Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Scalable Neural Quantum State based Kernel Polynomial Method for Optical Properties from the First Principle

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read This paper claims that combining autoregressive neural-network ground states with the kernel polynomial method reproduces exact absorption spectra for molecules with up to 52 electrons, using only the ground state.

desk verdict Original NQS+KPM combination for optical spectra, but the manuscript never explains how the KPM moments are computed from the neural ground state, which is a load-bearing gap; the code may help, but the text is incomplete. read the letter →

arxiv 2506.07430 v1 pith:2YMFD6DJ submitted 2025-06-09 physics.chem-ph cond-mat.dis-nn

Wei Liu , Rui-Hao Bi , Wenjie Dou This is my paper
classification physics.chem-phcond-mat.dis-nn
keywords neuralquantumstateskernelpolynomialmethodabsorptionspectravariationalMonteCarloautoregressivesamplingsecondquantizationChebyshevmomentsfullconfigurationinteraction
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 aims to make optical absorption spectra of molecules with dozens of electrons computationally accessible at full configuration interaction (FCI) accuracy. It does so by computing the spectrum from the ground state alone, using the kernel polynomial method to build the dipole autocorrelation function from Chebyshev moments, and it represents the ground state with an autoregressive neural-network quantum state trained by variational Monte Carlo. The reported results cover molecules from 8 to 52 electrons, with spectra that match FCI for water and ammonia and, the authors argue, FCI-level ground states for larger systems where no exact reference exists. If correct, this means spectra for strongly correlated molecules no longer require storing or diagonalizing excited states, reducing both runtime and memory.

What carries the argument

The load-bearing object is the Chebyshev moment sequence $\Omega_n = \langle 0|\hat{\mu}T_n(\tilde{H})\hat{\mu}|0\rangle$ evaluated recursively from the ground state, so that the spectrum is a polynomial expansion of the dipole autocorrelation function. The ground state is provided by an autoregressive neural-network quantum state whose amplitude is a product of conditional probabilities, enabling exact parallel sampling with a number-conserving constraint, and whose local energy is computed on GPUs from a tensorized Hamiltonian. A Jackson kernel multiplies the moments to control truncation error, and the empirically chosen number of moments is $N_\Omega = 400|e_g|$.

What would settle it

A converged DMRG or selected CI calculation of the absorption spectrum of CNa2O3 in the STO-3G basis, compared peak-by-peak with the sNQS-KPM spectrum; disagreement in peak positions beyond linewidth would disprove the FCI-level claim for large molecules.

Watch

Extended reading notes

Core claim

The central claim is that the pair (neural quantum state, kernel polynomial method) computes absorption spectra at FCI-level precision using only the ground state. The spectrum follows from moments $\Omega_n = \langle 0|\hat{\mu}T_n(\tilde{H})\hat{\mu}|0\rangle$, obtained by the Chebyshev recursion $|\alpha_{n+1}\rangle = 2\tilde{H}|\alpha_n\rangle - |\alpha_{n-1}\rangle$ starting from the dipole-excited state $|\alpha\rangle = \hat{\mu}|0\rangle$. Because the method never needs eigenstates, it avoids the exponential memory of configuration interaction. The authors validate against FCI for small molecules, report good peak placement, and apply the pipeline to molecules with up to 52 electrons and Hamiltonians with over one million terms, claiming ground-state energies that stay within about $10^{-4}$ Hartree of available references.

Load-bearing premise

The entire pipeline inherits the accuracy of the neural ground state: for the largest molecules (44 and 52 electrons), the paper asserts FCI-level accuracy without an FCI calculation to test against.

Editorial extensions

If this is right

  • With an FCI-quality ground state, absorption spectra come without storing any excited state; the memory cost drops to the Hamiltonian and the moment recursion.
  • The $O(N^4)$ scaling measured on H2 chains implies the method's advantage over exact diagonalization grows with molecule size.
  • Any two-point correlation function that can be written as $\langle 0| A T_n(\tilde H) B |0\rangle$ becomes accessible with the same machinery.
  • Hamiltonians with millions of Pauli terms are no longer a barrier, since local energy is computed term-wise in parallel across GPUs.
  • The empirical moment count $N_\Omega = 400|e_g|$ offers a practical, size-consistent recipe for choosing the resolution.

Reading between the lines

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

  • The spectral accuracy is only as good as the dipole-weighted part of the approximate ground state; agreement in total energy does not guarantee that the low-lying transition moments are correct, so spectra for the largest molecules should be treated as predictions pending independent checks.
  • Because the KPM moments are correlation functions, the same pipeline could yield conductivities, spin correlations, or higher-order response functions by swapping the dipole operator, provided the operator is cheap to apply in the autoregressive basis.
  • The number-conserving sampling constraint and the unique-sample pruning are what make 52 electrons feasible; pushing to larger systems will likely require the same two tricks rather than a larger network alone.
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 / 4 minor

Summary. The paper proposes a scalable neural quantum state (NQS) approach combined with the kernel polynomial method (KPM) to compute molecular absorption spectra. An autoregressive NQS is used to approximate the ground state of the ab initio electronic Hamiltonian in second quantization, and the dipole autocorrelation function is expressed through Chebyshev moments Ω_n = <0|μ T_n(H~) μ|0> (Eq. 26). The authors report ground-state energies for molecules with up to 52 electrons (CNa2O3) and claim FCI-level precision for the resulting spectra, with spectral comparisons for H2O and NH3 against truncated FCI baselines. The paper emphasizes parallel batch autoregressive sampling, GPU-based local energy computation, and a recursive moment evaluation that avoids storing excited states.

Significance. If correct, the method would extend NQS-based quantum chemistry from ground states to optical spectra for systems of roughly 50 electrons, beyond the reach of FCI and competitive with approximate excited-state methods. The paper's contributions include a parallel sampling scheme, a memory-efficient local energy tensor representation, and public code links. However, the manuscript's central algorithmic gap - the missing specification of how the KPM moments are computed from the NQS - currently prevents verification of the headline claim, and the spectral validation against exact references is limited to two small molecules with truncated FCI baselines.

major comments (3)
  1. [3 Methods, KPM for absorption spectra (Eqs. 30-31)] The manuscript does not specify how the states |α_n> = T_n(H~)|α> are represented or how the overlaps <α_n|α_n> and <α_{n+1}|α_n> in Eq. (31) are computed. The only wavefunction representation described in the paper is the autoregressive ground-state NQS; |α_n> is not a ground state and the sampling machinery in Section 3 (Variational Monte Carlo optimization) applies only to the probability distribution |Ψ(x,θ)|^2 of the ground-state ansatz. Evaluating <α_n|α_n> by sampling would require either a generator for |α_n|^2 or pointwise values α_n(x) for sampled x, and the recurrence (30) makes each α_n depend on α_{n-1} evaluated at K Pauli-flipped configurations (K=1,625,991 for CNa2O3). A direct implementation would therefore have cost growing rapidly with n, inconsistent with the near-linear scaling in Fig. 4b. The statement in the Introduction that 'only the ground state is needed' is unsupported by the algorithmic description; an additional representation or estimator for the |α_n> states is required. This gap is load-bearing for the central claim of computing spectra via Eq. (26).
  2. [1 Results, Table 1] The H2S row in Table 1 lists an HF ground-state energy of -349.3114 Hartree, about 45 Hartree above the CCSD and FCI values of -394.3546 Hartree. For the STO-3G basis, the HF energy should be within a few tenths of a Hartree of the correlated result; the tabulated value is unphysical and likely a data-entry error. Because Table 1 is the primary evidence for the ground-state accuracy of sNQS-KPM, the authors should correct this entry and clarify how the mean absolute errors in the last row are computed (which molecules are included for each method).
  3. [1 Results, 'Absorption spectra of different molecules' and Fig. 3] The only spectral baselines shown are for H2O and NH3, and those FCI references are obtained by diagonalizing only the lowest 1000 eigenstates of the full FCI matrix. The authors acknowledge minor discrepancies in relative peak heights arising from this truncation, so the comparison is indicative rather than exact. For the larger molecules in Fig. 3 (C2H4O, Li2CO3, C6H8, CNa2O3), no spectral reference is provided, so the claim of FCI-level precision for absorption spectra is not directly validated. The ground-state energy agreement in Table 1 is necessary but not sufficient: the KPM spectrum depends on the moments Ω_n via Eq. (26), and the Jackson kernel and truncation at N_Ω introduce additional approximations. The authors should either provide a spectral baseline for at least one molecule beyond H2O and NH3 using a high-level method (e.g., DMRG or FCI in a reduced space) or qualify the claim.
minor comments (4)
  1. [3 Methods, Eq. (21)] The Jackson kernel formula appears to be misprinted: the standard expression is (N-n+1) cos(π n/(N+1)) + sin(π n/(N+1)) cot(π/(N+1)) divided by (N+1), whereas the text has (N-n-1). Please check whether this is a typo in the formula or in the implementation.
  2. [1 Results, 'Resolution of absorption spectra'] The text states that the computation time for the moments is approximately linear in the number of moments 'as shown in Fig. 3b'; the correct reference appears to be Fig. 4b, which displays the time versus N_Ω relationship.
  3. [1 Results, 'Resolution of absorption spectra', Eq. (11)] The empirical formula N_Ω = 400|e_g| mixes a dimensionless count with an energy in Hartree; the authors should clarify its domain of validity (e.g., basis set, energy range) or present it as a practical guideline rather than a universal rule.
  4. [1 Results, Fig. 3 caption] The caption says 'The black dotted line represents the absorption spectra of H2O and NH3, obtained by diagonalizing the smallest 1000 eigenvalues...' but the figure contains separate panels for H2O and NH3; please clarify whether the black dotted line is the FCI reference for each panel.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is a standard KPM expansion around an independently benchmarked NQS ground state.

full rationale

The paper's central claim—that a KPM expansion of the dipole autocorrelation function can be built from an NQS ground state—contains no step in which a target output is equivalent by construction to an input. The KPM relations (Eqs. 5–6 and 21–26) are textbook identities: moments Ω_n = ⟨0|μ†T_n(H~)μ|0⟩ are exactly related to the Chebyshev expansion of the absorption spectrum, and the recursion (Eqs. 30–31) is the standard three-term Chebyshev recurrence. No 'prediction' is hidden in these definitions. The ground state |0⟩ is obtained variationally and benchmarked against independent FCI and CCSD references in Table 1; for molecules without FCI data, the FCI-level claim is an extrapolation, not a tautology. The empirical rule N_Ω = 400|e_g| (Eq. 11) is a convergence heuristic for the number of moments; it does not fix spectral peak positions, and Fig. 4a demonstrates explicit convergence with increasing N_Ω. The authors' self-citations (Refs. 16 and 17) accompany standard Kubo-formalism citations and are not load-bearing. A separate concern—that the paper does not spell out a tractable Monte Carlo estimator for ⟨α_n|α_n⟩ from the autoregressive NQS—is an algorithmic completeness and correctness issue, not a circularity, so under the stated hard rules it is not counted here. Overall, no circular derivation is present.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The method relies on standard quantum-chemistry and KPM machinery. The only genuinely fitted quantity is the empirical moment-count prefactor, and the strongest unproven ingredient is ansatz expressiveness for molecules without FCI references.

free parameters (2)
  • N_Omega prefactor = 400
    Eq. 11 sets N_Omega = 400|e_g|. The coefficient 400 is proposed as an empirical formula without derivation; it controls spectral resolution and computational cost.
  • FCI eigenstate truncation for baselines = 1000
    FCI baseline spectra for H2O and NH3 are computed from the smallest 1000 eigenvalues and eigenvectors. The paper concedes that this truncation changes relative peak heights, yet the truncation is used as the FCI reference.
assumptions (5)
  • domain assumption Born-Oppenheimer separation and second-quantized ab initio Hamiltonian in a finite STO-3G basis
    All results are computed within this approximation; basis-set incompleteness is acknowledged in the Discussion but not corrected.
  • standard math Jordan-Wigner mapping of fermionic operators to Pauli operators
    Used throughout to define the qubit Hamiltonian in Eqs. 13-14.
  • standard math Kernel polynomial method with Jackson kernel converges to the dipole autocorrelation spectrum
    Equations 5, 21, and 24 are taken from the KPM literature, Ref. [20], and rely on eigenvalue rescaling and sufficient moments.
  • domain assumption Linear-response Kubo formalism relates the dipole autocorrelation function to the absorption spectrum
    Eqs. 3 and 22 assume linear response and the dipole approximation; this is a physical modeling choice, not derived in the paper.
  • domain assumption Autoregressive neural-network ansatz can represent the FCI ground state for the molecules studied
    The claim of FCI-level spectra depends on this expressiveness and convergence assumption. It is tested directly only on small molecules with available FCI references.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Scalable Neural Quantum State based Kernel Polynomial Method for Optical Properties from the First Principle." pith.science (2026). https://pith.science/paper/2YMFD6DJ

@misc{pith2026250607430,
  author       = {Pith},
  title        = {Pith review of: Scalable Neural Quantum State based Kernel Polynomial Method for Optical Properties from the First Principle},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2YMFD6DJ}},
  note         = {Machine review of arXiv:2506.07430}
}
read the original abstract

Variational optimization of neural-network quantum state representations has achieved FCI-level accuracy for ground state calculations, yet computing optical properties involving excited states remains challenging. In this work, we present a neural-network-based variational quantum Monte Carlo approach for ab-initio absorption spectra. We leverage parallel batch autoregressive sampling and GPU-supported local energy parallelism to efficiently compute ground states of complex systems. By integrating neural quantum ground states with the kernel polynomial method, our approach accurately calculates absorption spectra for large molecules with over 50 electrons, achieving FCI-level precision. The proposed algorithm demonstrates superior scalability and reduced runtime compared to FCI, marking a significant step forward in optical property calculations for large-scale quantum systems.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stochastic resolution of identity to CC2 for large systems: Excited-state gradients and derivative couplings

    physics.chem-ph 2025-09 conditional novelty 5.0 of 10

    Partial stochastic-RI CC2 computes excited-state gradients and derivative couplings with quartic scaling and manageable noise, extending CC2 to larger molecules.

Reference graph

Works this paper leans on

45 extracted references · 41 canonical work pages · cited by 1 Pith paper

  1. [1]

    Proceedings of the National Academy of Sciences102(19), 6648–6653 (2005)

    Friesner, R.A.: Ab initio quantum chemistry: Methodology and applications. Proceedings of the National Academy of Sciences102(19), 6648–6653 (2005)

    work page 2005

  2. [2]

    Nature Reviews Chemistry7(10), 692–709 (2023)

    Hermann, J., Spencer, J., Choo, K., Mezzacapo, A., Foulkes, W.M.C., Pfau, D., Carleo, G., No´ e, F.: Ab initio quantum chemistry with neural-network wavefunctions. Nature Reviews Chemistry7(10), 692–709 (2023)

    work page 2023

  3. [3]

    Methods in Enzymologyvol 5002011(2000)

    Bv, D.C., Hydraulics, D.: Absorption spectroscopy. Methods in Enzymologyvol 5002011(2000)

    work page 2000

  4. [4]

    International Journal of Quantum Chemistry119(1), 25719 (2019) 15

    Zuehlsdorff, T.J., Isborn, C.M.: Modeling absorption spectra of molecules in solution. International Journal of Quantum Chemistry119(1), 25719 (2019) 15

    work page 2019

  5. [5]

    Annalen der Physik 389, 457–484 (1927)

    Born, M., Oppenheimer, R.: Zur quantentheorie der molekeln. Annalen der Physik 389, 457–484 (1927)

    work page 1927

  6. [6]

    Reviews of Modern Physics73(1), 33 (2001)

    Foulkes, W.M., Mitas, L., Needs, R., Rajagopal, G.: Quantum monte carlo simulations of solids. Reviews of Modern Physics73(1), 33 (2001)

    work page 2001

  7. [7]

    Courier Corporation, New York (1996)

    Szabo, A., Ostlund, N.S.: Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Courier Corporation, New York (1996)

    work page 1996

  8. [8]

    Chemical physics letters111(4-5), 315–321 (1984)

    Knowles, P.J., Handy, N.C.: A new determinant-based full configuration interac- tion method. Chemical physics letters111(4-5), 315–321 (1984)

    work page 1984

Show all 45 references
  1. [9]

    Computational many- particle physics, 529–544 (2008)

    Weiße, A., Fehske, H.: Exact diagonalization techniques. Computational many- particle physics, 529–544 (2008)

    2008

  2. [10]

    Chemical reviews112(1), 108–181 (2012)

    Szalay, P.G., Muller, T., Gidofalvi, G., Lischka, H., Shepard, R.: Multiconfigu- ration self-consistent field and multireference configuration interaction methods and applications. Chemical reviews112(1), 108–181 (2012)

    2012

  3. [11]

    Marques, M.A., Gross, E.K.: Time-dependent density functional theory. Annu. Rev. Phys. Chem.55(1), 427–455 (2004)

    2004

  4. [12]

    Statistical Physics II: Nonequilibrium Statistical Mechanics, 146–202 (1991)

    Kubo, R., Toda, M., Hashitsume, N., Kubo, R., Toda, M., Hashitsume, N.: Statistical mechanics of linear response. Statistical Physics II: Nonequilibrium Statistical Mechanics, 146–202 (1991)

    1991

  5. [13]

    Kubo, R.: Statistical-mechanical theory of irreversible processes. i. general theory and simple applications to magnetic and conduction problems. Journal of the physical society of Japan12(6), 570–586 (1957)

    1957

  6. [14]

    Kubo, R., Yokota, M., Nakajima, S.: Statistical-mechanical theory of irreversible processes. ii. response to thermal disturbance. Journal of the Physical Society of Japan12(11), 1203–1211 (1957)

    1957

  7. [15]

    Reports on progress in physics 29(1), 255 (1966)

    Kubo, R.: The fluctuation-dissipation theorem. Reports on progress in physics 29(1), 255 (1966)

    1966

  8. [16]

    The Journal of Chemical Physics159(14) (2023)

    Liu, W., Chen, Z.-H., Su, Y., Wang, Y., Dou, W.: Predicting rate kernels via dynamic mode decomposition. The Journal of Chemical Physics159(14) (2023)

    2023

  9. [17]

    arXiv preprint arXiv:2407.01923 (2024)

    Liu, W., Su, Y., Wang, Y., Dou, W.: Memory kernel coupling theory: Obtain time correlation function from higher-order moments. arXiv preprint arXiv:2407.01923 (2024)

    2024 arXiv

  10. [18]

    Physical Review E49(5), 4684 (1994)

    Iitaka, T.: Solving the time-dependent schr¨ odinger equation numerically. Physical Review E49(5), 4684 (1994)

    1994

  11. [19]

    Nature communica- tions15(1), 9404 (2024)

    Nys, J., Pescia, G., Sinibaldi, A., Carleo, G.: Ab-initio variational wave functions 16 for the time-dependent many-electron schr¨ odinger equation. Nature communica- tions15(1), 9404 (2024)

    2024

  12. [20]

    Reviews of modern physics78(1), 275–306 (2006)

    Weiße, A., Wellein, G., Alvermann, A., Fehske, H.: The kernel polynomial method. Reviews of modern physics78(1), 275–306 (2006)

    2006

  13. [21]

    Mathematical Notes80(2006)

    Vyazovskaya, M., Pupashenko, N.: On the normalizing multiplier of the general- ized jackson kernel. Mathematical Notes80(2006)

    2006

  14. [22]

    Reviews of Modern Physics35(3), 496 (1963)

    Lykos, P., Pratt, G.: Discussion on the hartree-fock approximation. Reviews of Modern Physics35(3), 496 (1963)

    1963

  15. [23]

    In: Methods of Electronic Structure Theory, pp

    Shavitt, I.: The method of configuration interaction. In: Methods of Electronic Structure Theory, pp. 189–275. Springer, New York (1977)

    1977

  16. [24]

    Sherrill, C.D., Schaefer III, H.F.: The configuration interaction method: Advances in highly correlated approaches34, 143–269 (1999)

    1999

  17. [25]

    Reviews of Modern Physics79(1), 291–352 (2007)

    Bartlett, R.J., Musia l, M.: Coupled-cluster theory in quantum chemistry. Reviews of Modern Physics79(1), 291–352 (2007)

    2007

  18. [26]

    Physical review letters69(19), 2863 (1992)

    White, S.R.: Density matrix formulation for quantum renormalization groups. Physical review letters69(19), 2863 (1992)

    1992

  19. [27]

    Physical review b48(14), 10345 (1993)

    White, S.R.: Density-matrix algorithms for quantum renormalization groups. Physical review b48(14), 10345 (1993)

    1993

  20. [28]

    Journal of Computational Chemistry42(8), 534–544 (2021)

    Brabec, J., Brandejs, J., Kowalski, K., Xantheas, S., Legeza, ¨O., Veis, L.: Mas- sively parallel quantum chemical density matrix renormalization group method. Journal of Computational Chemistry42(8), 534–544 (2021)

    2021

  21. [29]

    Journal of the American Chemical Society 144(35), 15932–15937 (2022)

    Larsson, H.R., Zhai, H., Umrigar, C.J., Chan, G.K.-L.: The chromium dimer: clos- ing a chapter of quantum chemistry. Journal of the American Chemical Society 144(35), 15932–15937 (2022)

    2022

  22. [30]

    arXiv preprint quant-ph/0608197 (2006)

    Perez-Garcia, D., Verstraete, F., Wolf, M.M., Cirac, J.I.: Matrix product state representations. arXiv preprint quant-ph/0608197 (2006)

    2006 arXiv

  23. [31]

    In: Iberoamerican Congress on Pattern Recognition, pp

    Fischer, A., Igel, C.: An introduction to restricted boltzmann machines. In: Iberoamerican Congress on Pattern Recognition, pp. 14–36 (2012). Springer

    2012

  24. [32]

    Nature communications11(1), 2368 (2020)

    Choo, K., Mezzacapo, A., Carleo, G.: Fermionic neural-network states for ab- initio electronic structure. Nature communications11(1), 2368 (2020)

    2020

  25. [33]

    Science355(6325), 602–606 (2017) 17

    Carleo, G., Troyer, M.: Solving the quantum many-body problem with artificial neural networks. Science355(6325), 602–606 (2017) 17

    2017

  26. [34]

    Nature Machine Intelligence4(4), 351–358 (2022)

    Barrett, T.D., Malyshev, A., Lvovsky, A.: Autoregressive neural-network wave- functions for ab initio quantum chemistry. Nature Machine Intelligence4(4), 351–358 (2022)

    2022

  27. [35]

    In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, pp

    Wu, Y., Guo, C., Fan, Y., Zhou, P., Shang, H.: Nnqs-transformer: an efficient and scalable neural network quantum states approach for ab initio quantum chemistry. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, ...

    2023

  28. [36]

    In: Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, pp

    Larochelle, H., Murray, I.: The neural autoregressive distribution estimator. In: Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, pp. 29–37 (2011). JMLR Workshop and Conference Proceedings

    2011

  29. [37]

    Machine Learning: Science and Technology4(2), 025034 (2023)

    Zhao, T., Stokes, J., Veerapaneni, S.: Scalable neural quantum states architecture for quantum chemistry. Machine Learning: Science and Technology4(2), 025034 (2023)

    2023

  30. [38]

    Physical review research2(3), 033429 (2020)

    Pfau, D., Spencer, J.S., Matthews, A.G., Foulkes, W.M.C.: Ab initio solution of the many-electron schr¨ odinger equation with deep neural networks. Physical review research2(3), 033429 (2020)

    2020

  31. [39]

    Nature Chemistry12(10), 891–897 (2020)

    Hermann, J., Sch¨ atzle, Z., No´ e, F.: Deep-neural-network solution of the electronic schr¨ odinger equation. Nature Chemistry12(10), 891–897 (2020)

    2020

  32. [40]

    Reviews of Modern Physics92(1), 015003 (2020)

    McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S.C., Yuan, X.: Quantum computational chemistry. Reviews of Modern Physics92(1), 015003 (2020)

    2020

  33. [41]

    Springer, Verlag Berlin Heidelberg (1993)

    Jordan, P., Wigner, E.P.: ¨Uber Das Paulische ¨Aquivalenzverbot. Springer, Verlag Berlin Heidelberg (1993)

    1993

  34. [42]

    The Journal of chemical physics137(22) (2012)

    Seeley, J.T., Richard, M.J., Love, P.J.: The bravyi-kitaev transformation for quan- tum computation of electronic structure. The Journal of chemical physics137(22) (2012)

    2012

  35. [43]

    Annals of Physics 298(1), 210–226 (2002)

    Bravyi, S.B., Kitaev, A.Y.: Fermionic quantum computation. Annals of Physics 298(1), 210–226 (2002)

    2002

  36. [44]

    arXiv preprint arXiv:1712.01887 (2017)

    Lin, Y., Han, S., Mao, H., Wang, Y., Dally, W.J.: Deep gradient compression: Reducing the communication bandwidth for distributed training. arXiv preprint arXiv:1712.01887 (2017)

    2017 arXiv

  37. [45]

    arXiv preprint arXiv:1412.6980 (2014) 18

    Kingma, D.P.: Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014) 18

    2014 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.