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arxiv: 2606.28255 · v1 · pith:3GMNJ4JLnew · submitted 2026-06-26 · 🪐 quant-ph · physics.chem-ph

Efficient targeting of arbitrary excited states with quantum inverse power iteration through filtering polynomials

Srushti Patil , Nina Glaser This is my paper

Pith reviewed 2026-06-29 03:12 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-ph
keywords quantum inverse power iterationeigenstate filteringQSVTexcited statesquantum chemistrymolecular Hamiltoniansfault-tolerant quantum computing
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The pith

Eigenstate filtering polynomials make quantum inverse power iteration robust for arbitrary excited states

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

This paper develops a quantum inverse power iteration algorithm using quantum singular value transformation to prepare arbitrary excited states given an energy shift. Earlier Fourier-based methods were unstable and limited mostly to ground states because they diverge with poor hyperparameter choices. The new approach replaces those decompositions with an eigenstate filtering polynomial that exploits symmetry to avoid divergence and suppress off-target states even when eigenvalues lie close together. Simulations on the Hamiltonians of H2, LiH and BeH2 demonstrate faster convergence to higher excited states, and the method requires only modest polynomial degrees under standard oracle access.

Core claim

EF-based QIPI is substantially more robust than Cheb-inv and other decomposition-based approaches due to the symmetry of the applied filtering polynomial, avoiding divergence with respect to the choice of ω and efficiently suppressing off-target eigenstates even in closely spaced spectra.

What carries the argument

The eigenstate filtering polynomial, applied iteratively via QSVT to approximate the action of the shifted inverse (H - ωI)^{-1} on a trial state.

If this is right

  • Improved convergence and access to higher excited states on the molecular Hamiltonians of H2, LiH and BeH2.
  • High target-state amplification achieved with modest polynomial degrees.
  • Logical T-gate counts remain practical for fault-tolerant implementations under standard oracle access.
  • Promising route to scalable excited-state preparation in fault-tolerant quantum chemistry.

Where Pith is reading between the lines

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

  • The same symmetry may reduce hyperparameter sensitivity across a wider range of quantum simulation tasks that currently rely on inverse or power methods.
  • If the polynomial degree stays modest on larger molecules, the approach could be paired with existing ground-state routines without large increases in circuit depth.
  • A direct comparison of wall-clock resources against variational excited-state methods on the same Hamiltonians would clarify practical trade-offs.
  • The method's reliance on an energy shift ω suggests it could be combined with classical diagonalization guesses to further accelerate targeting.

Load-bearing premise

The symmetry property of the eigenstate filtering polynomial will continue to suppress off-target states efficiently when spectra become denser or when the Hamiltonian oracle is implemented on actual hardware.

What would settle it

A simulation or hardware run on a molecular Hamiltonian with several closely spaced excited states that shows either divergence with respect to ω or failure to amplify the target state above a chosen threshold using the EF polynomial.

Figures

Figures reproduced from arXiv: 2606.28255 by Nina Glaser, Srushti Patil.

Figure 1
Figure 1. Figure 1: Illustration of the spectral transformation resulting from shifting and inverting a [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic illustration of QIPI. First, the system qubits are initialized and a trial [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Cheb-Inv QIPI application to H2 in the STO-3G basis. Left: The inverse of the shifted and scaled Hamiltonian A is decomposed with Chebyshev polynomials with different truncation orders to target the eigenstate corresponding to λ2. Right: Chebyshev-based QIPI convergence as measured by the target state fidelity of the projected trial state for different maximum polynomial degrees Nmax. The black dashed line… view at source ↗
Figure 4
Figure 4. Figure 4: Eigenstate filtering polynomials with different degrees [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of QSVT. (a) First, we block encode our matrix [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Transformation of eigenvalues {λ˜ i} of a shifted-and-inverted matrix H˜ by an eigenstate filtering polynomial of degree d = 8 through QSVT. Eigenvalues are transformed as {R8(λ˜ i , ∆)}, as indicated by the intersection points. The one closest to the origin, λ˜ 2 is amplified the most. trial state |Ψ0⟩ having nonzero overlap with the target state via U|Ψ0⟩ . Then, we block encode our rescaled and shifted … view at source ↗
Figure 7
Figure 7. Figure 7: Illustration of EFP-based QIPI. After initializing the guess state, each QIPI it [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: QIPI simulation results on H2 , LiH, and BeH2 with exact QSVT rotations. (Left) Varying degree EFP transformation of eigenvalues of H˜ . Vertical lines denote the spectrum of H˜ , with the target λ˜ t represented in bold. The eigenvalue closest to the spectral origin is amplified the most for all degrees of the EF polynomial. (Right) Convergence behaviour of QIPI for the corresponding EF polynomial. 20 [P… view at source ↗
Figure 9
Figure 9. Figure 9: Quantitative overview of T count per rotation decomposition for different preci [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: As the decomposition precision increases, the EF amplification is more faithfully [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: QIPI simulation results on H2 , LiH, and BeH2 with rotation decomposition for different precisions. (left) EFP transformations with finite-precision rotation synthesis. For lower precisions, amplification is not retrieved fully; as we go to higher precisions, the amplification effect is preserved. (right) Corresponding convergence behaviour of QIPI. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Amplification ratio ρamp of Eq. 12 versus T gate count for various rotation decomposition precisions ϵ across different window values ∆ and varying degrees d. Larger polynomial degrees only result in greater amplification for high-precision decompositions, thereby increasing the T-gate cost significantly compared to similar amplification with lower￾degree lower-precision EFP implementations. state itself.… view at source ↗
Figure 12
Figure 12. Figure 12: Number of queries to reach chemical accuracy ( [PITH_FULL_IMAGE:figures/full_fig_p030_12.png] view at source ↗
read the original abstract

In this work, we introduce a quantum inverse power iteration (QIPI) algorithm based on the quantum singular value transformation (QSVT) to target arbitrary excited states. Given an energy shift $\omega$, QIPI prepares the target excited state by iteratively applying an approximation of the shifted inverse Hamiltonian $(H-\omega I)^{-1}$ to a trial state. Prior quantum inverse power approaches typically relied on Fourier decompositions of the inverse Hamiltonian, with numerical quadrature used to reconstruct the transformation, but such methods are highly sensitive to hyperparameter choices and have been observed to be numerically unstable, effectively restricting their use to ground-state preparation. To enable robust excited-state targeting, we investigate two alternative transformation techniques: a Chebyshev decomposition of the inverse (Cheb-inv) and an eigenstate filtering (EF) approach based on QSVT. We find that EF-based QIPI is substantially more robust than Cheb-inv and other decomposition-based approaches due to the symmetry of the applied filtering polynomial, avoiding divergence with respect to the choice of $\omega$ and efficiently suppressing off-target eigenstates even in closely spaced spectra. Numerical simulations for molecular Hamiltonians of H$_2$, LiH, and BeH$_2$ show improved convergence and enhanced access to higher excited states relative to other quantum power methods. Assuming standard oracle access to the Hamiltonian, we further provide logical resource estimates in fault-tolerant settings in terms of T gate counts, and conclude that QIPI can achieve high target state amplification with modest polynomial degrees, thereby making it a promising candidate for scalable excited-state preparation in fault-tolerant quantum chemistry applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript introduces a QIPI algorithm based on QSVT that uses an eigenstate-filtering polynomial to target arbitrary excited states given an energy shift ω. It contrasts this EF approach with Chebyshev inversion (Cheb-inv) and other decompositions, attributing superior robustness—no divergence w.r.t. ω and efficient off-target suppression even for close eigenvalues—to the symmetry of the EF polynomial. Numerical demonstrations on the H2, LiH, and BeH2 Hamiltonians are reported to show improved convergence to higher excited states, and logical T-gate resource estimates under standard oracle access are supplied.

Significance. If the claimed robustness generalizes, the method would offer a structurally motivated route to excited-state preparation that avoids the hyperparameter sensitivity of quadrature-based inverses. The explicit T-gate counts constitute a concrete strength, enabling direct resource comparisons with other fault-tolerant quantum chemistry algorithms. The symmetry argument supplies a clear mechanistic explanation for the observed stability on the tested instances.

major comments (1)
  1. [Numerical simulations] Numerical simulations section: the central claim that EF-based QIPI is substantially more robust due to polynomial symmetry and efficiently suppresses off-target states even in closely spaced spectra is supported only by results on H2, LiH, and BeH2. These Hamiltonians possess relatively sparse spectra; no explicit scaling test or counter-example is provided for regimes in which eigenvalue gaps fall below the effective resolution set by the chosen polynomial degree, leaving the extrapolation to denser spectra as an unverified step for the robustness assertion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: Numerical simulations section: the central claim that EF-based QIPI is substantially more robust due to polynomial symmetry and efficiently suppresses off-target states even in closely spaced spectra is supported only by results on H2, LiH, and BeH2. These Hamiltonians possess relatively sparse spectra; no explicit scaling test or counter-example is provided for regimes in which eigenvalue gaps fall below the effective resolution set by the chosen polynomial degree, leaving the extrapolation to denser spectra as an unverified step for the robustness assertion.

    Authors: We agree that the numerical demonstrations use H₂, LiH, and BeH₂, whose spectra are relatively sparse compared with larger systems. The manuscript does not contain explicit scaling tests or counter-examples on denser spectra where gaps fall below the polynomial resolution. The robustness claim is grounded in the symmetry of the EF polynomial, which is an odd function around the shift ω; this structural property prevents divergence and ensures consistent off-target suppression for any spectrum provided the degree suffices to resolve the target gap. This argument is independent of the specific eigenvalue density. Nevertheless, we acknowledge that direct numerical verification on denser spectra would strengthen the extrapolation. In the revised manuscript we will add a short paragraph in the numerical simulations section discussing this limitation and the expected scaling of required degree with minimum gap size. revision: partial

Circularity Check

0 steps flagged

No circularity: robustness attributed to structural polynomial symmetry, supported by explicit simulations

full rationale

The manuscript constructs QIPI via QSVT with an eigenstate-filtering polynomial and attributes robustness (no ω-divergence, off-target suppression) to the polynomial's symmetry as a stated structural property. This is then validated by direct numerical runs on H2, LiH, and BeH2 Hamiltonians. No equation reduces a claimed prediction to a fitted input by construction, no load-bearing self-citation chain appears, and the symmetry is not imported via an ansatz from prior author work. The derivation chain remains self-contained against the reported benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the approach rests on standard quantum computing oracles for the Hamiltonian and the existence of efficient QSVT polynomial implementations; no new entities are introduced.

free parameters (2)
  • polynomial degree
    Chosen to achieve target amplification; abstract states modest degrees suffice but does not specify how the degree is selected.
  • energy shift ω
    User-provided input; robustness to its choice is claimed but the selection process is not detailed.
axioms (2)
  • domain assumption Standard oracle access to the Hamiltonian is available and implementable via QSVT block encodings.
    Invoked when stating logical resource estimates in fault-tolerant settings.
  • domain assumption The filtering polynomial can be constructed to have the required symmetry properties for any chosen ω.
    Central to the robustness claim in the abstract.

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Reference graph

Works this paper leans on

65 extracted references · 21 canonical work pages · 1 internal anchor

  1. [1]

    npj Quantum Inf

    Quantum inverse iteration algorithm for programmable quantum simulators , author=. npj Quantum Inf. , volume=. 2020 , publisher=

    2020

  2. [2]

    Preparing Ground States of Quantum Many-Body Systems on a Quantum Computer , author =. Phys. Rev. Lett. , volume =. 2009 , month =. doi:10.1103/PhysRevLett.102.130503 , url =

    work page doi:10.1103/physrevlett.102.130503 2009

  3. [3]

    and Kothari, Robin and Somma, Rolando D

    Childs, Andrew M. and Kothari, Robin and Somma, Rolando D. , year=. Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision , volume=. SIAM J. Comput. , publisher=. doi:10.1137/16m1087072 , number=

    work page internal anchor Pith review doi:10.1137/16m1087072

  4. [4]

    Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems , volume=

    Lin, Lin and Tong, Yu , year=. Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems , volume=. doi:10.22331/q-2020-11-11-361 , journal=

    work page doi:10.22331/q-2020-11-11-361 2020

  5. [5]

    Quantum , volume=

    Variational quantum computation of excited states , author=. Quantum , volume=. 2019 , publisher=

    2019

  6. [6]

    and Mitarai, Kosuke and Fujii, Keisuke , year=

    Nakanishi, Ken M. and Mitarai, Kosuke and Fujii, Keisuke , year=. Subspace-search variational quantum eigensolver for excited states , volume=. Phys. Rev. Res. , publisher=. doi:10.1103/physrevresearch.1.033062 , number=

    work page doi:10.1103/physrevresearch.1.033062

  7. [7]

    Simulating chemistry using quantum computers , author=. Annu. Rev. Phys. Chem. , volume=. 2011 , publisher=

    2011

  8. [8]

    Simulating quantum systems on a quantum computer , author=. Proc. R. Soc. A , volume=. 1998 , publisher=

    1998

  9. [9]

    Quantum chemistry in the age of quantum computing , author=. Chem. Rev. , volume=. 2019 , publisher=

    2019

  10. [10]

    1995 , eprint=

    Quantum measurements and the Abelian Stabilizer Problem , author=. 1995 , eprint=

    1995

  11. [11]

    Peruzzo, J

    Peruzzo, Alberto and McClean, Jarrod and Shadbolt, Peter and Yung, Man-Hong and Zhou, Xiao-Qi and Love, Peter J. and Aspuru-Guzik, Alán and O’Brien, Jeremy L. , year=. A variational eigenvalue solver on a photonic quantum processor , volume=. Nat. Commun. , publisher=. doi:10.1038/ncomms5213 , number=

    work page doi:10.1038/ncomms5213

  12. [12]

    Cadi Tazi, Lila and Thom, Alex J. W. , title =. J. Chem. Theory Comput. , volume =. 2024 , doi =

    2024

  13. [13]

    and Tsuchimochi, Takashi

    Yoshikura, Takahiro and Ten-no, Seiichiro L. and Tsuchimochi, Takashi. Quantum Inverse Algorithm via Adaptive Variational Quantum Linear Solver: Applications to General Eigenstates. J. Phys. Chem. A. 2023. doi:10.1021/acs.jpca.3c02800

    work page doi:10.1021/acs.jpca.3c02800 2023

  14. [14]

    Cainelli, Mauro and Baba, Reo and Kurashige, Yuki , title =. J. Chem. Theory Comput. , volume =. 2024 , doi =

    2024

  15. [15]

    Quantum Krylov subspace algorithms for ground- and excited-state energy estimation , author =. Phys. Rev. A , volume =. 2022 , month =. doi:10.1103/PhysRevA.105.022417 , url =

    work page doi:10.1103/physreva.105.022417 2022

  16. [16]

    and Childs, Andrew M

    Berry, Dominic W. and Childs, Andrew M. and Kothari, Robin , booktitle=. Hamiltonian Simulation with Nearly Optimal Dependence on all Parameters , year=

  17. [17]

    PRX Quantum , volume=

    Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation , author=. PRX Quantum , volume=. 2023 , publisher=

    2023

  18. [18]

    PRX Quantum , volume=

    Heisenberg-limited ground-state energy estimation for early fault-tolerant quantum computers , author=. PRX Quantum , volume=. 2022 , publisher=

    2022

  19. [19]

    npj Quantum Inf

    Quantum chemistry as a benchmark for near-term quantum computers , author=. npj Quantum Inf. , volume=. 2019 , publisher=

    2019

  20. [20]

    and Armaos, V

    Yordanov, Yordan S. and Armaos, V. and Barnes, Crispin H. W. and Arvidsson-Shukur, David R. M. , year=. Qubit-excitation-based adaptive variational quantum eigensolver , volume=. Commun. Phys. , publisher=. doi:10.1038/s42005-021-00730-0 , number=

    work page doi:10.1038/s42005-021-00730-0

  21. [21]

    A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons , author=. J. Chem. Theory Comput. , volume=. 2020 , doi=

    2020

  22. [22]

    Nature , publisher=

    Quantum error correction below the surface code threshold , volume=. Nature , publisher=. 2024 , month=dec, pages=. doi:10.1038/s41586-024-08449-y , number=

    work page doi:10.1038/s41586-024-08449-y 2024

  23. [23]

    Quantum chemistry of the excited state: 2005 overview , journal =

    Luis Serrano-Andrés and Manuela Merchán , keywords =. Quantum chemistry of the excited state: 2005 overview , journal =. 2005 , note =. doi:10.1016/j.theochem.2005.03.020 , url =

    work page doi:10.1016/j.theochem.2005.03.020 2005

  24. [24]

    2020 , publisher=

    Quantum chemistry and dynamics of excited states: methods and applications , author=. 2020 , publisher=

    2020

  25. [25]

    Charge and Energy Transfer Dynamics in Molecular Systems

    Chergui, Majed , year =. Charge and Energy Transfer Dynamics in Molecular Systems. 2nd, Revised and Enlarged Edition. By Volkhard May and Oliver Kühn , volume =. ChemPhysChem , doi =

  26. [26]

    * excited states in molecular photochemistry , author=. Phys. Chem. Chem. Phys. , volume=. 2010 , publisher=

    2010

  27. [27]

    Multireference Approaches for Excited States of Molecules , journal =

    Lischka, Hans and Nachtigallová, Dana and Aquino, Ad. Multireference Approaches for Excited States of Molecules , journal =. 2018 , doi =

    2018

  28. [28]

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

    work page doi:10.1103/revmodphys.79.291 2007

  29. [29]

    2011 , publisher=

    Numerical methods for large eigenvalue problems: revised edition , author=. 2011 , publisher=

    2011

  30. [30]

    Sun, Qiming and Zhang, Xing, Banerjee et al , title =. J. Chem. Phys. , volume =. 2020 , month =. doi:10.1063/5.0006074 , url =

    work page doi:10.1063/5.0006074 2020

  31. [31]

    Ignacio , title =

    Ge, Yimin and Tura, Jordi and Cirac, J. Ignacio , title =. J. Math. Phys. , volume =. 2019 , month =. doi:10.1063/1.5027484 , url =

    work page doi:10.1063/1.5027484 2019

  32. [32]

    Filtered

    Lee, Gwonhak and Kang, Minhyeok and Hong, Jungsoo and Fomichev, Stepan and Huh, Joonsuk , year =. Filtered. 2510.04294 , archivePrefix =

    arXiv

  33. [33]

    , author=

    Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: the Hitchhiker's guide to Fock space. , author=. Annu. Rev. Phys. Chem. , year=

  34. [34]

    , title =

    Ullrich, Carsten A. , title =. 2011 , doi =

    2011

  35. [35]

    , title =

    Werner, Hans‐Joachim and Knowles, Peter J. , title =. J. Chem. Phys. , volume =. 1985 , doi =

    1985

  36. [36]

    WIREs Comput

    Otis, Leon and Neuscamman, Eric , title =. WIREs Comput. Mol. Sci. , volume =. doi:10.1002/wcms.1659 , year =

    work page doi:10.1002/wcms.1659

  37. [37]

    Simulating physics with computers , volume =. Int. J. Theor. Phys. , author =. 1982 , pages =. doi:10.1007/BF02650179 , number =

    work page doi:10.1007/bf02650179 1982

  38. [38]

    and Tennyson, Jonathan , month = nov, year =

    Tilly, Jules and Chen, Hongxiang and Cao, Shuxiang and Picozzi, Dario and Setia, Kanav and Li, Ying and Grant, Edward and Wossnig, Leonard and Rungger, Ivan and Booth, George H. and Tennyson, Jonathan , month = nov, year =. The. doi:10.1016/j.physrep.2022.08.003 , journal =

    work page doi:10.1016/j.physrep.2022.08.003 2022

  39. [39]

    Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals. J. Chem. Phys. , year = 1969, month = sep, volume =

    1969

  40. [40]

    Gily\' e n, Y

    Gilyén, András and Su, Yuan and Low, Guang Hao and Wiebe, Nathan , year=. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics , url=. doi:10.1145/3313276.3316366 , booktitle=

    work page doi:10.1145/3313276.3316366

  41. [41]

    Quantum Inf

    Optimal ancilla-free Clifford+T approximation of z-rotations , author=. Quantum Inf. Comput. , volume=. 2016 , doi=

    2016

  42. [42]

    2025 , eprint=

    Generalized Quantum Signal Processing and Non-Linear Fourier Transform are equivalent , author=. 2025 , eprint=

    2025

  43. [43]

    PRX Quantum , volume=

    Grand unification of quantum algorithms , author=. PRX Quantum , volume=. 2021 , publisher=

    2021

  44. [44]

    Quantum block. Phys. Rev. A , author =. 2025 , pages =. doi:10.1103/p8wj-gplb , number =

    work page doi:10.1103/p8wj-gplb 2025

  45. [45]

    The Bravyi-Kitaev transformation for quantum computation of electronic structure , author=. J. Chem. Phys. , volume=. 2012 , publisher=

    2012

  46. [46]

    Universal quantum computation with ideal Clifford gates and noisy ancillas , author =. Phys. Rev. A , volume =. 2005 , month =. doi:10.1103/PhysRevA.71.022316 , url =

    work page doi:10.1103/physreva.71.022316 2005

  47. [47]

    Quantum , volume=

    A game of surface codes: Large-scale quantum computing with lattice surgery , author=. Quantum , volume=. 2019 , publisher=

    2019

  48. [48]

    2025 , eprint=

    Transversal Surface-Code Game Powered by Neutral Atoms , author=. 2025 , eprint=

    2025

  49. [49]

    2024 , eprint=

    Magic state cultivation: growing T states as cheap as CNOT gates , author=. 2024 , eprint=

    2024

  50. [50]

    Magic State Distillation: Not as Costly as You Think , volume=

    Litinski, Daniel , year=. Magic State Distillation: Not as Costly as You Think , volume=. doi:10.22331/q-2019-12-02-205 , journal=

    work page doi:10.22331/q-2019-12-02-205 2019

  51. [51]

    and Chuang, Isaac L

    Nielsen, Michael A. and Chuang, Isaac L. , biburl =

  52. [52]

    Surface codes: Towards practical large-scale quantum computation , author =. Phys. Rev. A , volume =. 2012 , doi =

    2012

  53. [53]

    Diagonal gates in the Clifford hierarchy , author =. Phys. Rev. A , volume =. 2017 , publisher =

    2017

  54. [54]

    Quantum , volume =

    Qubitization of arbitrary basis quantum chemistry leveraging sparsity and low rank factorization , author =. Quantum , volume =. 2019 , doi =

    2019

  55. [55]

    Quantum Information and Computation , volume =

    Hamiltonian simulation using linear combinations of unitary operations , author =. Quantum Information and Computation , volume =

  56. [56]

    QREChem: quantum resource estimation software for chemistry applications , author =. Front. Quantum Sci. Technol. , volume =. 2023 , doi =

    2023

  57. [57]

    Fixed-point quantum search with an optimal number of queries , author =. Phys. Rev. Lett. , volume =. 2014 , doi =

    2014

  58. [58]

    arXiv preprint arXiv:2507.11142 , year=

    Quantum Power Iteration Unified Using Generalized Quantum Signal Processing , author=. arXiv preprint arXiv:2507.11142 , year=. 2507.11142 , archivePrefix=

    arXiv

  59. [59]

    Imaginary Time Spectral Transforms for Excited State Preparation , author =. Phys. Rev. Research , volume =. 2026 , doi =

    2026

  60. [60]

    arXiv preprint arXiv:2302.06638 , year =

    Scalable Quantum Computation of Highly Excited Eigenstates with Spectral Transforms , author =. arXiv preprint arXiv:2302.06638 , year =. 2302.06638 , archivePrefix=

    arXiv

  61. [61]

    Filter-enhanced adiabatic quantum computing on a digital quantum processor , author =. Phys. Rev. Research , volume =. 2025 , doi =

    2025

  62. [62]

    PRX Quantum , volume =

    Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices , author =. PRX Quantum , volume =. 2022 , publisher =

    2022

  63. [63]

    PRX Quantum , volume =

    Initial State Preparation for Quantum Chemistry on Quantum Computers , author =. PRX Quantum , volume =. 2024 , doi =

    2024

  64. [64]

    Improved quantum power method and numerical integration using a quantum singular-value transformation , author =. Phys. Rev. A , volume =. 2025 , month =. doi:10.1103/PhysRevA.111.012434 , url =

    work page doi:10.1103/physreva.111.012434 2025

  65. [65]

    2025 , url =

    Lorenzo Laneve and Christoph Sünderhauf , title =. 2025 , url =

    2025