Pith. sign in

REVIEW 3 major objections 4 minor 60 references

Wave-function-based embedding with sample-based quantum diagonalization can drive molecular geometry optimization on real quantum hardware, reaching 33-orbital fragments (70 qubits) and matching classical references within a few picometers.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 21:01 UTC pith:Y6LNL62F

load-bearing objection First real-hardware EWF-SQD geometry optimization, with a careful workflow and honest scope; the 'sub-4-pm' accuracy claim is agreement between approximate methods, not absolute accuracy. the 3 major comments →

arxiv 2607.16410 v1 pith:Y6LNL62F submitted 2026-07-17 quant-ph physics.chem-ph

Quantum-Centric Geometry Optimization with Wave-Function-Based Embedding

Danil Kaliakin , Akhil Shajan , Fangchun Liang , Zhen Li , Kenneth M. Merz Jr This is my paper
classification quant-ph physics.chem-ph
keywords geometry optimizationwave-function-based embedding (EWF)sample-based quantum diagonalization (SQD)quantum-centric computinganalytic nuclear gradientsLambda equationsselected configuration interactionpotential energy surfaces
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Chemistry needs energies at many geometries, not just one point, but quantum-centric solvers based on sample-based quantum diagonalization (SQD) had only been demonstrated at single geometries. This paper puts SQD inside wave-function-based embedding (EWF), which fragments a molecule into atomic clusters, solves small fragments exactly and large fragments with SQD, and then assembles a global energy and an analytic nuclear gradient. The central claim is that this quantum-centric pipeline is stable enough to drive a geometry optimizer to a minimum, and that the optimized geometries agree with classical reference calculations to within a few picometers for most molecules. Demonstrated on molecules up to 29 atoms (menthone) and 82 molecular orbitals (benzidine) in the STO-3G basis, with the largest SQD fragment using 70 qubits, this is a step toward using quantum computers to explore potential energy surfaces rather than just single configurations.

Core claim

The paper reports that EWF-SQD geometry optimization converges on real quantum hardware. On a standard organic test set, EWF with an SCI solver reproduces unfragmented SCI geometries with RMSDs mostly below 0.02 Å (worst case allene, 0.033 Å). Replacing the SCI solver on large fragments with SQD—sampling single-layer LUCJ circuits, configuration recovery, ext-SQD expansion, then classical diagonalization—agrees with the EWF-SCI reference to 0.014 Å RMSD in the worst case and below 0.01 Å for most molecules. The largest fragments use 33 molecular orbitals (70 qubits) for benzidine and 30 (64 qubits) for menthone, molecules with 82 and 73 total MOs. The authors conclude SQD matches the classic

What carries the argument

The load-bearing mechanism is the energy-and-gradient assembly, not the quantum circuit itself. EWF fragments the molecule into atomic clusters with bath orbitals from a Schmidt decomposition of the mean-field density matrix, expanded with MP2 natural orbitals; clusters with ≤12 MOs are solved exactly with FCI, larger clusters with SCI or SQD. Because the assembled density is non-variational, the paper solves the Λ equations for effective cluster amplitudes and builds the analytic gradient from the relaxed density, using a corrected two-particle density to remove a spurious self-interaction term. SQD provides candidate configurations by sampling single-layer LUCJ circuits on hardware, applyi

Load-bearing premise

The accuracy claims rest on the truncated SCI reference (ε=10^-3) and the EWF fragmentation being unbiased; the allene benchmark, with a 0.04 Å maximum displacement in the fragmentation comparison and 0.018 Å in the SQD comparison, shows the 'few picometers' headline does not hold uniformly, so if those two errors share a systematic geometry bias the quoted accuracy overstates agreement with true equilibrium structures.

What would settle it

Optimize allene with unfragmented SCI at ε=10^-4 or ε=10^-5, or with a standard high-level method in the same basis, and compare with the reported EWF-(FCI,SCI) and EWF-(FCI,SQD) geometries; if the deviations shrink, the discrepancy is a reference-truncation artifact, and if they persist, the EWF/SQD geometry error itself is larger than the quoted few-picometer accuracy.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Geometry optimization with SQD inside EWF is feasible on real quantum hardware, not just simulators, for molecules up to 29 atoms in the STO-3G basis.
  • The largest SQD fragments reach 70 qubits / 33 MOs (benzidine) and 64 qubits / 30 MOs (menthone), putting systems beyond exact diagonalization within reach of quantum-centric potential-energy-surface exploration.
  • Replacing the classical SCI solver with SQD inside EWF does not change the required number of geometry-optimization steps by more than one, so the quantum solver is not the bottleneck in the optimization loop.
  • The analytic-gradient construction via Λ-relaxed densities makes the optimizer's convergence check and displacement step self-consistent, a prerequisite for stable minimization and, by extension, for molecular dynamics.
  • Within the stated limitations (STO-3G basis, single-layer ansatz, default optimizer threshold), the method's geometry accuracy is comparable to the classical SCI reference for all tested molecules except allene, where deviations are visibly larger.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the same Λ-equation gradient machinery is portable, it should also supply harmonic frequencies and response properties, which require the same relaxed-density technology; benchmarking those would test the gradient's accuracy more stringently than geometry optimization alone.
  • The per-step cost is 100,000 hardware shots per SQD fragment, and geometry scans accumulate many steps; reusing or warm-starting recovered bitstrings across nearby geometries is a natural cost-reduction experiment the paper does not run.
  • Allene repeatedly shows the largest deviations (0.033 Å fragmentation error, 0.014–0.018 Å SQD error), so it is the sharpest test case for whether the quoted few-picometer accuracy is an average artifact; re-running it with tighter SCI thresholds or a different reference method would clarify the source.
  • Fragmentation error and SQD solver error appear roughly additive in the worst case, suggesting that sub-picometer geometries will likely require improving the embedding bath and the ext-SQD expansion together, not just the quantum circuit.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper reports the first geometry optimizations using wave-function-based embedding (EWF) with sample-based quantum diagonalization (SQD) executed on real IBM quantum hardware. The workflow combines IAO-based fragmentation, MP2 natural-orbital bath expansion, FCI for fragments up to 12 MOs, SCI or SQD for larger fragments, assembled density-matrix gradients with Lambda-equation response, and the Sella optimizer. The authors benchmark EWF-(FCI,SCI) against unfragmented SCI for the first ten Baker-set molecules (Table 1), and then EWF-(FCI,SQD) against EWF-(FCI,SCI) for nine molecules, including menthone and benzidine, with the largest EWF fragment containing 33 MOs and mapped to 70 qubits (Table 2). They report sub-4 pm agreement between EWF-(FCI,SCI) and unfragmented SCI, and roughly 2 pm agreement between EWF-(FCI,SQD) and EWF-(FCI,SCI), concluding that quantum-centric EWF-SQD geometry optimization is feasible for molecules beyond exact diagonalization.

Significance. If the results hold, this is a substantive step toward using quantum-centric methods for potential-energy-surface exploration: it is the first EWF-SQD geometry optimization, it extends fragment-based QPU geometry optimization to 29-atom systems and to 70-qubit fragments, and it uses real IBM Heron processors rather than simulators. The manuscript is unusually transparent about numerical thresholds, circuit construction, shot counts, hardware choice, optimizer settings, and the software stack, and it includes an explicit disclaimer that quantum advantage is not demonstrated. These strengths are genuine. The main caveat, discussed below, is that the numerical accuracy claims are measured against an approximate classical reference that shares approximations with the tested method; this does not invalidate the feasibility demonstration but does require the accuracy statements to be qualified or backed by an independent reference.

major comments (3)
  1. [Results and Discussion, Tables 1 and 2; Eq. (3)] The central accuracy claim (sub-4 pm, and roughly 2 pm between SQD and SCI) is an agreement-with-reference statement, not an absolute accuracy statement. For the ten small molecules the reference is unfragmented SCI with epsilon_SCI = 1.0e-3 (Eq. 3); for menthone and benzidine the only reference is EWF-(FCI,SCI), which uses the same SCI truncation in each fragment. If the SCI truncation or the EWF fragmentation introduces a systematic geometry bias, the two methods could agree while both deviating from the true equilibrium geometry. The allene row already shows the error-chain magnitude: 0.040 A (4.0 pm) deviation between EWF-(FCI,SCI) and unfragmented SCI (Table 1), and 0.018 A (1.8 pm) between EWF-(FCI,SQD) and EWF-(FCI,SCI) (Table 2). The authors should either add an independent external reference for at least a subset of the small molecules (e.g., FCI or CCSD(T) geometries in STO-3G)
  2. [Methods, LUCJ Ansatz and Circuit Execution, Eqs. (5)-(6)] The LUCJ circuit parameters used to generate the SQD configurations are initialized from and then classically optimized against CCSD t2 amplitudes. The SQD sampling distribution is therefore not independent of a high-level classical calculation. The reported agreement between EWF-(FCI,SQD) and EWF-(FCI,SCI) validates the SQD protocol as deployed, including the classical initialization, but it does not by itself characterize the accuracy of the quantum-hardware-generated sampling. This is not fatal in view of the paper's explicit 'no quantum advantage' disclaimer, but it should be stated as a limitation. A useful control would be a comparison against classically simulated LUCJ sampling or against circuits with randomized/unoptimized parameters, to separate the hardware contribution from the classical CCSD-driven initialization.
  3. [Table 2 and Conclusions] For menthone and benzidine, no unfragmented reference is reported at all, so the scalability claim for these two systems rests entirely on the approximate chain unfragmented-SCI -> EWF-(FCI,SCI) -> EWF-(FCI,SQD). The paper should clearly state in the Results or Conclusions that the accuracy of the large-molecule geometries is not independently benchmarked, and that the 2-pm SQD/SCI agreement only measures the difference between two fragmented approximate solvers. This is a load-bearing point because the large-molecule demonstrations are the main scalability evidence.
minor comments (4)
  1. [Results, paragraph before Table 3] 'As can be seen from Table 2, all of the SQD simulations use more than 30 qubits' should refer to Table 3, which contains the qubit counts.
  2. [Methods, LUCJ Ansatz and Circuit Execution] The text says 'ibm marrakesh is utilized in simulations of benzamidine and menthone', but the molecule studied is benzidine throughout the rest of the paper. Please correct the name.
  3. [Eq. (6)] The citation number '54' appears inside the equation; move the citation to the surrounding text to avoid confusion with mathematical notation.
  4. [References] Reference 4 duplicates Reference 2; consider consolidating or citing one version.

Circularity Check

0 steps flagged

No identity-level circularity: SQD is benchmarked against an independently constructed SCI reference, and the only fitted input (LUCJ initialization from CCSD t2) is not asserted as the predicted output.

full rationale

The paper is an empirical benchmark, not a derivation that reduces to its inputs. The EWF energy and gradient follow a standard Lagrangian/Z-vector construction (Eq. 7 and the Lambda-equation section); the "EWF-consistent" density is constructed so its contraction reproduces E[gamma1, lambda2] by design, which is a consistency condition in gradient theory, not a scientific prediction. The only fitted element is the LUCJ parameter initialization from classical CCSD t2 amplitudes (Eqs. 5-6), but the SQD result is obtained by diagonalizing the Hamiltonian in the sampled subspace and is compared to an independently generated SCI reference; nothing in the equations forces these two geometry optimizations to coincide. The benchmark for menthone/benzidine uses EWF-(FCI,SCI) as reference, which shares the EWF fragmentation and the epsilon_SCI=1e-3 truncation (Eq. 3), so absolute accuracy for those two molecules is not independently certified; this is a benchmarking limitation and correctness risk rather than circularity. The stated "two/four picometer" deviations also appear inconsistent with the tabulated allene values (max 0.018 A = 18 pm in Table 2), another correctness issue, not circularity. Self-citations to prior EWF/SQD work are contextual and not load-bearing, and no uniqueness theorem or external ansatz is invoked to force the authors' choices.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

The central claim rests on EWF's systematic improvability, the adequacy of truncated SCI as a reference, the ability of a CCSD-initialized one-layer LUCJ circuit to sample chemically relevant configurations, and the validity of applying CC Λ-equation gradient theory to the assembled EWF density. None of these is verified by an independent experiment or exact calculation in this paper.

free parameters (6)
  • Bath occupation threshold η = 1×10^-5
    Controls fragment size in EWF by retaining MP2 natural orbitals with occupation above η; chosen globally with no sensitivity analysis (Methods, EWF).
  • SCI selection cutoff ε_SCI = 1.0×10^-3
    Truncates the variational subspace for both reference SCI and EWF-(FCI,SCI) calculations (Eq. 3); the paper relies on this default threshold as an accuracy anchor.
  • LUCJ circuit parameters (U, J) = Optimized via L-BFGS-B to match classical CCSD t2 amplitudes (Eq. 6)
    The quantum sampling distribution is fitted to a classical high-level calculation; this is central to the SQD agreement and weakens the independence of the quantum result.
  • ext-SQD CI coefficient threshold = c > 1×10^-5
    Selects dominant configurations for the final ext-SQD diagonalization; chosen ad hoc (Methods, SQD).
  • SQD recovery convergence thresholds = 1×10^-8 (energy), 1×10^-5 (occupancy)
    Stopping criteria for configuration recovery; numerical tolerances, not physical inputs (Methods, SQD).
  • LUCJ layer count L = 1
    Single-layer ansatz fixed to limit circuit depth; expressiveness not independently benchmarked (Eq. 4).
axioms (5)
  • domain assumption The EWF fragment+bath decomposition from mean-field density and MP2 natural orbitals is systematically improvable and converges to the full molecule as η→0.
    Invoked in Methods (EWF); underpins the entire fragmentation. Relies on prior work (refs 27, 39); no sensitivity study in this paper.
  • domain assumption SCI with ε_SCI = 1×10^-3 is an adequate reference for optimized geometries.
    Used for the unfragmented reference and the EWF-(FCI,SCI) benchmark (Eq. 3). Truncated CI; not benchmarked against FCI or experiment here.
  • ad hoc to paper A one-layer LUCJ circuit initialized from CCSD t2 amplitudes samples the configurations needed for near-FCI energies in each fragment.
    Eqs. 4–6; the circuit family and initialization are specific to this work's SQD protocol and are not proven to be unbiased.
  • domain assumption The EWF density assembled from fragment RDMs, relaxed via Λ equations, yields a gradient accurate enough for Sella convergence.
    Gradient section; standard CC analytic-gradient theory (ref 37) applied to EWF, but no direct gradient check against finite differences is reported.
  • domain assumption The STO-3G minimal basis set is sufficient to demonstrate geometry-optimization feasibility.
    Stated in Introduction and Conclusions; limits generalization to practical basis sets.

pith-pipeline@v1.3.0-alltime-deepseek · 14776 in / 16086 out tokens · 142578 ms · 2026-08-01T21:01:09.156970+00:00 · methodology

0 comments
read the original abstract

The EWF-(FCI,SQD) method, a wave-function-based embedding approach combining full configuration interaction (FCI) and sample-based quantum diagonalization (SQD), is a promising new tool for the simulation of molecular systems. However, applications of EWF-(FCI,SQD) have so far been limited to single-point calculations, whereas the study of complex chemical processes requires the ability to explore potential energy surfaces. In this work, we demonstrate geometry optimization with EWF-(FCI,SQD), scaling our simulations to molecules as large as menthone and benzidine within the STO-3G basis set. Without fragmentation, these systems comprise 73 and 82 molecular orbitals respectively, presenting an intractable Hilbert space for conventional exact or high-level subspace solvers and establishing a clear necessity for fragmentation-based methodologies. The underlying fragment SQD simulations in the EWF-(FCI,SQD) geometry optimizations use up to 70 qubits. The resulting geometries show exceptional accuracy relative to the classical reference, with deviations below 4 picometers.

Figures

Figures reproduced from arXiv: 2607.16410 by Akhil Shajan, Danil Kaliakin, Fangchun Liang, Kenneth M. Merz Jr, Zhen Li.

Figure 1
Figure 1. Figure 1: Overall workflow of the EWF geometry optimization framework. ASE together with Sella drives the geometry optimization by repeatedly requesting the electronic energy and analytical gradient from the geometry driver. For fragmented calculations, EWF clusters are constructed in the IAO basis using Vayesta, expanded with MP2 natural orbitals, and solved using FCI or SQD/SCI depending on the fragment size. The … view at source ↗
Figure 2
Figure 2. Figure 2: Example qubit layout for the largest EWF cluster in benzidine (33 molecular [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overlay of the optimized geometries for each molecule. The unfragmented SCI [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Overlay of the optimized geometries for each molecule. The EWF-(FCI,SCI) [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 5 canonical work pages

  1. [1]

    Sung and Maika Takita and Minh C

    Javier Robledo-Moreno and Mario Motta and Holger Haas and Ali Javadi-Abhari and Petar Jurcevic and William Kirby and Simon Martiel and Kunal Sharma and Sandeep Sharma and Tomonori Shirakawa and Iskandar Sitdikov and Rong-Yang Sun and Kevin J. Sung and Maika Takita and Minh C. Tran and Seiji Yunoki and Antonio Mezzacapo , title =. Science Advances , volume...

    2025

  2. [2]

    Systematic Improvability in Quantum Embedding for Real Materials , author =. Phys. Rev. X , volume =. 2022 , month =. doi:10.1103/PhysRevX.12.011046 , url =

    doi:10.1103/physrevx.12.011046 2022

  3. [3]

    Pople, J. A. and Krishnan, R. and Schlegel, H. B. and Binkley, J. S. , title =. International Journal of Quantum Chemistry , year=. doi:https://doi.org/10.1002/qua.560160825 , url =

    work page doi:10.1002/qua.560160825

  4. [4]

    2017 , month =

    Hjorth Larsen, Ask and Jørgen Mortensen, Jens and Blomqvist, Jakob and Castelli, Ivano E and Christensen, Rune and Dułak, Marcin and Friis, Jesper and Groves, Michael N and Hammer, Bjørk and Hargus, Cory and Hermes, Eric D and Jennings, Paul C and Bjerre Jensen, Peter and Kermode, James and Kitchin, John R and Leonhard Kolsbjerg, Esben and Kubal, Joseph a...

    2017

  5. [5]

    2025 , eprint=

    Closed-loop calculations of electronic structure on a quantum processor and a classical supercomputer at full scale , author=. 2025 , eprint=

    2025

  6. [6]

    and Whaley, K

    Motta, Mario and Sung, Kevin J. and Whaley, K. Birgitta and Head-Gordon, Martin and Shee, James , title =. Chemical Science , volume =. 2023 , month =. doi:10.1039/d3sc02516k , url =

    doi:10.1039/d3sc02516k 2023

  7. [7]

    Garrison and Jennifer R

    Abdullah Ash Saki and Stefano Barison and Bryce Fuller and James R. Garrison and Jennifer R. Glick and Caleb Johnson and Antonio Mezzacapo and Javier Robledo-Moreno and Max Rossmannek and Paul Schweigert and Iskandar Sitdikov and Kevin J. Sung , title =

  8. [8]

    2024 , eprint=

    Quantum-centric computation of molecular excited states with extended sample-based quantum diagonalization , author=. 2024 , eprint=

    2024

  9. [9]

    Wan-Hsuan Lin and Fangchun Liang and Mario Motta and Haimeng Zhang and Kenneth M. Merz Jr. and Kevin J. Sung , title =. arXiv preprint arXiv:2511.22476 , year =

    arXiv

  10. [10]

    2026 , eprint=

    ffsim: Faster simulation of fermionic quantum circuits , author=. 2026 , eprint=

    2026

  11. [11]

    2026 , eprint=

    Crossing the 12,000-atom barrier with heterogeneous quantum-classical supercomputing: quantum chemistry of protein-ligand complexes , author=. 2026 , eprint=

    2026

  12. [12]

    and Jette, Morris A

    Yoo, Andy B. and Jette, Morris A. and Grondona, Mark. SLURM: Simple Linux Utility for Resource Management. Job Scheduling Strategies for Parallel Processing. 2003

    2003

  13. [13]

    2026 , eprint=

    Quantum Computations on Fusion Blanket Molten Salts , author=. 2026 , eprint=

    2026

  14. [14]

    2026 , eprint=

    GPU-Accelerated Selected Basis Diagonalization with Thrust for SQD-based Algorithms , author=. 2026 , eprint=

    2026

  15. [15]

    2026 , month =

    MPICH User's Guide, Version 5.0.1 , author =. 2026 , month =

    2026

  16. [16]

    2024 , organization =

    Clang: A C-Language Family Frontend for LLVM, Version 18.1.8 , author =. 2024 , organization =

    2024

  17. [17]

    2023 , organization =

    NVIDIA CUDA Toolkit, Version 12.3 , author =. 2023 , organization =

    2023

  18. [18]

    2025 , note =

    Xianyi Zhang and Martin Kroeker and. 2025 , note =

    2025

  19. [19]

    Quantum-selected configuration interaction: Classical diagonalization of Hamiltonians in subspaces selected by quantum computers , author =. Phys. Rev. Res. , volume =. 2026 , month =. doi:10.1103/dmn4-snfx , url =

    doi:10.1103/dmn4-snfx 2026

  20. [20]

    Sung and Maika Takita and Minh C

    Javier Robledo-Moreno and Mario Motta and Holger Haas and Ali Javadi-Abhari and Petar Jurcevic and William Kirby and Simon Martiel and Kunal Sharma and Sandeep Sharma and Tomonori Shirakawa and Iskandar Sitdikov and Rong-Yang Sun and Kevin J. Sung and Maika Takita and Minh C. Tran and Seiji Yunoki and Antonio Mezzacapo , title =. Sci. Adv. , volume =. 202...

    2025

  21. [21]

    Accurate quantum-centric simulations of intermolecular interactions , author=. Commun. Phys. , volume=. 2025 , publisher=

    2025

  22. [22]

    Quantum-Centric Computational Study of Methylene Singlet and Triplet States , author=. J. Chem. Theory Comput. , volume=. 2025 , publisher=

    2025

  23. [23]

    2025 , month =

    Nützel, Ludwig and Gresch, Alexander and Hehn, Lukas and Marti, Lucas and Freund, Robert and Steiner, Alex and Marciniak, Christian D and Eckstein, Timo and Stockinger, Nina and Wolf, Stefan and Monz, Thomas and Kühn, Michael and Hartmann, Michael J , title =. 2025 , month =. doi:10.1088/2058-9565/ad9ed3 , url =

    work page doi:10.1088/2058-9565/ad9ed3 2025

  24. [24]

    Implicit solvent sample-based quantum diagonalization , author=. J. Phys. Chem. , volume=. 2025 , publisher=

    2025

  25. [25]

    Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer , author=. Phys. Chem. Chem. Phys. , volume=. 2025 , publisher=

    2025

  26. [26]

    arXiv preprint arXiv:2508.02578 , year=

    Quantum chemistry with provable convergence via randomized sample-based quantum diagonalization , author=. arXiv preprint arXiv:2508.02578 , year=

    arXiv

  27. [27]

    ACS omega , volume=

    Enhancing Accuracy of Quantum-Selected Configuration Interaction Calculations Using Multireference Perturbation Theory: Application to Aromatic Molecules , author=. ACS omega , volume=. 2025 , publisher=

    2025

  28. [28]

    arXiv preprint arXiv:2510.23154 , year=

    Size-consistent implementation of Hamiltonian simulation-based quantum-selected configuration interaction method for the supramolecular approach , author=. arXiv preprint arXiv:2510.23154 , year=

    arXiv

  29. [29]

    ACS Omega , volume =

    Shirai, Soichi and Tseng, Shih-Yen and Iwakiri, Hokuto and Horiba, Takahiro and Hirai, Hirotoshi and Koh, Sho , title =. ACS Omega , volume =. 2025 , doi =

    2025

  30. [30]

    arXiv e-prints , pages=

    Surface reaction simulations for battery materials through sample-based quantum diagonalization and local embedding , author=. arXiv e-prints , pages=

  31. [31]

    and Van, Richard and Pickard, Frank C

    Shivpuje, Saurabh and Gujarati, Tanvi P. and Van, Richard and Pickard, Frank C. IV and Friedhoff, Triet and Liepuoniute, Ieva and Davis, Wade and Jones, Gavin O. and Galda, Alexey , title =. Journal of Chemical Theory and Computation , volume =. 2026 , doi =

    2026

  32. [32]

    arXiv preprint arXiv:2505.00914 , year=

    Symmetry-adapted sample-based quantum diagonalization: Application to lattice model , author=. arXiv preprint arXiv:2505.00914 , year=

    Pith/arXiv arXiv

  33. [33]

    arXiv preprint arXiv:2512.04962 , year=

    Convergence of sample-based quantum diagonalization on a variable-length cuprate chain , author=. arXiv preprint arXiv:2512.04962 , year=

    arXiv

  34. [34]

    arXiv preprint arXiv:2512.01012 , year=

    From Promise to Practice: Benchmarking Quantum Chemistry on Quantum Hardware , author=. arXiv preprint arXiv:2512.01012 , year=

    arXiv

  35. [35]

    Badar, Mohammad Sufian and Shamsi, Shazmeen and Ahmed, Jawed and Alam, Md. Afshar. Molecular Dynamics Simulations: Concept, Methods, and Applications. Transdisciplinarity. 2022. doi:10.1007/978-3-030-94651-7_7

    work page doi:10.1007/978-3-030-94651-7_7 2022

  36. [36]

    Journal of Computational Chemistry , volume =

    Alvarez, Jorge Alberto Sanchez and Calaminici, Patrizia , title =. Journal of Computational Chemistry , volume =. doi:https://doi.org/10.1002/jcc.70243 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.70243 , year =

    work page doi:10.1002/jcc.70243

  37. [37]

    Journal of Chemical Theory and Computation , volume=

    Geometry optimization: a comparison of different open-source geometry optimizers , author=. Journal of Chemical Theory and Computation , volume=. 2023 , publisher=

    2023

  38. [38]

    Journal of Chemical Theory and Computation , year=

    Quantum-centric alchemical free energy calculations , author=. Journal of Chemical Theory and Computation , year=

  39. [39]

    arXiv preprint arXiv:2604.09857 , year=

    Protein-Ligand Free Energy Perturbation on Quantum Hardware , author=. arXiv preprint arXiv:2604.09857 , year=

    Pith/arXiv arXiv

  40. [40]

    Proceedings of the National Academy of Sciences of the United States of America , volume=

    Localized sample-based quantum diagonalization for strongly correlated chemistry , author=. Proceedings of the National Academy of Sciences of the United States of America , volume=

  41. [41]

    Toward quantum-centric simulations of extended molecules: Sample-based quantum diagonalization enhanced with density matrix embedding theory , author=. J. Chem. Theory Comput. , volume=. 2025 , publisher=

    2025

  42. [42]

    Shajan, Akhil and Kaliakin, Danil and Liang, Fangchun and Pellegrini, Thaddeus and Doga, Hakan and Bhowmik, Subhamoy and Das, Susanta and Mezzacapo, Antonio and Motta, Mario and Merz, Kenneth M. Jr. , title =. Journal of Chemical Theory and Computation , volume =. 2026 , doi =

    2026

  43. [43]

    arXiv preprint arXiv:2511.22158 , year=

    Quantum Simulation of Ligand-like Molecules through Sample-based Quantum Diagonalization in Density Matrix Embedding Framework , author=. arXiv preprint arXiv:2511.22158 , year=

    Pith/arXiv arXiv

  44. [44]

    Digital Discovery , volume =

    Bierman, Joel and Liu, Yuan , title =. Digital Discovery , volume =. 2026 , month =. doi:10.1039/d5dd00416k , url =

    doi:10.1039/d5dd00416k 2026

  45. [45]

    , title =

    Nusspickel, Max and Ibrahim, Basil and Booth, George H. , title =. J. Chem. Theory Comput. , volume =. 2023 , doi =

    2023

  46. [46]

    Journal of Computational Chemistry , volume =

    Baker, Jon , title =. Journal of Computational Chemistry , volume =. doi:https://doi.org/10.1002/jcc.540140910 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.540140910 , year =

    work page doi:10.1002/jcc.540140910

  47. [47]

    Journal of Chemical Theory and Computation , volume=

    Large-Scale Efficient Molecule Geometry Optimization with Hybrid Quantum--Classical Computing , author=. Journal of Chemical Theory and Computation , volume=. 2026 , publisher=

    2026

  48. [48]

    , title =

    Eriksen, Janus J. , title =. The Journal of Physical Chemistry Letters , volume =. 2021 , doi =

    2021

  49. [49]

    and Freeman, C

    Tubman, Norm M. and Freeman, C. Daniel and Levine, Daniel S. and Hait, Diptarka and Head-Gordon, Martin and Whaley, K. Birgitta , title =. Journal of Chemical Theory and Computation , volume =. 2020 , doi =

    2020

  50. [50]

    Coupled-cluster theory in quantum chemistry , author =. Rev. Mod. Phys. , volume =. 2007 , month =. doi:10.1103/RevModPhys.79.291 , url =

    doi:10.1103/revmodphys.79.291 2007

  51. [51]

    and Sargsyan, Khachik and Najm, Habib N

    Hermes, Eric D. and Sargsyan, Khachik and Najm, Habib N. and Zádor, Judit , title =. Journal of Chemical Theory and Computation , volume =. 2022 , doi =

    2022

  52. [52]

    and Ma, Dongxia and Olsen, Jeppe and Gagliardi, Laura and de Jong, Wibe A

    Vogiatzis, Konstantinos D. and Ma, Dongxia and Olsen, Jeppe and Gagliardi, Laura and de Jong, Wibe A. , title = ". The Journal of Chemical Physics , volume =. 2017 , month =. doi:10.1063/1.4989858 , url =

    doi:10.1063/1.4989858 2017

  53. [53]

    Journal of Chemical Theory and Computation , volume =

    Gao, Hong and Imamura, Satoshi and Kasagi, Akihiko and Yoshida, Eiji , title =. Journal of Chemical Theory and Computation , volume =. 2024 , doi =

    2024

  54. [54]

    Scott and Martínez, Todd J

    Fales, B. Scott and Martínez, Todd J. , title =. Journal of Chemical Theory and Computation , volume =. 2020 , doi =

    2020

  55. [55]

    Dynamical decoupling for superconducting qubits: A performance survey , author=. Phys. Rev. Appl. , volume=. 2023 , publisher=

    2023

  56. [56]

    PyCI: A Python-scriptable library for arbitrary determinant CI , author=. J. Chem. Theory Comput. , volume=. 2024 , publisher=

    2024

  57. [57]

    Wiley Interdisciplinary Reviews: Computational Molecular Science , volume=

    PySCF: the Python-based simulations of chemistry framework , author=. Wiley Interdisciplinary Reviews: Computational Molecular Science , volume=. 2018 , publisher=

    2018

  58. [58]

    The Journal of chemical physics , volume=

    Recent developments in the PySCF program package , author=. The Journal of chemical physics , volume=. 2020 , publisher=

    2020

  59. [59]

    Forces in Molecules , author =. Phys. Rev. , volume =. 1939 , month =. doi:10.1103/PhysRev.56.340 , url =

    doi:10.1103/physrev.56.340 1939

  60. [60]

    Journal of molecular modeling , volume=

    The Hellmann-Feynman theorem: a perspective , author=. Journal of molecular modeling , volume=. 2018 , publisher=

    2018