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REVIEW 4 major objections 5 minor 1 cited by

Ground and excited-state energies with analytic errors and short time evolution on a quantum computer

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read QPD reads ground and excited molecular energies from short autocorrelation signals at the Heisenberg limit.

desk verdict A salvageable hybrid algorithm whose headline scaling claims are mutually inconsistent and whose key error theorems live in the first author's preprints. read the letter →

arxiv 2507.15148 v2 pith:VTKGOBUW submitted 2025-07-20 quant-ph math-phmath.MPphysics.chem-phphysics.comp-ph

Timothy Stroschein , Davide Castaldo , Markus Reiher This is my paper
classification quant-phmath-phmath.MPphysics.chem-phphysics.comp-ph MSC 65F1568Q1281P68
keywords autocorrelationfunctionprolatespheroidalwavefunctionsfilterdiagonalizationquantumphaseestimationHeisenberglimitchemistryeigenvalueHadamardtest
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper claims that molecular energy levels can be recovered as frequencies of the autocorrelation function $C(t)=\langle\Psi|e^{iHt}|\Psi\rangle$ without ever solving for wave functions, and that this can be done from finitely many noisy samples measured by a single-ancilla Hadamard test. The classical post-processing, called sampled prolate filter diagonalization, uses prolate spheroidal wave functions — the functions optimally concentrated in time and frequency — to build a generalized eigenvalue problem whose eigenvalues are the energies inside a chosen band. The paper proves analytic error bounds for this procedure and identifies a sharp accuracy transition controlled by the ratio of spectral density to observation time. In numerical experiments on benzene, LiH, and H8, the resulting hybrid algorithm QPD reaches chemical accuracy for ground and excited states, with runtime scaling as $\epsilon^{-1}$ and maximal evolution time scaling as $\epsilon^{-1/3}$, which is cubic faster in $T_{\max}$ than standard quantum phase estimation. If these claims hold, early fault-tolerant quantum computers could replace deep phase-estimation circuits with a short-time evolution and classical spectral analysis.

What carries the argument

Prolate spheroidal wave functions $\{\xi_n\}$ — the eigenfunctions of the time-and-band-limiting operator $B_W D_T$, hence the functions that fit optimally in both a frequency band and a time window — carry the argument. Their eigenvalue parameters $\gamma_n(c)$ are the accuracy currency: every subspace error and every sampling error in PFD is controlled by $1-\gamma_M(c_f)$, which decays exponentially until $M$ approaches the essential dimension $2W_f T/\pi$ and then rises sharply. The sampled generalized eigenvalue problem is built from the prolate sampling formula applied twice to the matrix elements $C(\tau-t)\xi_l(t)$, and the resulting errors are propagated through the subspace-protocol master theorem with the help of the alternant matrix $F_M(\vec E)$ of filter Fourier transforms and the amplitude matrix $\Lambda(\vec a)$.

What would settle it

Take a molecular Hamiltonian with two near-degenerate eigenvalues inside the target band, run QPD with $m$ inferred from the weight-matrix spectrum using only the noise threshold, and compare the resulting errors with the Theorem 2.2 bound; a single case where the empirical error exceeds the bound, or where the fitted slope deviates from $\epsilon = O(T_{\max}^{-3})$, would show that the guarantees depend on reference-supplied dimensions rather than on end-to-end detection.

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Extended reading notes

Core claim

On its own terms, the discovery is that the spectrum of a self-adjoint Hamiltonian is encoded in the autocorrelation function $C(t)$, and its frequencies can be recovered through the convolution eigenvalue problem $-i\partial_\tau (C*f_n)(\tau)=E_n (C*f_n)(\tau)$ on time-limited functions, merging spectral analysis and phase estimation into one framework. Restricting the filters to prolate spheroidal wave functions supported on $[-T,T]$ yields error bounds governed by $1-\gamma_M(c_f)$, the energy a prolate leaks outside its concentration region; because $\gamma_M$ drops sharply after about $2W_f T/\pi$ filters, accuracy stays high while the effective spectral density remains below $T/\pi$ and then degrades in a phase-transition-like way. Discretizing by the prolate sampling formula keeps the same bound, up to a sampling error with the same transition, and requires only $O(W_s T)$ equidistant autocorrelation samples. Generating those samples by the Hadamard test defines QPD; the paper's experiments on benzene, LiH, and H8 show errors below 1 mH and empirical scalings $\epsilon = O(T_{\mathrm{runtime}}^{-1})$ and $\epsilon = O(T_{\max}^{-3})$, the latter a cubic improvement over standard QPE's $O(T_{\max}^{-1})$.

Load-bearing premise

The analytic error bounds hold only if the algorithm already knows the exact number $m$ of frequencies inside the target band and the refined generalized eigenvalue problem satisfies the well-conditioning inequality $\lambda_m(B_m^M)>\|N^{(B)}_M\|$; in the paper's numerical tests, $m$ is taken from exact CASCI/FCI reference calculations rather than detected from the sampled data.

Editorial extensions

If this is right

  • The same set of Hadamard-test shots estimates several low-lying energies simultaneously, so the per-state cost of spectroscopy on a quantum computer drops relative to sequential QPE runs.
  • Total quantum runtime $T_{\mathrm{runtime}}=O(\epsilon^{-1})$ is Heisenberg-limited, meaning the shot-noise limit $\epsilon^{-2}$ is avoided by classical averaging of samples.
  • Maximal evolution time $T_{\max}=O(\epsilon^{-1/3})$ in the demonstrated regime gives shallower circuits than standard QPE, for which $T_{\max}=O(\epsilon^{-1})$.
  • The phase transition at effective spectral density $\delta_{\mathrm{eff}}\approx T/\pi$ provides a planning rule: use a cheap classical estimate of the in-band spectral density to set the observation time before running the quantum circuit.

Reading between the lines

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

  • Editorial extension: the prolate sampling and spectral-transition machinery is a signal-processing formalism, so the same finite-sample frequency estimator could be applied to classical time-domain data such as NMR or molecular spectroscopy without a quantum computer; the paper's error bounds would carry over unchanged.
  • Editorial extension: the speedup claim would be put to a stricter test by a protocol that detects $m$ from the noisy weight matrix, since Theorems 2.1 and 2.2 explicitly condition on $m$ coinciding with the true number of in-band frequencies, while the numerical sections supply this number from reference calculations.
  • Editorial extension: near-degenerate in-band frequencies weaken the conditioning of the refined GEP, so the practical route to the cubic $T_{\max}$ scaling for dense spectra is adaptive band narrowing, which the paper mentions but does not analyze as a resource count.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript proposes quantum prolate diagonalization (QPD), a hybrid classical-quantum algorithm that estimates multiple eigenvalues of a molecular Hamiltonian from samples of the autocorrelation function C(t)=⟨Ψ|e^{iHt}|Ψ⟩ obtained by a Hadamard test. The theoretical core is an approximation framework based on prolate spheroidal wave functions, leading to prolate filter diagonalization (PFD) and a sampled variant, with error bounds that separate subspace error from discretization error. Numerical experiments on benzene, LiH, and H8 report chemical accuracy for ground and excited states and claim Heisenberg-limited total runtime T_runtime=O(ε^{-1}) together with a cubic improvement in the maximum evolution time, ε=O(T_max^{-3}). The paper also studies the effect of initial-state quality on accuracy.

Significance. If the results were correct, QPD would be a notable advance: a single-ancilla, short-evolution algorithm for simultaneous ground- and excited-state energies with Heisenberg-limited precision, supported by a sharp prolate-based error analysis. The paper has several strengths: it clearly separates subspace and discretization errors, presents a substantial numerical campaign (more than a thousand QPD runs), and introduces prolate concentration inequalities and a sampling theorem that are of independent interest. However, the central scaling claims contain an internal contradiction under the paper's own runtime model, the numerical evidence relies on fixed-exponent fits rather than free fits, and the analytic guarantees rest on theorems imported from the first author's own unpublished preprints. These issues are load-bearing for the advertised quantum advantage, so the significance is conditional and, in the present form, not established.

major comments (4)
  1. [§3.1 and §3.3.1, Eqs. (57)–(59)] Under the paper's own runtime accounting, T_runtime = #shots Σ t_k with #shots = F sqrt(N_s log N_s) and N_s = W_s T_max/π, which gives T_runtime = Θ(T_max^{5/2} sqrt(log T_max)). Combining this with the claimed ε = O(T_max^{-3}) (Figs. 3b, 4b, 4d) gives ε = O(T_runtime^{-6/5} sqrt(log T_runtime)) asymptotically, which is strictly better than the Heisenberg limit ε = Ω(T_runtime^{-1}) that the paper claims to achieve. Since the Heisenberg limit is a lower bound for phase estimation with total evolution time, the two central claims cannot both hold. Moreover, the red dashed lines in Figs. 3 and 4 are not free fits: the exponents b are fixed to -1 and -3, so these plots do not validate either scaling law. The authors need to reconcile the runtime model with the claimed error scaling, or provide free-exponent fits with residuals and an explanation of how the Heisenberg limit is respected.
  2. [Appendices A, B, C; Theorems 2.1 and 2.2] The central analytic error guarantees, Theorems 2.1 and 2.2, follow from Theorem A.1, Theorem B.4, and Theorem C.1, none of which is proved in this manuscript. These theorems are restated from the first author's preprints Refs. [60] and [61]; the text states that Theorem B.4 is proven in Ref. [60, Chapter 2] and Theorem C.1 in Ref. [60, Chapter 3]. Because these results carry the full weight of the error bounds, the manuscript is not self-contained, and the correctness of the analytic claims cannot be verified from the submitted material. The authors should include complete proofs, or precise references to publicly available, peer-reviewed versions, of the claimed new prolate identities and sampling bounds.
  3. [§3.2 and §3.3.2, Theorems 2.1–2.2] The numerical experiments do not verify the hypotheses of the error theorems. In §3.3.2, for H8 the dimension m=7 is set from the FCI/CASCI reference ('the number of frequencies within B_{f,ω*} was set to m=7'), rather than detected from the weight-matrix spectrum as in Algorithm 1. For benzene in §3.2, m=2 is read off the weight-matrix spectrum, but the noise threshold ε_th is not specified, and the conditioning assumption λ_m(B_m^M) > ||N^{(B)}_M|| is not quantitatively checked for the reported H8 and LiH runs. Consequently, the analytic error bounds of Theorems 2.1 and 2.2 cannot be invoked for these numerical results, and the reported errors are not covered by the paper's own error analysis.
  4. [§2.6 and §3.1, Eq. (54)] The shot count #shots = F sqrt(N_s log N_s) yields a per-sample standard deviation O(N_s^{-1/4}) for the Hadamard-test estimates. The paper does not analyze how this statistical noise propagates through the generalized eigenvalue problem; the δA and δB terms in Definition A.1 are never bounded for sampling noise, and Theorems 2.1 and 2.2 assume a noiseless or separately bounded error model. Thus the numerical accuracy obtained in Figs. 3–4, including the benzene run with only 13 shots per sample, is not supported by the analytic framework, and the effect of the shot allocation on the claimed Heisenberg scaling is left unexplained.
minor comments (5)
  1. [Eq. (41)] In the definition of B_sl, the second occurrence of ξ_{n1}(0) is likely meant to be ξ_{n2}(0); as written the two prolate factors at t=0 are identical, which appears to be a typographical error.
  2. [§3.3.1] The text describes T_runtime = O(T_max^{2.5} sqrt(log T_max)) as 'almost cubical'; the exponent is 2.5, not 3, so this wording is misleading.
  3. [Theorem 2.2] The statement contains a typo: 'coincidenceswithnumber' should read 'coincides with the number'.
  4. [References] Several citations contain placeholder question marks, e.g., '[69, 81 ?]' in §2.4 and '[115? ?]' in Appendix B.3; these should be resolved before publication.
  5. [§3.1] The manuscript states that the code 'StrawnoteSteward' will be made open source upon publication but provides no code or data repository in the current submission; given the central role of the numerical experiments, providing the code and raw data would materially improve reproducibility.

Circularity Check

1 steps flagged · score 4.0 of 10

Analytic error theorems are inherited from the first author's prior preprints; the numerical core is otherwise self-contained.

  1. self citation load bearing [Introduction; Section A (Theorem A.1); Section B.2 (Theorem B.4); Section C (Theorem C.1)]
    "We make use of a new framework to characterize errors in the accuracy and dimensionality of subspace methods [60, 61] to derive tight error bounds for an improved version of the filter diagonalization method. ... In this section, we briefly review subspace-based methods and present key results adapted from Ref. [61]. ... Theorem B.4 presents our new inequalities, which are proven in Ref. [60, Chapter 2] ... A proof is given in Ref. [60, Chapter 3]."

    The paper's central analytic guarantees, Theorems 2.1 and 2.2, are corollaries of the imported subspace-protocol master theorem (Theorem A.1, 'adapted from Ref. [61]') and of the prolate concentration and sampling estimates (Theorem B.4 and Theorem C.1), whose proofs are explicitly deferred to Ref. [60]. Both [60] and [61] are the first author's own preprints; they are not machine-checked, not reproduced in this manuscript, and not otherwise independently verified here. Thus the claimed rigorous error framework is not established by the present derivation but is inherited from an unverified self-citation chain. This is load-bearing because all analytic error bounds, including the Heisenberg-scaling narrative, depend on these imported theorems.

full rationale

The numerical QPD experiments are substantially self-contained: they implement sampled PFD, generate autocorrelation samples via a classically emulated Hadamard circuit, and compare the resulting energies against independent CASCI/FCI references. Those energy estimates are therefore not circular reductions. However, two support gaps should be weighed. First, the preconditions of Theorems 2.1 and 2.2 (detected dimension equals true in-band frequency count, and conditioning of the refined GEP) are not verified in the examples; in the H8 multi-eigenvalue calculation, 'the number of frequencies within B_{f,ω*} was set to m = 7' from the FCI/CASCI reference rather than detected, so the detection step is not validated. Second, the empirical scaling claims are based on fixed-exponent fits ('b values are kept fixed and set to b = −1 (−3)'), so the reported O(Tmax^-3) exponent is not inferred from the data; moreover, combining the stated Truntime = O(Tmax^2.5 sqrt(log Tmax)) with epsilon = O(Tmax^-3) would give Truntime = O(epsilon^-5/6 sqrt(log epsilon)), which is inconsistent with the separately claimed Heisenberg scaling Truntime = O(epsilon^-1). These are correctness and evidence concerns rather than additional circular reductions. The remaining circularity-adjacent issue is the load-bearing self-citation of the analytic error theorems, which warrants a moderate score of 4 rather than 0 or 2.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a chain of theorems from the first author's own earlier preprints (Refs. [60] and [61]) for the error bounds, plus several hand-tuned numerical parameters (F, M, W_s, W_f, m) that are set with knowledge of the reference solution.

free parameters (6)
  • F = 2 (weak correlation), 10 (strong correlation)
    Prefactor in shot count #shots = F sqrt(N_s log N_s); tuned by the authors based on target amplitude strength.
  • M (guess dimension) = e.g., 16 for benzene, half of essential dimension
    Chosen as half the essential dimension floor(W_f T / pi), a heuristic balance between conditioning and subspace error.
  • W_s (sampling rate) = 3 a.u. or 6 a.u.
    Hand-picked per system to satisfy W_s >= W_f + W_C; not derived from a rigorous W_C estimate.
  • W_f (filter width) = 1 (benzene), 0.47 (H8 multiple)
    Chosen ad hoc to define the target frequency band.
  • m (number of in-band frequencies) = 2 (benzene), 7 (H8)
    Set equal to the number of eigenvalues known from CASCI/FCI reference calculations, used as input to Algorithm 1.
  • omega* (filter center) = 6.3 (benzene)
    Obtained from a CISD calculation, i.e., a classical preprocessing step rather than an ab initio parameter.
assumptions (7)
  • ad hoc to paper Theorem A.1 (master theorem for subspace protocols)
    Adapted from Ref. [61], a preprint by the same first author; the accuracy bounds of PFD and sampled PFD are corollaries of this theorem.
  • ad hoc to paper Theorem B.4 (new prolate concentration identities)
    Stated to be proven in Ref. [60, Chapter 2], another preprint by the same first author; used for the sharp error bounds and sampling estimates.
  • ad hoc to paper Theorem C.1 (truncated prolate sampling formula bound)
    Proof attributed to Ref. [60, Chapter 3]; the sampling-based discretization error is controlled through this theorem.
  • standard math Standard prolate Fourier theory (2WT theorem, eigenvalue asymptotics)
    Properties of prolate spheroidal wave functions and their eigenvalue transition are taken from Slepian, Landau, Pollak.
  • standard math Bochner's theorem and GNS construction
    Used to represent the positive-definite signal C(t) as an autocorrelation of a Hamiltonian evolution.
  • domain assumption Finite bandwidth W_C of the signal
    The discretized sampled PFD requires the signal to be band-limited; no rigorous W_C is provided for the molecular examples, only bounds from Ref. [95] are mentioned.
  • domain assumption Well-conditioning of the refined GEP
    Theorems 2.1 and 2.2 assume lambda_m(B) > ||N|| and exact dimension detection; these are not verified for the numerical runs.

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Cite this review

Pith. "Pith review of Ground and excited-state energies with analytic errors and short time evolution on a quantum computer." pith.science (2026). https://pith.science/paper/VTKGOBUW

@misc{pith2026250715148,
  author       = {Pith},
  title        = {Pith review of: Ground and excited-state energies with analytic errors and short time evolution on a quantum computer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VTKGOBUW}},
  note         = {Machine review of arXiv:2507.15148}
}
read the original abstract

Accurately solving the Schr\"odinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding direct reference to a wave function. In particular, we develop a rigorous approximation framework that enables precise frequency estimation from a finite number of signal samples. Our analysis builds on new results involving prolate spheroidal wave functions and yields error bounds that reveal a sharp accuracy transition governed by the observation time and spectral density of the signal. These results are very general and thus carry far. As one important example application we consider the quantum computation for molecular systems. By combining our spectral method with a quantum subroutine for signal generation, we define quantum prolate diagonalization (QPD) - a hybrid classical-quantum algorithm. QPD simultaneously estimates ground and excited state energies within chemical accuracy at the Heisenberg limit. An analysis of different input states demonstrates the robustness of the method, showing that high precision can be retained even under imperfect state preparation.

Figures

Figures reproduced from arXiv: 2507.15148 by the authors.

Figure 1
Figure 1. Logical dependency graph of the theory underlying our approach: for the main part of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. QPD applied to the benzene molecule. (a) Noisy samples of the electronic autocorrelation [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Empirical scaling of QPD for the task of ground state energy estimation for H [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Empirical scaling of QPD in the weak (LiH molecule, a-b) and strong (H8 system, c-d) correlation limit for the task of simultaneous multiple eigenvalue estimation. Left: average error on the excitation energies as a function of the total runtime (see Eq. (57)). Right: …
Figure 5
Figure 5. Figure 5: Initial input state characterization for the calculations on H [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]
Figure 6
Figure 6. Figure 6: Effect of the initial input state on the QPD algorithm for the H [PITH_FULL_IMAGE:figures/full_fig_p020_6.png]

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Reference graph

Works this paper leans on

119 extracted references · 67 canonical work pages · cited by 1 Pith paper

  1. [60]

    Prolatespheroidalwavefunctionsandtheaccuracyanddimensionality of spectral analysis.arXiv preprint arXiv:2409.16584, 2024

    TimothyStroschein. Prolatespheroidalwavefunctionsandtheaccuracyanddimensionality of spectral analysis.arXiv preprint arXiv:2409.16584, 2024

    arXiv 2024

  2. [61]

    An approximation framework for subspace-based methods in spectral analysis with accuracy guarantees.arXiv preprint arXiv:2505.07513, 2025

    Timothy Stroschein. An approximation framework for subspace-based methods in spectral analysis with accuracy guarantees.arXiv preprint arXiv:2505.07513, 2025

    arXiv 2025

  3. [1]

    Langhoff and Ernest R

    Stephen R. Langhoff and Ernest R. Davidson. Configuration interaction calculations on the nitrogen molecule.International Journal of Quantum Chemistry, 8(1):61–72, 1974

    1974

  4. [2]

    IterativeKrylovMethodsforLargeLinearSystems ,volume13of Cam- bridge Monographs on Applied and Computational Mathematics

    H.A.vanderVorst. IterativeKrylovMethodsforLargeLinearSystems ,volume13of Cam- bridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge, UK, 2003

    2003

  5. [3]

    Inflationarydynamicsformatrixeigenvalue problems

    EricJHeller,LevKaplan,andFrankPollmann. Inflationarydynamicsformatrixeigenvalue problems. Proceedings of the National Academy of Sciences, 105(22):7631–7635, 2008

    2008

  6. [4]

    Solution methods for eigenvalue problems in structural mechanics

    Klaus-Jürgen Bathe and Edward L Wilson. Solution methods for eigenvalue problems in structural mechanics. International Journal for Numerical Methods in Engineering, 6(2):213–226, 1973

    1973

  7. [5]

    Large scale quantum chemistry with tensor processing units.Journal of Chemical Theory and Computation, 19(1):25–32, 2022

    RyanPederson,JohnKozlowski,RuyiSong,JacksonBeall,MartinGanahl,MarkusHauru, Adam GM Lewis, Yi Yao, Shrestha Basu Mallick, Volker Blum, and Guifre Vidal. Large scale quantum chemistry with tensor processing units.Journal of Chemical Theory and Computation, 19(1):25–32, 2022

    2022

  8. [6]

    The anatomy of a large-scale hypertextual web search engine

    Sergey Brin and Lawrence Page. The anatomy of a large-scale hypertextual web search engine. Computer Networks and ISDN Systems, 30(1-7):107–117, 1998

    1998

Show all 119 references
  1. [7]

    Support from the relationship of genetic and geographic distance in human populations for a serial founder effect originating in Africa

    Sohini Ramachandran, Omkar Deshpande, Charles C Roseman, Noah A Rosenberg, Mar- cus W Feldman, and L Luca Cavalli-Sforza. Support from the relationship of genetic and geographic distance in human populations for a serial founder effect originating in Africa. Proceedings of the...

    2005

  2. [8]

    Derivative pricing using quantum signal pro- cessing

    Nikitas Stamatopoulos and William J Zeng. Derivative pricing using quantum signal pro- cessing. Quantum, 8:1322, 2024

    2024

  3. [9]

    Exponential quantum speedup in simulating coupled classical oscillators.Physical Review X, 13(4):041041, 2023

    Ryan Babbush, Dominic W Berry, Robin Kothari, Rolando D Somma, and Nathan Wiebe. Exponential quantum speedup in simulating coupled classical oscillators.Physical Review X, 13(4):041041, 2023

    2023

  4. [10]

    Quantum annealing versus classical machine learning applied to a simplified computational biology problem.NPJ Quantum Information, 4(1):14, 2018

    Richard Y Li, Rosa Di Felice, Remo Rohs, and Daniel A Lidar. Quantum annealing versus classical machine learning applied to a simplified computational biology problem.NPJ Quantum Information, 4(1):14, 2018

    2018

  5. [11]

    Quantum computing for classical problems: variational quantum eigensolver for activated processes.New Journal of Physics, 23(12):123045, 2021

    Pierpaolo Pravatto, Davide Castaldo, Federico Gallina, Barbara Fresch, Stefano Corni, and Giorgio J Moro. Quantum computing for classical problems: variational quantum eigensolver for activated processes.New Journal of Physics, 23(12):123045, 2021. 31

    2021

  6. [12]

    Paul Benioff. The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines.Journal of Statistical Physics, 22:563–591, 1980

    1980

  7. [13]

    Quantum mechanical computers.Foundations of Physics, 16(6):507– 532, 1986

    Richard P Feynman. Quantum mechanical computers.Foundations of Physics, 16(6):507– 532, 1986

    1986

  8. [14]

    ChemBioChem, 24(13):e202300120, 2023

    AlbertoBaiardi,MatthiasChristandl,andMarkusReiher.Quantumcomputingformolecular biology. ChemBioChem, 24(13):e202300120, 2023

    2023

  9. [15]

    Quantum computational chemistry.Reviews of Modern Physics, 92(1):015003, 2020

    Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C Benjamin, and Xiao Yuan. Quantum computational chemistry.Reviews of Modern Physics, 92(1):015003, 2020

    2020

  10. [16]

    Joshua J Goings, Alec White, Joonho Lee, Christofer S Tautermann, Matthias Deg- roote, Craig Gidney, Toru Shiozaki, Ryan Babbush, and Nicholas C Rubin. Reliably assessing the electronic structure of cytochrome p450 on today’s classical computers and tomorrow’s quantum computer...

    2022

  11. [17]

    Quantum computing enhanced computational catalysis

    Vera von Burg, Guang Hao Low, Thomas Häner, Damian S Steiger, Markus Reiher, Martin Roetteler, and Matthias Troyer. Quantum computing enhanced computational catalysis. Physical Review Research, 3(3):033055, 2021

    2021

  12. [18]

    Quantumalgorithmsoftwareforcondensedmatterphysics

    TFarajollahpour. Quantumalgorithmsoftwareforcondensedmatterphysics. arXivpreprint arXiv:2506.09308, 2025

    2025 arXiv

  13. [19]

    MaterialsTheory, 6(1):11, 2022

    Hongbin Liu, Guang Hao Low, Damian S Steiger, Thomas Häner, Markus Reiher, and MatthiasTroyer.Prospectsofquantumcomputingformolecularsciences. MaterialsTheory, 6(1):11, 2022

    2022

  14. [20]

    Quantum algorithms forquantumchemistryandquantummaterialsscience

    Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin-Lic Chan. Quantum algorithms forquantumchemistryandquantummaterialsscience. ChemicalReviews,120(22):12685– 12717, 2020

    2020

  15. [21]

    Eluci- dating reaction mechanisms on quantum computers.Proceedings of the National Academy of Sciences, 114(29):7555–7560, 2017

    Markus Reiher, Nathan Wiebe, Krysta M Svore, Dave Wecker, and Matthias Troyer. Eluci- dating reaction mechanisms on quantum computers.Proceedings of the National Academy of Sciences, 114(29):7555–7560, 2017

    2017

  16. [22]

    Quantum error detection in qubit-resonator star architecture

    Florian Vigneau, Sourav Majumder, Aniket Rath, Pedro Parrado-Rodríguez, Francisco Revson Fernandes Pereira, Stefan Pogorzalek, Tyler Jones, Nicola Wurz, Michael Renger, Jeroen Verjauw, Ping Yang, Hsiang-Sheng Ku, William Kindel, Frank Deppe, Johannes Heinsoo. Quantum error det...

    2025

  17. [23]

    Fusion-basedquantumcomputation

    Sara Bartolucci, Patrick Birchall, Hector Bombin, Hugo Cable, Chris Dawson, Mercedes Gimeno-Segovia, Eric Johnston, Konrad Kieling, Naomi Nickerson, Mihir Pant, Fernando Pastawski, TerryRudolph, andChrisSparrow. Fusion-basedquantumcomputation. Nature Communications, 14(1):912, 2023

    2023

  18. [24]

    Aghaee Rad, T

    H. Aghaee Rad, T. Ainsworth, R.N. Alexander, B. Altieri, M. F. Askarani, R. Baby, L. Banchi, B. Q. Baragiola, J. E. Bourassa, R. S. Chadwick, I. Charania, H. Chen, M. J. Collins, P. Contu, N. D’Arcy, G. Dauphinais, R. De Prins, D. Deschenes, I. Di Luch, S. Duque, P. Edke, S. E...

    2025

  19. [25]

    Neyenhuis

    Juan M Pino, Jennifer M Dreiling, Caroline Figgatt, John P Gaebler, Steven A Moses, MSAllman,CHBaldwin,MichaelFoss-Feig,DavidHayes,KarlMayer,C.Ryan-Anderson, and B. Neyenhuis. Demonstration of the trapped-ion quantum CCD computer architecture. Nature, 592(7853):209–213, 2021

    2021

  20. [26]

    Cambridge University Press, 2013

    Daniel A Lidar and Todd A Brun.Quantum error correction. Cambridge University Press, 2013

    2013

  21. [27]

    Sur- face codes: Towards practical large-scale quantum computation

    Austin G Fowler, Matteo Mariantoni, John M Martinis, and Andrew N Cleland. Sur- face codes: Towards practical large-scale quantum computation. Physical Review A, 86(3):032324, 2012

    2012

  22. [28]

    Low-overhead magic state distillation with color codes

    Seok-Hyung Lee, Felix Thomsen, Nicholas Fazio, Benjamin J Brown, and Stephen D Bartlett. Low-overhead magic state distillation with color codes. arXiv preprint arXiv:2409.07707, 2024

    2024

  23. [29]

    Magic state cultivation: growing T states as cheap as CNOT gates.arXiv preprint arXiv:2409.17595, 2024

    Craig Gidney, Noah Shutty, and Cody Jones. Magic state cultivation: growing T states as cheap as CNOT gates.arXiv preprint arXiv:2409.17595, 2024

    2024 arXiv

  24. [30]

    Quantumalgorithms revisited

    RichardCleve,ArturEkert,ChiaraMacchiavello,andMicheleMosca. Quantumalgorithms revisited. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1969):339–354, 1998

    1969

  25. [31]

    Quantum metrology.Physical Review Letters, 96(1):010401, 2006

    Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Quantum metrology.Physical Review Letters, 96(1):010401, 2006

    2006

  26. [32]

    Quantum algorithms: A survey of applications and end-to-end complexities

    Alexander M Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T Hann, Michael J Kastoryano, Emil T Khabiboulline, Aleksander Kubica, et al. Quantum algorithms: A survey of applications and end-to-end complexities. arXiv preprint arXiv:...

    arXiv

  27. [33]

    Assessment of quantum phase estimation protocols for early fault-tolerant quantum computers.Physical Review A, 110(4):042420, 2024

    Jacob S Nelson and Andrew D Baczewski. Assessment of quantum phase estimation protocols for early fault-tolerant quantum computers.Physical Review A, 110(4):042420, 2024

    2024

  28. [34]

    Highgroundstateoverlapviaquantumembeddingmethods

    Mihael Erakovic, Freek Witteveen, Dylan Harley, Jakob Günther, Moritz Bensberg, Oinam Romesh Meitei, Minsik Cho, Troy Van Voorhis, Markus Reiher, and Matthias Chri- standl. Highgroundstateoverlapviaquantumembeddingmethods. PRXLife,3(1):013003, 2025

    2025

  29. [35]

    Initial state preparation for quantum chemistry on quantum computers

    Stepan Fomichev, Kasra Hejazi, Modjtaba Shokrian Zini, Matthew Kiser, Joana Frax- anet, Pablo Antonio Moreno Casares, Alain Delgado, Joonsuk Huh, Arne-Christian Voigt, Jonathan E Mueller, et al. Initial state preparation for quantum chemistry on quantum computers. PRX Quantum,...

    2024

  30. [36]

    Enhancing initial state overlap through orbital optimization for faster molecular electronic ground-state energy estimation.Physical Review Letters, 133(25):250601, 2024

    Pauline J Ollitrault, Cristian L Cortes, Jérôme F Gonthier, Robert M Parrish, Dario Rocca, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif. Enhancing initial state overlap through orbital optimization for faster molecular electroni...

    2024

  31. [37]

    Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry.Nature Communications, 14(1):1952, 2023

    Seunghoon Lee, Joonho Lee, Huanchen Zhai, Yu Tong, Alexander M Dalzell, Ashutosh Kumar, Phillip Helms, Johnnie Gray, Zhi-Hao Cui, Wenyuan Liu, et al. Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry.Nature Communications, 14(1):1952, 2023

    1952

  32. [38]

    Exponential improvement in precision for simulating sparse hamiltonians

    DominicWBerry,AndrewMChilds,RichardCleve,RobinKothari,andRolandoDSomma. Exponential improvement in precision for simulating sparse hamiltonians. InProceedings of the forty-sixth annual ACM symposium on Theory of computing, pages 283–292, 2014

    2014

  33. [39]

    Hamiltonian simulation by qubitization.Quantum, 3:163, 2019

    Guang Hao Low and Isaac L Chuang. Hamiltonian simulation by qubitization.Quantum, 3:163, 2019

    2019

  34. [40]

    Shadow hamiltonian simulation.Nature Communications, 16(1):2690, 2025

    Rolando D Somma, Robbie King, Robin Kothari, Thomas E O’Brien, and Ryan Babbush. Shadow hamiltonian simulation.Nature Communications, 16(1):2690, 2025

    2025

  35. [41]

    Quantumcomputations: algorithmsanderrorcorrection

    AYuKitaev. Quantumcomputations: algorithmsanderrorcorrection. RussianMathemat- ical Surveys, 52(6):1191, 1997

    1997

  36. [42]

    Even shorter quantum circuit for phase estimation on early fault-tolerantquantumcomputerswithapplicationstoground-stateenergyestimation

    Zhiyan Ding and Lin Lin. Even shorter quantum circuit for phase estimation on early fault-tolerantquantumcomputerswithapplicationstoground-stateenergyestimation. PRX Quantum, 4(2):020331, 2023

    2023

  37. [43]

    Simultaneousestimationofmultipleeigenvalueswithshort-depth quantum circuit on early fault-tolerant quantum computers.Quantum, 7:1136, 2023

    ZhiyanDingandLinLin. Simultaneousestimationofmultipleeigenvalueswithshort-depth quantum circuit on early fault-tolerant quantum computers.Quantum, 7:1136, 2023

    2023

  38. [44]

    Adaptive low-depth quantum algorithms for robust multiple-phase estimation.Physical Review A, 108(6):062408, 2023

    Haoya Li, Hongkang Ni, and Lexing Ying. Adaptive low-depth quantum algorithms for robust multiple-phase estimation.Physical Review A, 108(6):062408, 2023

    2023

  39. [45]

    M. E. Stroeks, Jonas Helsen, and B. M. Terhal. Spectral estimation for hamiltonians: a comparison between classical imaginary-time evolution and quantum real-time evolution. New Journal of Physics, 24(10):103024, 2022

    2022

  40. [46]

    Quantum phase estimation by compressed sensing

    Changhao Yi, Cunlu Zhou, and Jun Takahashi. Quantum phase estimation by compressed sensing. Quantum, 8:1579, 2024

    2024

  41. [47]

    Phase estimation with partially randomized time evolution.arXiv preprint arXiv:2503.05647, 2025

    Jakob Günther, Freek Witteveen, Alexander Schmidhuber, Marek Miller, Matthias Chris- tandl, and Aram Harrow. Phase estimation with partially randomized time evolution.arXiv preprint arXiv:2503.05647, 2025

    2025 arXiv

  42. [48]

    Heisenberg-limitedquantum phase estimation of multiple eigenvalues with few control qubits.Quantum, 6:830, 2022

    AlicjaDutkiewicz,BarbaraMTerhal,andThomasEO’Brien. Heisenberg-limitedquantum phase estimation of multiple eigenvalues with few control qubits.Quantum, 6:830, 2022

    2022

  43. [49]

    Error mitigation and circuit division for early fault-tolerant quantum phase estimation.arXiv preprint arXiv:2410.05369, 2024

    Alicja Dutkiewicz, Stefano Polla, Maximilian Scheurer, Christian Gogolin, William J Hug- gins, and Thomas E O’Brien. Error mitigation and circuit division for early fault-tolerant quantum phase estimation.arXiv preprint arXiv:2410.05369, 2024

  44. [50]

    Quantum multiple eigenvalue Gaussian filtered search: an efficient and versatile quantum phase estimation method.Quantum, 8:1487, 2024

    ZhiyanDing,HaoyaLi,LinLin,HongKangNi,LexingYing,andRuizheZhang. Quantum multiple eigenvalue Gaussian filtered search: an efficient and versatile quantum phase estimation method.Quantum, 8:1487, 2024

    2024

  45. [51]

    The Journal of Chemical Physics, 93(4):2611–2616, 1990

    DanielNeuhauser.Boundstateeigenfunctionsfromwavepackets: Time →energyresolution. The Journal of Chemical Physics, 93(4):2611–2616, 1990

    1990

  46. [52]

    Mandelshtam

    V.A. Mandelshtam. FDM: the filter diagonalization method for data processing in NMR experiments.ProgressinNuclearMagneticResonanceSpectroscopy ,38(2):159–196,2001

    2001

  47. [53]

    de Jong, and Norm M

    Katherine Klymko, Carlos Mejuto-Zaera, Stephen J Cotton, Filip Wudarski, Miroslav Ur- banek, Diptarka Hait, Martin Head-Gordon, K Birgitta Whaley, Jonathan Moussa, Nathan Wiebe, Wibe A. de Jong, and Norm M. Tubman. Real-time evolution for ultracompact Hamiltonian eigenstates o...

    2022

  48. [54]

    Real-time Krylov theory for quantum computing algorithms.Quantum, 7:1066, 2023

    YizhiShen,KatherineKlymko,JamesSud,DavidBWilliams-Young,WibeAdeJong,and Norm M Tubman. Real-time Krylov theory for quantum computing algorithms.Quantum, 7:1066, 2023

    2023

  49. [55]

    QuantumKrylovsubspacealgorithmsforground-and excited-state energy estimation.Physical Review A, 105(2):022417, 2022

    CristianLCortesandStephenKGray. QuantumKrylovsubspacealgorithmsforground-and excited-state energy estimation.Physical Review A, 105(2):022417, 2022

    2022

  50. [56]

    Quantum filter diagonalization: Quantum eigen- decomposition without full quantum phase estimation.arXiv preprint arXiv:1909.08925, 2019

    Robert M Parrish and Peter L McMahon. Quantum filter diagonalization: Quantum eigen- decomposition without full quantum phase estimation.arXiv preprint arXiv:1909.08925, 2019

    1909 arXiv

  51. [57]

    Quantum filter diagonalization with compressed double-factorized hamiltonians.PRX Quantum, 2(4):040352, 2021

    Jeffrey Cohn, Mario Motta, and Robert M Parrish. Quantum filter diagonalization with compressed double-factorized hamiltonians.PRX Quantum, 2(4):040352, 2021

    2021

  52. [58]

    A theory of quantum subspace diagonal- ization

    Ethan N Epperly, Lin Lin, and Yuji Nakatsukasa. A theory of quantum subspace diagonal- ization. SIAM Journal on Matrix Analysis and Applications, 43(3):1263–1290, 2022

    2022

  53. [59]

    Analysis of quantum Krylov algorithms with errors.Quantum, 8:1457, 2024

    William Kirby. Analysis of quantum Krylov algorithms with errors.Quantum, 8:1457, 2024

    2024

  54. [62]

    Slepian and H

    D. Slepian and H. O. Pollak. Prolate spheroidal wave functions, Fourier analysis and uncertainty — I.The Bell System Technical Journal, 40(1):43–63, 1961

    1961

  55. [63]

    H. J. Landau and H. O. Pollak. Prolate spheroidal wave functions, Fourier analysis and uncertainty — II.The Bell System Technical Journal, 40(1):65–84, 1961

    1961

  56. [64]

    H. J. Landau and H. O. Pollak. Prolate spheroidal wave functions, Fourier analysis and uncertainty—III:Thedimensionofthespaceofessentiallytime-andband-limitedsignals. The Bell System Technical Journal, 41(4):1295–1336, 1962

    1962

  57. [65]

    David Slepian. Prolate spheroidal wave functions, Fourier analysis and uncertainty — IV: Extensions to many dimensions; generalized prolate spheroidal functions.The Bell System Technical Journal, 43(6):3009–3057, 1964

    1964

  58. [66]

    D. Slepian. Prolate spheroidal wave functions, fourier analysis, and uncertainty — V: The discrete case.The Bell System Technical Journal, 57(5):1371–1430, 1978

    1978

  59. [67]

    D. Slepian. On bandwidth.Proceedings of the IEEE, 64(3):292–300, 1976

    1976

  60. [68]

    Onthedensityofphase-spaceexpansions

    H.J.Landau. Onthedensityofphase-spaceexpansions. IEEETransactionsonInformation Theory, 39(4):1152–1156, 1993

    1993

  61. [69]

    Some comments on fourier analysis, uncertainty and modeling

    David Slepian. Some comments on fourier analysis, uncertainty and modeling. SIAM Review, 25(3):379–393, 1983

    1983

  62. [70]

    Levitina and E.J

    T. Levitina and E.J. Brändas. Filter diagonalization: Filtering and postprocessing with prolates. Computer Physics Communications, 180(9):1448–1457, 2009

    2009

  63. [71]

    Boisvert

    Arnie Lee Van Buren and Jeffrey E. Boisvert. Accurate calculation of prolate spheroidal radialfunctionsofthefirstkindandtheirfirstderivatives. QuarterlyofAppliedMathematics , 60:589–599, 2002

    2002

  64. [72]

    Sampling Theory in Signal and Image Processing, 2(1):25–52, 2003

    GilbertG.WalterandXiaopingA.Shen.SamplingWithProlateSpheroidalWaveFunctions. Sampling Theory in Signal and Image Processing, 2(1):25–52, 2003. 35

    2003

  65. [73]

    Mathematische Begründung der Quantenmechanik.Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, pages 1–57, 1927

    John von Neumann. Mathematische Begründung der Quantenmechanik.Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, pages 1–57, 1927

    1927

  66. [74]

    Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik

    John von Neumann. Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch- Physikalische Klasse, pages 245–272, 1927

    1927

  67. [75]

    Allgemeine Eigenwerttheorie Hermitischer Funktionaloperatoren

    John von Neumann. Allgemeine Eigenwerttheorie Hermitischer Funktionaloperatoren. Mathematische Annalen, 102:49-131, 1930

    1930

  68. [76]

    Lectures on Fourier Integrals

    Salomon Bochner. Lectures on Fourier Integrals. Princeton University Press, Princeton, NJ, 1932

    1932

  69. [77]

    FundamentalsoftheTheoryofOperatorAlgebras, Volume I: Elementary Theory, volume 15 ofGraduate Studies in Mathematics

    RichardV.KadisonandJohnR.Ringrose. FundamentalsoftheTheoryofOperatorAlgebras, Volume I: Elementary Theory, volume 15 ofGraduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1997

    1997

  70. [78]

    The Journal of Chemical Physics, 102(20):8011–8022, May 1995

    MichaelR.WallandDanielNeuhauser.Extraction,throughfilter-diagonalization,ofgeneral quantumeigenvaluesorclassicalnormalmodefrequenciesfromasmallnumberofresidues orashort-timesegmentofasignal.I.Theoryandapplicationtoaquantum-dynamicsmodel. The Journal of Chemical Physics, 102(20...

    1995

  71. [79]

    Mandelshtam and Howard S

    Vladimir A. Mandelshtam and Howard S. Taylor. Harmonic inversion of time signals and its applications.The Journal of Chemical Physics, 107(17):6756–6769, November 1997

    1997

  72. [80]

    Matrix bispectrality and noncommutativealgebras: Beyondtheprolatespheroidals

    Alberto Grunbaum, Brian Vasquez Campos, and Jorge Zubelli. Matrix bispectrality and noncommutativealgebras: Beyondtheprolatespheroidals. L’EnseignementMathématique, 69:335–351, 06 2023

    2023

  73. [81]

    The uv prolate spectrum matches the zeros of zeta

    Alain Connes and Henri Moscovici. The uv prolate spectrum matches the zeros of zeta. Proceedings of the National Academy of Sciences, 119(22):e2123174119, 2022

    2022

  74. [82]

    Ontheeigenvaluesofanintegralequationarisinginthetheoryofband-limited signals

    W.H.JFuchs. Ontheeigenvaluesofanintegralequationarisinginthetheoryofband-limited signals. Journal of Mathematical Analysis and Applications, 9(3):317–330, 1964

    1964

  75. [83]

    Someasymptoticexpansionsforprolatespheroidalwavefunctions

    DavidSlepian. Someasymptoticexpansionsforprolatespheroidalwavefunctions. Journal of Mathematics and Physics, 44(1-4):99–140, 1965

    1965

  76. [84]

    Communicationinthepresenceofnoise

    C.E.Shannon. Communicationinthepresenceofnoise. ProceedingsoftheIRE ,37(1):10– 21, 1949

    1949

  77. [85]

    Simulatingphysicswithcomputers

    RichardP.Feynman. Simulatingphysicswithcomputers. InternationalJournalofTheoret- ical Physics, 21(6):467–488, June 1982

    1982

  78. [86]

    Universal quantum simulators.Science, 273(5278):1073–1078, 1996

    Seth Lloyd. Universal quantum simulators.Science, 273(5278):1073–1078, 1996

    1996

  79. [87]

    Pennylane: Automatic differentiation of hybrid quantum-classical computations

    Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, Shahnawaz Ahmed, Vishnu Ajith, M Sohaib Alam, Guillermo Alonso-Linaje, B AkashNarayanan, Ali Asadi, et al. Pennylane: Automatic differentiation of hybrid quantum-classical computations. arXiv preprint arXiv:1811.04968, 2018

    2018 arXiv

  80. [88]

    Quantum chemistry exchange program, indiana university, no

    WJ Hehre, WA Lathan, R Ditchfield, and MD Newton. Quantum chemistry exchange program, indiana university, no. 236, wj hehre, rf stewart, and ja pople.The Journal of Chemical Physics, 51:2657, 1969

    1969

  81. [89]

    Overlapper

    Fomichev Stepan, Hejazi Kasra, Fraxanet Joana, and Juan Miguel Arrazola. Overlapper. GitHub repository, https://github.com/XanaduAI/Overlapper, 2024. 36

    2024

  82. [90]

    Recent developments in the pyscf program package.The Journal of Chemical Physics, 153(2), 2020

    Qiming Sun, Xing Zhang, Samragni Banerjee, Peng Bao, Marc Barbry, Nick S Blunt, Nikolay A Bogdanov, George H Booth, Jia Chen, Zhi-Hao Cui, et al. Recent developments in the pyscf program package.The Journal of Chemical Physics, 153(2), 2020

    2020

  83. [91]

    JAX: composable transformations of Python+NumPy programs, 2018

    JamesBradbury,RoyFrostig,PeterHawkins,MatthewJamesJohnson,ChrisLeary,Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang. JAX: composable transformations of Python+NumPy programs, 2018

    2018

  84. [92]

    Theconfigurationinteractionmethod: Advances in highly correlated approaches

    CDavidSherrillandHenryFSchaeferIII. Theconfigurationinteractionmethod: Advances in highly correlated approaches. InAdvances in Quantum Chemistry, volume 34, pages 143–269. Elsevier, 1999

    1999

  85. [93]

    Ab initio excitation spectra and collective electronic response in atoms and clusters.Physical Review Letters, 82(9):1919, 1999

    Igor Vasiliev, Serdar Öğüt, and James R Chelikowsky. Ab initio excitation spectra and collective electronic response in atoms and clusters.Physical Review Letters, 82(9):1919, 1999

    1919

  86. [94]

    John Wiley & Sons, 2013

    Trygve Helgaker, Poul Jorgensen, and Jeppe Olsen.Molecular electronic-structure theory. John Wiley & Sons, 2013

    2013

  87. [95]

    Assessingthequerycomplexitylimitsofquantumphaseestimationusingsymmetry- aware spectral bounds.Physical Review A, 110(2):022420, 2024

    Cristian L Cortes, Dario Rocca, Jérôme F Gonthier, Pauline J Ollitrault, Robert M Parrish, Gian-LucaRAnselmetti,MatthiasDegroote,NikolajMoll,RaffaeleSantagati,andMichael Streif. Assessingthequerycomplexitylimitsofquantumphaseestimationusingsymmetry- aware spectral bounds.Physi...

    2024

  88. [96]

    Journal of Chemical Theory and Computation, 12(4):1760–1771, 2016

    ChristopherJSteinandMarkusReiher.Automatedselectionofactiveorbitalspaces. Journal of Chemical Theory and Computation, 12(4):1760–1771, 2016

    2016

  89. [97]

    Strong electronic correlation in the hydrogen chain: A variational monte carlo study.Physical Review B, 84(24):245117, 2011

    Lorenzo Stella, Claudio Attaccalite, Sandro Sorella, and Angel Rubio. Strong electronic correlation in the hydrogen chain: A variational monte carlo study.Physical Review B, 84(24):245117, 2011

    2011

  90. [98]

    Towards thesolutionofthemany-electronprobleminrealmaterials: Equationofstateofthehydrogen chain with state-of-the-art many-body methods.Physical Review X, 7(3):031059, 2017

    Mario Motta, David M Ceperley, Garnet Kin-Lic Chan, John A Gomez, Emanuel Gull, Sheng Guo, Carlos A Jiménez-Hoyos, Tran Nguyen Lan, Jia Li, Fengjie Ma, et al. Towards thesolutionofthemany-electronprobleminrealmaterials: Equationofstateofthehydrogen chain with state-of-the-art ...

    2017

  91. [99]

    Ground-state properties of the hydrogen chain: Dimerization, insulator-to-metal transition, and magnetic phases.Physical Review X, 10(3):031058, 2020

    Mario Motta, Claudio Genovese, Fengjie Ma, Zhi-Hao Cui, Randy Sawaya, Garnet Kin- Lic Chan, Natalia Chepiga, Phillip Helms, Carlos Jiménez-Hoyos, Andrew J Millis, et al. Ground-state properties of the hydrogen chain: Dimerization, insulator-to-metal transition, and magnetic ph...

    2020

  92. [100]

    Classificationofelectronicstructuresandstatepreparationforquantum computation of reaction chemistry.arXiv preprint arXiv:2409.08910, 2024

    Maximilian Mörchen, Guang Hao Low, Thomas Weymuth, Hongbin Liu, Matthias Troyer, andMarkusReiher. Classificationofelectronicstructuresandstatepreparationforquantum computation of reaction chemistry.arXiv preprint arXiv:2409.08910, 2024

    2024 arXiv

  93. [101]

    The esprit algorithm under high noise: Optimal error scaling and noisy super-resolution

    Zhiyan Ding, Ethan N Epperly, Lin Lin, and Ruizhe Zhang. The esprit algorithm under high noise: Optimal error scaling and noisy super-resolution. In2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS), pages 2344–2366. IEEE, 2024

    2024

  94. [102]

    Effects of cosine tapering window on quantum phase estimation.Physical Review D, 106(3):034503, 2022

    Gumaro Rendon, Taku Izubuchi, and Yuta Kikuchi. Effects of cosine tapering window on quantum phase estimation.Physical Review D, 106(3):034503, 2022

    2022

  95. [103]

    Emergingquantumcomputingalgorithmsforquantumchem- istry

    MarioMottaandJuliaERice. Emergingquantumcomputingalgorithmsforquantumchem- istry. Wiley Interdisciplinary Reviews: Computational Molecular Science, 12(3):e1580, 2022

    2022

  96. [104]

    Robust interpolation between weak-and strong-correlation regimes of quantum systems.The Journal of Chemical Physics, 136(4), 2012

    Jerzy Cioslowski. Robust interpolation between weak-and strong-correlation regimes of quantum systems.The Journal of Chemical Physics, 136(4), 2012. 37

    2012

  97. [105]

    Quantum information reveals that orbital-wise correlation is essentially classical in natural orbitals

    Davide Materia, Leonardo Ratini, Celestino Angeli, and Leonardo Guidoni. Quantum information reveals that orbital-wise correlation is essentially classical in natural orbitals. The Journal of Chemical Physics, 161(24), 2024

    2024

  98. [106]

    Environment-induced superselection rules

    Wojciech H Zurek. Environment-induced superselection rules. Physical Review D, 26(8):1862, 1982

    1982

  99. [107]

    Infrared catastrophe in fermi gases with local scattering potentials

    Philip W Anderson. Infrared catastrophe in fermi gases with local scattering potentials. Physical Review Letters, 18(24):1049, 1967

    1967

  100. [108]

    The complexity of the local hamiltonian problem

    Julia Kempe, Alexei Kitaev, and Oded Regev. The complexity of the local hamiltonian problem. Siam Journal on Computing, 35(5):1070–1097, 2006

    2006

  101. [109]

    Intractability of electronic structure in a fixed basis.PRX Quantum, 3(2):020322, 2022

    Bryan O’Gorman, Sandy Irani, James Whitfield, and Bill Fefferman. Intractability of electronic structure in a fixed basis.PRX Quantum, 3(2):020322, 2022

    2022

  102. [110]

    Early fault-tolerant quantum algorithms in practice: Application to ground-state energy estimation.Quantum, 9:1682, 2025

    Oriel Kiss, Utkarsh Azad, Borja Requena, Alessandro Roggero, David Wakeham, and Juan Miguel Arrazola. Early fault-tolerant quantum algorithms in practice: Application to ground-state energy estimation.Quantum, 9:1682, 2025

    2025

  103. [111]

    Analysis of a Differential Operator

    Andrei Osipov, Vladimir Rokhlin, and Hong Xiao. Analysis of a Differential Operator. In Prolate Spheroidal Wave Functions of Order Zero: Mathematical Tools for Bandlimited Approximation, pages 73–133. Springer US, Boston, MA, 2013

    2013

  104. [112]

    Efficient strategies forreducingsamplingerrorinquantumkrylovsubspacediagonalization

    Gwonhak Lee, Seonghoon Choi, Joonsuk Huh, and Artur F Izmaylov. Efficient strategies forreducingsamplingerrorinquantumkrylovsubspacediagonalization. DigitalDiscovery, 4(4):954–969, 2025

    2025

  105. [113]

    Eigenvaluedistributionoftimeandfrequencylimiting

    H.JLandauandHWidom. Eigenvaluedistributionoftimeandfrequencylimiting. Journal of Mathematical Analysis and Applications, 77(2):469–481, October 1980

    1980

  106. [114]

    F. A. Grünbaum and M. Yakimov. The prolate spheroidal phenomenon as a consequence of bispectrality. In Superintegrability in Classical and Quantum Systems, volume 37 of CRM Proceedings and Lecture Notes, pages 301–312. American Mathematical Society, Providence, RI, 2004

    2004

  107. [115]

    Riley Casper, F

    W. Riley Casper, F. Alberto Grünbaum, Milen Yakimov, and Ignacio Zurrián. Algebras of Commuting Differential Operators for Kernels of Airy Type. In Estelle Basor, Albrecht Böttcher, Torsten Ehrhardt, and Craig A. Tracy, editors,Toeplitz Operators and Random Matrices: InMemoryo...

    2022

  108. [116]

    Matrixvalued discrete-continuous functions with the prolate spheroidal property and bispectrality.arXiv preprint arXiv:2302.05750, 2024

    W.RileyCasper,F.AlbertoGrünbaum,MilenYakimov,andIgnacioZurrian. Matrixvalued discrete-continuous functions with the prolate spheroidal property and bispectrality.arXiv preprint arXiv:2302.05750, 2024

    2024 arXiv

  109. [117]

    Reed and B

    M. Reed and B. Simon.IV: Analysis of Operators. Methods of Modern Mathematical Physics. Elsevier Science, 1978

    1978

  110. [118]

    H. Nyquist. Certain topics in telegraph transmission theory.Transactions of the American Institute of Electrical Engineers, 47(2):617–644, 1928

    1928

  111. [119]

    Hogan and Joseph D

    Jeffrey A. Hogan and Joseph D. Lakey.Duration and Bandwidth Limiting: Prolate Func- tions, Sampling, and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Boston, Boston, 2012. 38

    2012

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.