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REVIEW 2 major objections 6 minor 54 references

Quantum signal processing implements the overlap fermion Hamiltonian at only logarithmic cost above Wilson-Dirac while keeping chiral symmetry controllable.

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

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2026-07-31 04:40 UTC pith:XAQFPTPO

load-bearing objection Clean QSP construction for the overlap Hamiltonian that delivers controllable GW violation at near-Wilson gate cost and fewer qubits than domain-wall, with the fixed-κ caveat properly flagged. the 2 major comments →

arxiv 2607.28524 v1 pith:XAQFPTPO submitted 2026-07-30 hep-lat nucl-thquant-ph

Exact chiral symmetry with quantum signal processing

Henry Lamm , Alessandro Roggero , Hersh Singh , Luca Spagnoli This is my paper
classification hep-lat nucl-thquant-ph PACS 11.15.Ha12.38.Gc03.67.Ac
keywords overlap fermionsquantum signal processingGinsparg-Wilson relationchiral symmetrydomain-wall fermionslattice gauge theoryblock encodingHamiltonian simulation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Lattice quantum simulations of Dirac fermions need chiral symmetry, but the standard Wilson-Dirac Hamiltonian breaks it on the lattice. Overlap fermions restore an exact lattice chiral symmetry via the Ginsparg-Wilson relation, yet they look expensive because they require a sign function of a nonlocal operator. This paper shows that quantum signal processing can approximate that sign function so the overlap Hamiltonian costs only a factor logarithmic in the approximation error more than Wilson-Dirac to apply, while violating chiral symmetry only at that same controllable error. Compared with domain-wall fermions, the method uses fewer qubits at a mild gate-count overhead. The polynomial degree that appears in the quantum algorithm plays the same role as the extra dimension of domain-wall fermions, so the resource scaling itself reproduces the known physics that overlap fermions live at the boundary of a higher-dimensional theory.

Core claim

A QSP block encoding of a degree-M polynomial approximation to the sign of the Wilson-Dirac operator yields an overlap Hamiltonian whose Ginsparg-Wilson relation and modified chiral commutator are violated only at O(ε_e), with block-encoding cost O(Q κ^{-1} log(1/ε_e)) and time-evolution cost O(Q κ^{-1} log(1/ε_e)[Qt + log(1/ε_t)]), using O(Q) qubits rather than the O(Q L_5) of domain-wall formulations.

What carries the argument

Quantum signal processing (in its quantum singular value transformation form) applied to a block encoding of the Wilson-Dirac Hamiltonian: a degree-M odd polynomial approximates the matrix sign function, with M = O(κ^{-1} log(1/ε_e)), and that polynomial is exactly the object that both implements the overlap operator and generates an effective extra dimension of size L_5 ~ κ^{-1} log(1/ε_e).

Load-bearing premise

The construction assumes a fixed positive lower bound on the absolute eigenvalues of the Wilson Hamiltonian even when dynamical gauge fields are present, and quotes all costs at that fixed gap.

What would settle it

Compute or bound the smallest absolute eigenvalue of the block-encoded Wilson-Dirac operator for a concrete interacting gauge theory (e.g. truncated SU(2) or SU(3) on a small lattice); if that gap collapses so that κ^{-1} grows with volume or coupling, the claimed near-Wilson cost no longer holds without a deflation step.

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

If this is right

  • Exact lattice chiral symmetry in Hamiltonian quantum simulation becomes available at only a logarithmic overhead in the target error relative to Wilson fermions.
  • Overlap formulations reduce qubit count from O(Q L_5) to O(Q) compared with domain-wall, trading geometric locality for all-to-all gates.
  • The same QSP block encoding immediately supplies a modified γ_5 operator that nearly commutes with the Hamiltonian, at the same asymptotic cost as one application of the single-particle overlap operator.
  • Resource tables for chiral lattice fermions can treat ε_e ~ exp(-c L_5) as the explicit dictionary between overlap polynomial degree and domain-wall extent.
  • Gauge-field block encodings (Abelian or truncated non-Abelian) enter only through the overall normalization and do not change the leading Q and κ scalings.

Where Pith is reading between the lines

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

  • If a quantum analogue of classical deflation can remove or soften the κ^{-1} factor, overlap QSP would become strictly preferable to domain-wall on both qubits and asymptotic gates for large volumes.
  • The sparsity growth s^M of the approximate overlap operator suggests that intermediate-M regimes could be simulated with hybrid local/nonlocal circuit layouts before full all-to-all cost is paid.
  • Hardware with scarce qubits but decent connectivity would favor the overlap route; hardware with abundant qubits and strict locality would still favor domain-wall—making the paper’s tradeoff a concrete architecture choice rather than a purely asymptotic one.
  • Extending QSP to rational (Zolotarev-type) approximations, left open by the authors, would be the natural next algorithmic step if classical overlap experience carries over.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The paper constructs a quantum-signal-processing (QSP) block encoding of the overlap fermion Hamiltonian of Creutz–Horvath–Neuberger type, approximating the sign function ε(h_W) by a degree-M polynomial so that the Ginsparg–Wilson relation and the modified chiral commutator are violated only at O(ε_e). Under a fixed spectral lower bound κ on the block-encoded Wilson operator, the Hamiltonian block-encoding cost is O(Q κ^{-1} log(1/ε_e))—a κ^{-1} log factor above Wilson—and time evolution via QSP costs O(Q κ^{-1} log(1/ε_e)[Qt + log(1/ε_t)]), while using O(Q) qubits rather than O(Q L_5) for domain-wall fermions (Table I; Eqs. 25–32 and SM). The authors identify M ∼ κ^{-1} log(1/ε_e) with the extra-dimension extent L_5, recovering the known overlap/domain-wall correspondence at the level of quantum resource scaling.

Significance. If the stated scalings hold in the intended regime, this is a clean and useful algorithmic contribution for Hamiltonian lattice QCD with exact chiral symmetry: it makes overlap fermions competitive with domain-wall on qubit count while keeping chiral violation under explicit control, and it gives a precise quantum-algorithmic reading of the extra-dimension picture. Strengths include a carefully derived block encoding of the quadratic fermionic Hamiltonian (SM Theorem 1), standard LCU prepare/select for Wilson with gauge links, direct use of QSVT degree bounds, and an explicit operator-norm bound ∥[γ̂_5, ĥ]∥ ≤ 2ε_e (SM Eqs. 47–62). The resource table and the sparsity/L_5 interpolation are concrete and falsifiable against future resource estimates. The main caveat is that headline “nearly free” claims are conditioned on fixed κ, which the authors flag but do not establish for dynamical gauges.

major comments (2)
  1. [Abstract; text after Eq. 23; Eqs. 26–29; Table I] Abstract and the phrase “nearly free” (also Introduction) state that applying the overlap Hamiltonian “costs only a factor logarithmic in ε_e more than the Wilson–Dirac Hamiltonian.” Body Eqs. (26)–(29) and Table I give O(Q κ^{-1} log(1/ε_e)), i.e. an extra 1/κ. For free fields κ ∼ m is O(1), but with dynamical gauges near-zero modes are generic classically; if typical κ shrinks with volume or a, the prefactor is not a pure log and can erase the advertised advantage versus domain-wall (where L_5 ∼ log(1/ε_e) is chosen independently of that gap). The paper correctly fixes κ > 0 and defers deflation (text after Eq. 23; final paragraphs), but the abstract and “nearly free” language should be qualified to match the body, and the regime of validity for interacting theories should be stated up front as a limitation of the resource claim rather than only as future work.
  2. [Abstract; Table I; paragraph after Table I] Table I and the abstract’s “mild overhead in circuit complexity” compare overlap QSP time evolution O(Q κ^{-1} log(1/ε_e)[Qt + log(1/ε_t)]) to near-optimal local simulation for Wilson/domain-wall O(Q L_5 t polylog(...)). With the identification L_5 ∼ κ^{-1} log(1/ε_e), overlap still carries an extra factor of Q from nonlocality (explicitly noted in the text after Table I). For large volume this is not mild. The comparison is fair if stated as a qubit-vs-depth tradeoff; the abstract should not call the circuit overhead mild without that volume caveat.
minor comments (6)
  1. [Throughout] Notation switches between qsp/QSP and ε_e/ϵ_e; pick one convention and use it consistently in the abstract, main text, and Table I.
  2. [Eq. (5); footnote 2; SM GW section] Eq. (5) and footnote 2: the mostly-minus Γ conventions are standard but dense; a one-line reminder that all Γ_μ are Hermitian and anticommute would help non-lattice readers following the SM conjugation identities.
  3. [Eqs. (14)–(18)] The prepare state in Eq. (14) uses α in the normalization while the 1-norm is later called α = d + 2dr + m; confirm the prepare amplitudes square-sum to 1 for the stated α (the √(r/2) and √(m+dr) pieces).
  4. [SM Theorem 1; Eq. (28)] SM Theorem 1: the improvement from subnormalization 2^q to Q via approximate uniform superposition is mentioned then set aside; a sentence on when 2^q ≫ Q matters for the Λ_H = O(Q) used in Eq. (28) would tighten the cost accounting.
  5. [Introduction; section headers] Typos: “eave the qubit encoding” → “leave”; “aqspbased”/“qspeffectively” spacing; “LA TTICE HAMIL TONIANS” header spacing; “trotterization” capitalization consistency.
  6. [Paragraph on rational approximations before Acknowledgments] Cite or briefly point to the classical Zolotarev/Möbius literature already mentioned when discussing why rational approximations are left as future QSP work; the connection is good and a primary reference line would help lattice readers.

Circularity Check

0 steps flagged

No circularity: resource bounds and GW error follow from external QSP theorems plus algebra under a stated fixed-κ axiom.

full rationale

The paper's load-bearing chain is: (i) LCU/unary-iteration block-encoding of the Wilson single-particle operator (standard constructions, external refs); (ii) degree-M odd polynomial approximation to the sign via QSVT/QSP with M = O(κ^{-1} log(1/ε_e)) from Low–Chuang / Gilyén et al., not derived internally; (iii) algebraic bound ∥E_M^{2} - 1∥ ≤ 2ε_e and thence ∥[γ̂_5, ĥ]∥ ≤ 2ε_e and the GW residual, proved in the SM from ∥E_M - ε(h_w)∥ ≤ ε_e without fitting; (iv) time-evolution cost by composing the block-encoding cost with the standard QSP exponential approximation. The L_5 ∼ κ^{-1} log(1/ε_e) remark is an interpretive correspondence with known continuum/lattice lore (Narayanan–Neuberger, domain-wall o overlap), not a definition that forces the cost table. Self-citations ([9], [15], [16]) supply background Hamiltonian formulations only; they are not used as uniqueness theorems or as the sole support for the complexity claims. No parameter is fitted to data and re-labeled a prediction. The fixed-κ assumption is a regime-of-validity caveat (correctness risk), not a circular step. Derivation is self-contained against the cited external algorithmic benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 0 invented entities

The result rests on standard QSP/block-encoding mathematics, standard lattice-fermion Hamiltonians, and a few domain modeling choices (fixed gap κ, Jordan-Wigner, existence of link block encodings). No fitted physical constants. The main non-standard load is treating κ as an external positive constant despite known near-zero modes in gauge backgrounds.

free parameters (2)
  • κ (spectral lower bound on |eigenvalues| of block-encoded Wilson h_w) = fixed > 0 (unspecified numerical value)
    Chosen by hand as a fixed positive lower bound; all overlap cost scalings are linear in κ^{-1}. Not derived for dynamical gauge fields; classical near-zero modes make it problem-dependent.
  • ε_e (sign-function approximation error)
    User-chosen accuracy target that sets polynomial degree M and GW violation; free algorithmic parameter, not fitted to data.
axioms (6)
  • standard math QSP/QSVT can apply a degree-M odd polynomial to a block-encoded Hermitian operator with M uses of the block encoding (Gilyén et al. / Low-Chuang lemmas cited).
    Invoked for E_M = P_M(U_ĥw) and the M = O(κ^{-1} log ε_e^{-1}) degree bound (after Eq. 22–23).
  • domain assumption Wilson-Dirac single-particle operator with 0 < m < 2r has the standard nearest-neighbor structure and, without gauges, gap of order m; with gauges, a positive κ is assumed to exist.
    Defines h_w and the interval where the sign approximant is controlled; κ fix stated explicitly after Eq. 23.
  • domain assumption Link operators U_(x,i) admit a block encoding G_U with normalization Λ_G and O(1) cost at fixed gauge truncation (or exact unitarity in finite-group digitization).
    Used to promote Â_i → Â_i Σ_i and obtain ĥ^G / (α Λ_G) (Eqs. 19–21); asymptotics claimed independent of truncation details.
  • domain assumption Fermions are Jordan-Wigner encoded so that unary iteration implements the quadratic promotion with O(Q) gates and O(log Q) ancillae.
    Theorem 1 in SM; authors note other encodings change constants/locality but not the headline comparison they emphasize.
  • domain assumption Overlap single-particle Hamiltonian is h_ov = Γ_0 + ε(h_w) as proposed by Creutz-Horvath-Neuberger / related Hamiltonian overlap works.
    Starting definition Eq. 6; the paper algorithms this operator rather than re-deriving it.
  • standard math For local (Wilson/domain-wall) Hamiltonians, near-optimal simulation achieves almost-linear O(Qt polylog(Qt/ε_t)) cost via Lieb-Robinson (Rhodes et al. 2024).
    Used only for the domain-wall/Wilson columns of Table I; overlap cannot use it because of nonlocality.

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read the original abstract

We give a quantum signal processing (QSP) algorithm for the overlap fermion Hamiltonian which preserves the Ginsparg-Wilson relation up to a controllable error $\epsilon_e$. Quantum simulations of Dirac fermions with exact chiral symmetry are thus nearly free: applying the overlap Hamiltonian costs only a factor logarithmic in $\epsilon_e$ more than the Wilson-Dirac Hamiltonian. Comparing to domain-wall fermions, a mild overhead is found in circuit complexity while reducing qubit costs. We show how QSP effectively constructs an extra dimension when simulating the overlap operator, illustrating that the scaling of quantum algorithms reflects the deeper physics of overlap fermions arising at the boundary of domain-wall fermions.

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Reference graph

Works this paper leans on

54 extracted references · 20 linked inside Pith

  1. [1]

    H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice: (I). Proof by homotopy theory, Nuclear Physics B185, 20 (1981)

    1981

  2. [2]

    H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice: (II). Intuitive topological proof, Nuclear Physics B193, 173 (1981)

    1981

  3. [3]

    L. H. Karsten, Lattice Fermions in Euclidean Space-time, Phys. Lett. B104, 315 (1981)

    1981

  4. [4]

    P. H. Ginsparg and K. G. Wilson, A Remnant of Chiral Symmetry on the Lattice, Phys. Rev. D25, 2649 (1982)

    1982

  5. [5]

    Neuberger, Vectorlike gauge theories with almost mass- less fermions on the lattice, Phys

    H. Neuberger, Vectorlike gauge theories with almost mass- less fermions on the lattice, Phys. Rev. D57, 5417 (1998)

    1998

  6. [6]

    Neuberger, More about exactly massless quarks on the lattice, Physics Letters B427, 353 (1998), arXiv:hep- lat/9801031

    H. Neuberger, More about exactly massless quarks on the lattice, Physics Letters B427, 353 (1998), arXiv:hep- lat/9801031

    arXiv 1998

  7. [7]

    D. B. Kaplan, A method for simulating chiral fermions on the lattice, Physics Letters B288, 342 (1992)

    1992

  8. [8]

    D. B. Kaplan, Chiral fermions on the lattice, Nuclear Physics B - Proceedings Supplements Proceedings of the International Symposium On,30, 597 (1993)

    1993

  9. [9]

    Singh, Ginsparg-Wilson Hamiltonians with Improved Chiral Symmetry (2025), arXiv:2505.20419 [hep-lat]

    H. Singh, Ginsparg-Wilson Hamiltonians with Improved Chiral Symmetry (2025), arXiv:2505.20419 [hep-lat]. 7

    Pith/arXiv arXiv 2025

  10. [10]

    Gioia and R

    L. Gioia and R. Thorngren, Exact Chiral Symme- tries of 3+1D Hamiltonian Lattice Fermions (2025), arXiv:2503.07708 [cond-mat]

    Pith/arXiv arXiv 2025

  11. [11]

    Clancy, Toward a Ginsparg-Wilson lattice Hamilto- nian, Phys

    M. Clancy, Toward a Ginsparg-Wilson lattice Hamilto- nian, Phys. Rev. D110, L011502 (2024)

    2024

  12. [12]

    Chatterjee, S

    A. Chatterjee, S. D. Pace, and S.-H. Shao, Quantized axial charge of staggered fermions and the chiral anomaly (2024), arXiv:2409.12220

    Pith/arXiv arXiv 2024

  13. [13]

    Yamaoka, Quantized Axial Charge in the Hamiltonian Approach to Wilson Fermions (2025), arXiv:2504.10263 [hep-lat]

    T. Yamaoka, Quantized Axial Charge in the Hamiltonian Approach to Wilson Fermions (2025), arXiv:2504.10263 [hep-lat]

    Pith/arXiv arXiv 2025

  14. [14]

    Haegeman, L

    J. Haegeman, L. Lootens, Q. Mortier, A. Stottmeister, A. Ueda, and F. Verstraete, Interacting chiral fermions on the lattice with matrix product operator norms (2024), arXiv:2405.10285 [cond-mat, physics:hep-lat, physics:hep- th, physics:quant-ph]

    Pith/arXiv arXiv 2024

  15. [15]

    Cheluvaraja and N

    S. Cheluvaraja and N. D. Hari Dass, Axial anomaly and Ginsparg-Wilson fermions in the lattice Dirac sea picture, Nucl. Phys. B598, 134 (2001)

    2001

  16. [16]

    Creutz, I

    M. Creutz, I. Horvath, and H. Neuberger, A New fermion Hamiltonian for lattice gauge theory, Nucl. Phys. B Proc. Suppl.106, 760 (2002)

    2002

  17. [17]

    M. L. Rhodes, M. Kreshchuk, and S. Pathak, Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-Optimal Techniques, PRX Quantum5, 040347 (2024), arXiv:2405.10416 [quant-ph]

    Pith/arXiv arXiv 2024

  18. [18]

    H. F. Trotter, On the product of semi-groups of operators, Proc. Am. Math. Soc.10, 545 (1959)

    1959

  19. [19]

    Suzuki, Generalized Trotter’s Formula and System- atic Approximants of Exponential Operators and Inner Derivations with Applications to Many Body Problems, Commun

    M. Suzuki, Generalized Trotter’s Formula and System- atic Approximants of Exponential Operators and Inner Derivations with Applications to Many Body Problems, Commun. Math. Phys.51, 183 (1976)

    1976

  20. [20]

    M. Suzuki, Decomposition formulas of exponential op- erators and lie exponentials with some applications to quantum mechanics and statistical physics, Journal of Mathematical Physics26, 10.1063/1.526596 (1985), https://doi.org/10.1063/1.526596

    doi:10.1063/1.526596 1985

  21. [21]

    A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu, Theory of trotter error with commutator scaling, Phys. Rev. X11, 011020 (2021)

    2021

  22. [22]

    G. H. Low and I. L. Chuang, Hamiltonian simulation by uniform spectral amplification (2017), arXiv:1707.05391 [quant-ph]

    Pith/arXiv arXiv 2017

  23. [23]

    G. H. Low and I. L. Chuang, Hamiltonian simulation by qubitization, Quantum3, 163 (2019)

    2019

  24. [24]

    Gily´ en, Y

    A. Gily´ en, Y. Su, G. H. Low, and N. Wiebe, Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics, inPro- ceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC ’19 (ACM, 2019) p. 193–204

    2019

  25. [25]

    D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, Simulating Hamiltonian Dynamics with a Truncated Taylor Series, Phys. Rev. Lett.114, 090502 (2015), arXiv:1412.4687 [quant-ph]

    Pith/arXiv arXiv 2015

  26. [26]

    Rajput, A

    A. Rajput, A. Roggero, and N. Wiebe, Hybridized Meth- ods for Quantum Simulation in the Interaction Picture, Quantum6, 780 (2022), arXiv:2109.03308 [quant-ph]

    Pith/arXiv arXiv 2022

  27. [27]

    C. F. Kane, N. Gomes, and M. Kreshchuk, Nearly op- timal state preparation for quantum simulations of lat- tice gauge theories, Phys. Rev. A110, 012455 (2024), arXiv:2310.13757 [quant-ph]

    Pith/arXiv arXiv 2024

  28. [28]

    Hariprakash, N

    S. Hariprakash, N. S. Modi, M. Kreshchuk, C. F. Kane, and C. W. Bauer, Strategies for simulating the time evo- lution of Hamiltonian lattice field theories, Phys. Rev. A 111, 022419 (2025), arXiv:2312.11637 [quant-ph]

    Pith/arXiv arXiv 2025

  29. [29]

    Spagnoli, A

    L. Spagnoli, A. Roggero, and N. Wiebe, Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes, Quantum10, 1968 (2026), arXiv:2405.19293 [quant- ph]

    arXiv 1968

  30. [30]

    O. Kiss, U. Azad, B. Requena, A. Roggero, D. Wakeham, and J. M. Arrazola, Early Fault-Tolerant Quantum Algo- rithms in Practice: Application to Ground-State Energy Estimation, Quantum9, 1682 (2025), arXiv:2405.03754 [quant-ph]

    Pith/arXiv arXiv 2025

  31. [31]

    C. F. Kane, S. Hariprakash, N. S. Modi, M. Kreshchuk, and C. W. Bauer, Block encoding bosons by signal process- ing, Quantum9, 1747 (2025), arXiv:2408.16824 [quant- ph]

    Pith/arXiv arXiv 2025

  32. [32]

    Spagnoli, C

    L. Spagnoli, C. Lissoni, and A. Roggero, Quantum Simu- lation of Nuclear Dynamics in First Quantization (2025), arXiv:2507.22814 [quant-ph]

    arXiv 2025

  33. [33]

    A. Borici, Computational methods for the fermion deter- minant and the link between overlap and domain wall fermions, in3rd International Workshop on Numerical Analysis and Lattice QCD(2004) pp. 25–39, arXiv:hep- lat/0402035

    arXiv 2004

  34. [34]

    R. C. Brower, H. Neff, and K. Orginos, Mobius fermions, Nucl. Phys. B Proc. Suppl.153, 191 (2006)

    2006

  35. [35]

    Narayanan and H

    R. Narayanan and H. Neuberger, Infinitely many regulator fields for chiral fermions, Physics Letters B302, 62 (1993)

    1993

  36. [36]

    A. M. Childs and N. Wiebe, Hamiltonian Simulation Using Linear Combinations of Unitary Operations, Quant. Inf. Comput.12, 0901 (2012), arXiv:1202.5822 [quant-ph]

    Pith/arXiv arXiv 2012

  37. [37]

    Gidney, Halving the cost of quantum addition, Quan- tum2, 74 (2018)

    C. Gidney, Halving the cost of quantum addition, Quan- tum2, 74 (2018)

    2018

  38. [38]

    Plesch and ˇC

    M. Plesch and ˇC. Brukner, Quantum-state preparation with universal gate decompositions, Physical Review A 83, 10.1103/physreva.83.032302 (2011)

    doi:10.1103/physreva.83.032302 2011

  39. [39]

    Babbush, C

    R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. Mc- Clean, A. Paler, A. Fowler, and H. Neven, Encoding electronic spectra in quantum circuits with linear t com- plexity, Phys. Rev. X8, 041015 (2018)

    2018

  40. [40]

    Luscher, Local coherence and deflation of the low quark modes in lattice QCD, JHEP07, 081, arXiv:0706.2298 [hep-lat]

    M. Luscher, Local coherence and deflation of the low quark modes in lattice QCD, JHEP07, 081, arXiv:0706.2298 [hep-lat]

    Pith/arXiv arXiv

  41. [41]

    Luscher, Deflation acceleration of lattice QCD simula- tions, JHEP12, 011, arXiv:0710.5417 [hep-lat]

    M. Luscher, Deflation acceleration of lattice QCD simula- tions, JHEP12, 011, arXiv:0710.5417 [hep-lat]

    Pith/arXiv arXiv

  42. [42]

    R. D. Somma and S. Boixo, Spectral gap amplification, SIAM Journal on Computing42, 593 (2013)

    2013

  43. [43]

    M. E. S. Morales, L. Pira, P. Schleich, K. Koor, P. C. S. Costa, D. An, A. Aspuru-Guzik, L. Lin, P. Rebentrost, and D. W. Berry, Quantum linear system solvers: A survey of algorithms and applications, Rev. Mod. Phys. 98, 025005 (2026)

    2026

  44. [44]

    P. C. Costa, D. An, Y. R. Sanders, Y. Su, R. Babbush, and D. W. Berry, Optimal scaling quantum linear-systems solver via discrete adiabatic theorem, PRX Quantum3, 040303 (2022)

    2022

  45. [45]

    H. Mori, Y. Kikuchi, M. Benedetti, and M. Rosenkranz, Sparsity-dependent complexity lower bound of quantum linear system solvers, Quantum Science and Technology (2026)

    2026

  46. [46]

    J. Haah, M. B. Hastings, R. Kothari, and G. H. Low, Quantum Algorithm for Simulating Real Time Evolution of Lattice Hamiltonians, SIAM J. Comput.52, FOCS18 (2023), arXiv:1801.03922 [quant-ph]

    Pith/arXiv arXiv 2023

  47. [47]

    Chiu, T.-H

    T.-W. Chiu, T.-H. Hsieh, C.-H. Huang, and T.-R. Huang, A Note on the Zolotarev optimal rational approximation 8 for the overlap Dirac operator, Phys. Rev. D66, 114502 (2002), arXiv:hep-lat/0206007

    Pith/arXiv arXiv 2002

  48. [48]

    van den Eshof, A

    J. van den Eshof, A. Frommer, T. Lippert, K. Schilling, and H. A. van der Vorst, Numerical methods for the QCD overlap operator. I. Sign function and error bounds, Comput. Phys. Commun.146, 203 (2002), arXiv:hep- lat/0202025

    arXiv 2002

  49. [49]

    H. Lamm, S. Lawrence, and Y. Yamauchi, General Meth- ods for Digital Quantum Simulation of Gauge Theories, Phys. Rev. D100, 034518 (2019), arXiv:1903.08807 [hep- lat]

    Pith/arXiv arXiv 2019

  50. [50]

    S. B. Bravyi and A. Y. Kitaev, Fermionic Quantum Com- putation, Annals Phys.298, 210 (2002), arXiv:quant- ph/0003137

    arXiv 2002

  51. [51]

    Havl ´ ıˇ cek, M

    V. Havl ´ ıˇ cek, M. Troyer, and J. D. Whitfield, Operator locality in the quantum simulation of fermionic models, Phys. Rev. A95, 032332 (2017), arXiv:1701.07072 [quant- ph]

    Pith/arXiv arXiv 2017

  52. [52]

    L. K. Grover, Synthesis of quantum superpositions by quantum computation, Phys. Rev. Lett.85, 1334 (2000)

    2000

  53. [53]

    Høyer, Arbitrary phases in quantum amplitude ampli- fication, Phys

    P. Høyer, Arbitrary phases in quantum amplitude ampli- fication, Phys. Rev. A62, 052304 (2000)

    2000

  54. [54]

    J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. McClean, N. Wiebe, and R. Babbush, Even more effi- cient quantum computations of chemistry through tensor hypercontraction, PRX Quantum2, 030305 (2021). Supplementary Material BLOCK ENCODING THE QUADRA TIC FERMIONIC HAMIL TONIAN In this section we will construct the block-encoding for a generic quadrati...

    2021