ps.0302503

    doi

  13. [22]

    Protein structure: insights from graph theory,

    S. Vishveshwara, K. Brinda, and N. Kannan, “Protein structure: insights from graph theory,”Journal of Theoretical and Computational Chemistry, vol. 1, no. 01, pp. 187–211, 2002. [Online]. Available: https://doi.org/10.1142/S0219633602000117

    2002 doi

  14. [23]

    Modular decomposition of protein structure using community detection,

    W. P. Grant and S. E. Ahnert, “Modular decomposition of protein structure using community detection,”Journal of Complex Networks, vol. 7, no. 1, pp. 101–113, 2019. [Online]. Available: https://doi.org/10.1093/comnet/cny014

    2019 doi

  15. [24]

    Assortative mixing in protein contact networks and protein folding kinetics,

    G. Bagler and S. Sinha, “Assortative mixing in protein contact networks and protein folding kinetics,”Bioinformatics, vol. 23, no. 14, pp. 1760–1767, 2007. [Online]. Available: https://doi.org/10.1093/bioinformatics/btm257

    2007 doi

  16. [25]

    Task-based parallel computation of the density matrix in quantum-based molecular dynamics using graph partitioning,

    P. Ghale, M. P. Kroonblawd, S. Mniszewski, C. F. Negre, R. Pavel, S. Pino, V . Sardeshmukh, G. Shi, and G. Hahn, “Task-based parallel computation of the density matrix in quantum-based molecular dynamics using graph partitioning,”SIAM Journal on Scientific Computing, vol. 39, ...

    2017 doi

  17. [26]

    Cost function dependent barren plateaus in shallow parametrized quantum circuits,

    M. Cerezo, A. Sone, T. V olkoff, L. Cincio, and P. J. Coles, “Cost function dependent barren plateaus in shallow parametrized quantum circuits,”Nature communications, vol. 12, no. 1, p. 1791, 2021. [Online]. Available: https://doi.org/10.1038/s41467-021-21728-w

    2021 doi

  18. [27]

    Noise-induced barren plateaus in variational quantum algorithms,

    S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cincio, and P. J. Coles, “Noise-induced barren plateaus in variational quantum algorithms,”Nature communications, vol. 12, no. 1, p. 6961, 2021. [Online]. Available: https://doi.org/10.1038/s41467-021-27045-6

    2021 doi

  19. [28]

    Multilevel algorithms for multi-constraint graph partitioning,

    G. Karypis and V . Kumar, “Multilevel algorithms for multi-constraint graph partitioning,” inSC’98: Proceedings of the 1998 ACM/IEEE Conference on Supercomputing. IEEE, 1998, pp. 28–28. [Online]. Available: https://doi.org/10.1109/SC.1998.10018

    1998 doi

  20. [29]

    Eqc: ensembled quantum computing for variational quantum algorithms,

    S. Stein, N. Wiebe, Y . Ding, P. Bo, K. Kowalski, N. Baker, J. Ang, and A. Li, “Eqc: ensembled quantum computing for variational quantum algorithms,” inProceedings of the 49th annual international symposium on computer architecture, 2022, pp. 59–71. [Online]. Available: https:...

    2022 doi

  21. [30]

    A quantum framework for protein binding-site structure prediction on utility-level quantum processors,

    Y . Zhang, Y . Yang, W. Martin, K. Lin, Z. Wang, C.-C. Lu, W. Jiang, R. Nussinov, J. Loscalzo, and Q. Guan, “A quantum framework for protein binding-site structure prediction on utility-level quantum processors,”Advanced Science, p. e13641, 2025. [Online]. Available: https://d...

    2025 doi

  22. [31]

    T. C.-Q. development team, “Cuda-q,” Mar. 2026. [Online]. Available: https://doi.org/10.5281/zenodo.19057431

    2026 doi

  23. [32]

    cuquantum sdk: A high-performance library for accelerating quantum science,

    H. Bayraktar, A. Charara, D. Clark, S. Cohen, T. Costa, Y .-L. L. Fang, Y . Gao, J. Guan, J. Gunnels, A. Haidaret al., “cuquantum sdk: A high-performance library for accelerating quantum science,” in2023 IEEE International Conference on Quantum Computing and Engineering (QCE),...

    2023 doi

  24. [33]

    Multi-gpu quantum circuit simulation and the impact of network performance,

    W. M. Brown, A. Ramesh, T. Lubinski, T. Nguyen, and D. E. B. Neira, “Multi-gpu quantum circuit simulation and the impact of network performance,”arXiv preprint arXiv:2511.14664, 2025. [Online]. Available: https://doi.org/10.1016/j.cpc.2026.110126

    2025 doi

  25. [34]

    Shaping up the protein folding funnel by local interaction: lesson from a structure prediction study,

    G. Chikenji, Y . Fujitsuka, and S. Takada, “Shaping up the protein folding funnel by local interaction: lesson from a structure prediction study,”Proceedings of the National Academy of Sciences, vol. 103, no. 9, pp. 3141–3146, 2006. [Online]. Available: https://doi.org/10.1073...

    2006 doi

  26. [35]

    Resource-efficient quantum algorithm for protein folding,

    A. Robert, P. K. Barkoutsos, S. Woerner, and I. Tavernelli, “Resource-efficient quantum algorithm for protein folding,”npj Quantum Information, vol. 7, no. 1, p. 38, 2021. [Online]. Available: https://doi.org/10.1038/s41534-021-00368-4

    2021 doi

  27. [36]

    A quantum alternating operator ansatz with hard and soft constraints for lattice protein folding,

    M. Fingerhuth, T. Babejet al., “A quantum alternating operator ansatz with hard and soft constraints for lattice protein folding,”arXiv preprint arXiv:1810.13411, 2018. [Online]. Available: https://doi.org/10.48550/arXiv.1810.13411

    2018 doi arXiv

  28. [37]

    Penalty methods for a variational quantum eigensolver,

    K. Kuroiwa and Y . O. Nakagawa, “Penalty methods for a variational quantum eigensolver,”Physical Review Research, vol. 3, no. 1, p. 013197, 2021. [Online]. Available: https://doi.org/10.1103/PhysRevResearch.3.013197

    2021 doi

  29. [38]

    Potential of quantum computing for drug discovery,

    Y . Cao, J. Romero, and A. Aspuru-Guzik, “Potential of quantum computing for drug discovery,”IBM Journal of Research and Development, vol. 62, no. 6, pp. 6:1–6:20, 2018. [Online]. Available: https://doi.org/10.1147/JRD.2018.2888987

    2018 doi

  30. [39]

    Highly accurate protein structure prediction with alphafold,

    J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A. ˇZ´ıdek, A. Potapenkoet al., “Highly accurate protein structure prediction with alphafold,”nature, vol. 596, no. 7873, pp. 583–589, 2021. [Online]. Available: https://doi.o...

    2021 doi

  31. [40]

    The prospects of quantum computing in computational molecular biology,

    C. Outeiral, M. Strahm, J. Shi, G. M. Morris, S. C. Benjamin, and C. M. Deane, “The prospects of quantum computing in computational molecular biology,”Wiley Interdisciplinary Reviews: Computational Molecular Science, vol. 11, no. 1, p. e1481, 2021. [Online]. Available: https:/...

    2021 doi

  32. [41]

    Variational quantum algorithms,

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincioet al., “Variational quantum algorithms,”Nature Reviews Physics, vol. 3, no. 9, pp. 625–644, 2021. [Online]. Available: https://doi.org/10.1038/s42254- 021-00348-9

    2021 doi

  33. [42]

    An adaptive variational algorithm for exact molecular simulations on a quantum computer,

    H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, “An adaptive variational algorithm for exact molecular simulations on a quantum computer,”Nature communications, vol. 10, no. 1, p. 3007,

  34. [43]

    Available: https://doi.org/10.1038/s41467-019-10988-2

    [Online]. Available: https://doi.org/10.1038/s41467-019-10988-2

    doi

  35. [44]

    Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, “Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets,” nature, vol. 549, no. 7671, pp. 242–246, 2017. [Online]. Available: https://doi.org/10.1038/na...

    2017 doi

  36. [45]

    Improving variational quantum optimization using cvar,

    P. K. Barkoutsos, G. Nannicini, A. Robert, I. Tavernelli, and S. Woerner, “Improving variational quantum optimization using cvar,”Quantum, vol. 4, p. 256, 2020. [Online]. Available: https://doi.org/10.22331/q- 2020-04-20-256

    2020 doi

  37. [46]

    Contextual subspace variational quantum eigensolver,

    W. M. Kirby, A. Tranter, and P. J. Love, “Contextual subspace variational quantum eigensolver,”Quantum, vol. 5, p. 456, 2021. [Online]. Available: https://doi.org/10.22331/q-2021-05-14-456

    2021 doi

  38. [47]

    Harnessing cuda-q’s mps for tensor network simulations of large-scale quantum circuits,

    G. Schieffer, S. Markidis, and I. Peng, “Harnessing cuda-q’s mps for tensor network simulations of large-scale quantum circuits,” in2025 33rd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP). IEEE, 2025, pp. 94–103. [Online]. Avai...

    2025 doi

  39. [48]

    Error estimates for extrapolations with matrix-product states,

    C. Hubig, J. Haegeman, and U. Schollw ¨ock, “Error estimates for extrapolations with matrix-product states,”Physical Review B, vol. 97, no. 4, p. 045125, 2018. [Online]. Available: https://doi.org/10.1103/PhysRevB.97.045125

    2018 doi

  40. [49]

    Classical benchmarks for variational quantum eigensolver simulations of the hubbard model,

    A. M. Alvertis, A. Khan, T. Iadecola, P. P. Orth, and N. Tubman, “Classical benchmarks for variational quantum eigensolver simulations of the hubbard model,”Quantum, vol. 9, p. 1748, 2025. [Online]. Available: https://doi.org/10.22331/q-2025-05-20-1748

    2025 doi

Pith tools

Reviewed July 12, 2026 · model on record in the stance chip above.