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A framework for robust quantum speedups in practical correlated electronic structure and dynamics

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The paper derives a quantum speedup equal to the ratio of correlation volume to block-encoding cost, yielding up to O(L_c^18) speedups for crystalline tri-exciton Bethe–Salpeter calculations and correlation-length-dependent polynomial gains

desk verdict A genuinely new framing for quantum speedup where classical heuristics work, with honest cost accounting; the headline exponents lean on a sparse baseline that compressed classical methods may erode. read the letter →

arxiv 2508.15765 v1 pith:CAEMMDIG submitted 2025-08-21 quant-ph

Jielun Chen , Garnet Kin-Lic Chan This is my paper
classification quant-ph
keywords quantumspeedupelectronicstructureBethe–Salpeterequationlinearizedcoupledclusterblock-encodingcorrelationvolumeexcitationbasissimulation
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

Most quantum-chemistry speedup proposals hunt for problems where classical heuristics fail. This paper inverts that search: it claims a substantial quantum speedup exactly where classical heuristics already work, namely small numbers of particle-hole excitations around a mean-field state with local correlations. Both the classical sparse solver and the quantum algorithm apply a polynomial of the same geometrically local operator of range R_c; the polynomial degree and operator sparsity cancel, leaving quantum speedup = correlation volume / block-encoding cost. For tri-excitons in a crystal this yields up to O(L_c^18) relative speedup, making thousands-of-atom simulations plausible with moderate fault-tolerant resources. For linearized coupled cluster ground-state energies, the same mechanism gives polynomial speedups in the correlation length.

What carries the argument

The machinery is the effective Hamiltonian or Liouvillian in the m-fold excitation basis, taken to be geometrically local with range R_c and sparsity s ~ 2mR_c^D, together with the ratio speedup = correlation volume / block-encoding cost. The correlation volume is the 2m-particle lightcone volume (dR_c)^{2mD} that a classical sparse solver must track; the block-encoding cost is the data and arithmetic needed to specify the operator, which depends on the input model (integrals, atomic data, or crystal parameters) and never grows exponentially in m. Quantum singular value transform (QSVT), a polynomial-application primitive on block-encoded matrices, applies the same polynomial as the classica

What would settle it

Compute the off-diagonal matrix elements of the m-exciton BSE Hamiltonian (or the LCC Liouvillian) in a localized orbital basis for a specific material and measure their decay with separation r. If the envelope is not bounded by the screened 1/r^2 and exchange 1/r^3 tails beyond some R_c, the geometric-locality premise fails and the claimed speedup ratio would not hold; a direct check is whether converged m-exciton energies with truncation radius R_c match untruncated results.

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Extended reading notes

Core claim

The central claim is that the linear algebra of post-mean-field electronic structure—the m-exciton Bethe–Salpeter equation and linearized coupled cluster—can be viewed as a sparse, geometrically local operator in an m-excitation basis. A classical solver tracks the lightcone of correlation data, whose volume grows as L_c^{2mD}; a quantum block-encoding stores only the operator data, not the correlation cloud. Since polynomial degree and sparsity appear in both costs, the ratio of costs is exactly correlation volume over block-encoding cost. Under the standard heuristic assumptions (m ≤ 3, local correlations, screened Coulomb tails), this yields speedups up to O(L_c^18) for crystalline tri-ex

Load-bearing premise

Everything rests on the assumption that the off-diagonal Coulomb matrix elements in the excitation basis really are short-range after screening, so a finite range R_c captures them; if long-range tails appear off the diagonal, both the classical and quantum cost models change and the speedup formula no longer applies.

Editorial extensions

If this is right

  • For m = 3, D = 3 exciton problems in a crystalline input model, the quantum/classical cost ratio is O(L_c^18), equivalent to a 19th power in polynomial degree and a 7th power in interaction range.
  • Dynamical multi-exciton Bethe–Salpeter evolution inherits the same speedup without the initial-state-overlap factor, giving a cleaner testbed for practical advantage.
  • Linearized coupled cluster ground-state energy calculations, including crystalline cases, also acquire correlation-length-dependent polynomial speedups; in the crystal setting initial-state preparation can be made effectively constant-cost via translation invariance.
  • The excitation-basis encoding uses only O(2m log L) qubits: for L = 10^5 and m = 3, about 99 logical qubits, making thousands-of-atom correlated systems plausible.

Reading between the lines

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

  • [Editorial extension] A direct numerical measurement of the off-diagonal decay of the effective m-exciton Hamiltonian in localized bases for real materials such as CdSe or PbSe would test the load-bearing screening and truncation assumption; if decay is slower than screened Coulomb (1/r^2) or exchange (1/r^3), the speedup ratio needs revision.
  • [Editorial extension] The cleanest way to see the claimed advantage may be m-exciton dynamics rather than eigenvalues, since the initial-state overlap cancels; a small-model exact simulation could validate the lightcone cost model before fault-tolerant hardware is available.
  • [Editorial extension] The speedup is polynomial in L_c, and L_c is a material property rather than a tunable system size, so practical advantage must be assessed per material; classical rank-compressed or stochastic algorithms could reduce the gap in specific cases.
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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

3 major / 5 minor

Summary. The paper proposes a framework for quantum speedups in post-mean-field electronic structure methods in the regime where classical heuristics are already successful. The central idea is to work in the low-rank m-excitation manifold (m ≤ 3) and exploit geometric locality of the effective Hamiltonian (m-exciton BSE) or Liouvillian (linearized coupled cluster). For a sparse iterative classical solver, the cost is argued to scale as the correlation volume V_m = (d R_c)^{2mD} times the operator sparsity. A quantum implementation using block-encoding and QSVT/phase estimation has cost controlled by the block-encoding cost and sparsity, yielding Eq. (1): quantum speedup = correlation volume / block-encoding cost. For three input models (integrals, atomic data, crystals), the paper derives speedups up to O(L_c^{18}) for crystalline tri-excitons. The manuscript includes a cost table, discussions of state preparation, initial-state overlap, QROM, and explicit discussion of limitations such as QTT/THC compression and the role of the exponential m-dependence.

Significance. If the assumptions hold, the paper identifies a clean and potentially important source of quantum advantage: the quantum algorithm avoids storing the correlation volume that arises in classical sparse lightcone arguments. The cost accounting is transparent, the input-model hierarchy is useful, and the authors are explicit about many caveats. The paper also honestly acknowledges the main weakness in the Discussion and Appendix B.3: the speedup is relative to a sparse linear algebra baseline, and compressed classical representations could erode it. The framework is likely to stimulate more careful resource estimates and may be a valuable conceptual contribution. However, the abstract's claims of 'robust' practical speedups and 'moderate fault-tolerant resources' for thousands of atoms go beyond what is demonstrated, because the analysis is asymptotic and depends on unquantified locality and incompressibility assumptions.

major comments (3)
  1. [Eq. (1); Discussion; App. B.3] The speedup formula takes the classical cost to be the worst-case support size V_m = (d R_c)^{2mD} of a sparse vector under d applications of the local operator. This is not the cost of the reduced-scaling classical heuristics the paper says it speeds up: local CC methods use domains and pair/triple lists, and QTT/THC-type compression can reduce the polynomial exponent in L_c. The manuscript itself concedes in App. B.3 that if the exponential m-dependence is removed classically, 'we lose the main source of asymptotic polynomial speedup in L_c.' Since m is fixed at 3, the remaining speedup is polynomial in L_c, and a classical representation with cost L_c^9 instead of L_c^18 would reduce the headline O(L_c^18) speedup to at most O(L_c^9). Thus the 'robust' practical speedup claim is not established. Please either provide evidence of incompressibility for the specific triexciton/LCC states
  2. [Multi-exciton energies and dynamics; locality assumptions] The load-bearing assumption is that A (and the LCC Liouvillian) is geometrically local with range R_c and sparsity s ∼ 2m R_c^D, justified by decay of off-diagonal Coulomb terms as 1/r^2 and 1/r^3 and screening of the direct term. No numerical evidence is given for the target materials (CdSe, PbSe, or TMDs). In 3D, 1/r^3 tails are only marginally integrable, and truncation at R_c introduces state-dependent errors; if significant tails survive screening, both the classical lightcone support and the quantum block-encoding cost change, and Eq. (1) is invalid. Since the paper targets practical materials, it should include at least a model calculation of the decay of off-diagonal A or Liouvillian matrix elements in a relevant system, or clearly state that the framework is conditional on an unverified empirical assumption. The current 'under relevant assumptions' wording is too weak for the ab
  3. [Abstract; LCC cost discussion] The abstract promises 'moderate fault-tolerant resources' for thousands of atoms, but no end-to-end resource estimate is provided. Constants, arithmetic costs, block-encoding subnormalization, phase-estimation 1/γ, condition numbers, and logical overheads are dropped. In the LCC section, the quantum cost is O(s d) with d = O(κ log(1/ϵ)); κ for small-gap semiconductors may be large and is not discussed. Either provide resource estimates for a concrete system (e.g., a CdSe nanocrystal triexciton) or temper the abstract to an asymptotic speedup relative to sparse linear algebra.
minor comments (5)
  1. [Table I] The entries such as 'd^{2D+1} R^{3D}_c L^{12}_c (2.7, 2.3)' are difficult to parse. The notation for the two speedup columns should be defined in the caption and ideally accompanied by an explicit example with m=3, D=3.
  2. [Multi-exciton energies and dynamics] The phrase 'the one-particle eigenvalue differences ... ∼ mD' appears to use D (dimensionality) where a gap symbol was likely intended. This is confusing.
  3. [General framework for speedup] The assumption 'd′ ∝ d' between classical and quantum iteration counts is stated without discussion; the cancellation of polynomial degree in Eq. (1) depends on it. Please justify or state it as an explicit assumption.
  4. [App. B.2] The QROM vs QRAM discussion is useful but is not reflected explicitly in Table I. If the block-encoding costs assume QROM, this should be stated in the table caption.
  5. [Footnote [42]] The O(1) assumption for matrix elements is central to the speedup ratio, yet it appears only in a footnote. It should be stated prominently in the main text and its validity for m=3 discussed.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Eq. (1) is an arithmetic ratio of two independently stated cost models; the only same-author citation is non-load-bearing.

full rationale

The central claim is the speedup ratio in Eq. (1), quantum speedup = correlation volume / block-encoding cost. The derivation costs the classical sparse algorithm as (lightcone support Lc^{2mD}) x (sparsity s) x (degree d), and the quantum QSVT/block-encoding algorithm as CBE x s x d; s and d cancel. Neither side is fitted to the other: the classical lightcone bound is a standard support-growth argument for sparse matvec, and the quantum cost is the standard QSVT/block-encoding query model with alpha ~ s. The three input models (integrals, atomic data, crystals) change only CBE and are justified by data-loading and translation-invariance arguments, not by importing the paper's conclusion. The only same-author citation is Ref. [35], cited with [32-34] for conceptual similarity of exponential compression; the compression itself is simply O(m log L) qubits, and no derivation step relies on [35]. The paper explicitly flags its main limitation in the Discussion and App. B.3: if classical methods use rank reduction (QTT/THC) or if the exponential m-dependence is removed, 'we lose the main source of asymptotic polynomial speedup in Lc.' That is a caveat about the chosen sparse baseline, not a circular step: the speedup is defined relative to 'classical sparse techniques', as stated. No fitted parameter is renamed as a prediction, and no uniqueness theorem or ansatz is smuggled in via self-citation. Therefore no circularity is present.

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

The framework introduces no new physical entities or fitted parameters. It rests on the standard domain assumptions of local post-mean-field electronic structure theory and on standard quantum/classical cost models. The main load-bearing axioms are the locality and sparsity of the effective operators, which determine both the classical and quantum complexity estimates.

assumptions (5)
  • domain assumption The electronic structure is accurately described by small fluctuations around the mean-field Slater determinant, parametrized by operators in the manifold of m-fold particle-hole excitations for small m (m ≤ 3).
    This is the regime where classical heuristics (coupled cluster, BSE) are accurate; it is stated in the 'General framework for speedup' section as the first assumption for classical heuristics.
  • domain assumption The effective Hamiltonian/Liouvillian in the excitation basis is geometrically local with range Rc, with sparsity s ~ 2m Rc^D, due to diagonal long-range Coulomb and screened off-diagonal terms.
    This is the central sparsity assumption, argued in 'Locality and connectedness' and 'Multi-exciton energies and dynamics'.
  • domain assumption Matrix elements of the effective operators are bounded by O(1), per footnote [42].
    Used to set alpha ~ s and simplify the quantum cost; the paper drops poly(m) factors since m ≤ 3.
  • standard math The classical cost of applying a degree-d polynomial of the sparse operator is proportional to the correlation volume times operator sparsity times d (lightcone argument).
    Standard sparse matrix-vector multiplication cost model with lightcone sparsity growth; assumed in the 'General framework for speedup' section.
  • standard math QSVT, sparse block-encoding and phase estimation have the stated costs.
    Standard quantum algorithm results from Refs [41, 53-59].

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Cite this review

Pith. "Pith review of A framework for robust quantum speedups in practical correlated electronic structure and dynamics." pith.science (2026). https://pith.science/paper/CAEMMDIG

@misc{pith2026250815765,
  author       = {Pith},
  title        = {Pith review of: A framework for robust quantum speedups in practical correlated electronic structure and dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CAEMMDIG}},
  note         = {Machine review of arXiv:2508.15765}
}
read the original abstract

Proposed quantum advantage in electronic structure has so far required significant fine-tuning to find problems where classical heuristics fail. We describe how to obtain robust quantum speedups for correlated electronic structure and dynamics precisely in the regime where widely used classical heuristics are most successful.

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Reference graph

Works this paper leans on

112 extracted references · 68 canonical work pages · cited by 1 Pith paper

  1. [1]

    Aspuru-Guzik, A

    A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head- Gordon, Simulated Quantum Computation of Molecular Energies, Science 309, 1704 (2005)

    2005

  2. [2]

    J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Simulation of electronic structure Hamiltonians us- ing quantum computers, Molecular Physics 109, 735 (2011)

    2011

  3. [3]

    J. T. Seeley, M. J. Richard, and P. J. Love, The Bravyi- Kitaev transformation for quantum computation of elec- tronic structure, The Journal of Chemical Physics 137, 224109 (2012)

    2012

  4. [5]

    Wecker, B

    D. Wecker, B. Bauer, B. K. Clark, M. B. Hastings, and M. Troyer, Gate-count estimates for performing quan- tum chemistry on small quantum computers, Physical Review A 90, 022305 (2014)

    2014

  5. [6]

    Toloui and P

    B. Toloui and P. J. Love, Quantum Algorithms for Quantum Chemistry based on the sparsity of the CI- matrix (2013)

    2013

  6. [7]

    M. B. Hastings, D. Wecker, B. Bauer, and M. Troyer, Improving Quantum Algorithms for Quantum Chem- istry (2014)

    2014

  7. [8]

    Poulin, M

    D. Poulin, M. B. Hastings, D. Wecker, N. Wiebe, A. C. Doherty, and M. Troyer, The Trotter Step Size Required for Accurate Quantum Simulation of Quantum Chem- istry (2014)

    2014

  8. [9]

    J. R. McClean, R. Babbush, P. J. Love, and A. Aspuru- Guzik, Exploiting Locality in Quantum Computation for Quantum Chemistry, The Journal of Physical Chem- istry Letters 5, 4368 (2014)

    2014

Show all 112 references
  1. [10]

    Babbush, J

    R. Babbush, J. McClean, D. Wecker, A. Aspuru-Guzik, and N. Wiebe, Chemical basis of Trotter-Suzuki errors in quantum chemistry simulation, Physical Review A 91, 022311 (2015)

    2015

  2. [11]

    Babbush, D

    R. Babbush, D. W. Berry, I. D. Kivlichan, A. Y. Wei, P. J. Love, and A. Aspuru-Guzik, Exponentially more precise quantum simulation of fermions I: Quan- tum chemistry in second quantization, New Journal of Physics 18, 033032 (2016)

    2016

  3. [12]

    Babbush, D

    R. Babbush, D. W. Berry, Y. R. Sanders, I. D. Kivlichan, A. Scherer, A. Y. Wei, P. J. Love, and A. Aspuru-Guzik, Exponentially more precise quantum simulation of fermions in the configuration interaction representation, Quantum Science and Technology 3, 015006 (2017)

    2017

  4. [13]

    Reiher, N

    M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, Elucidating reaction mechanisms on quan- tum computers, Proceedings of the National Academy of Sciences 114, 7555 (2017)

    2017

  5. [14]

    Babbush, N

    R. Babbush, N. Wiebe, J. McClean, J. McClain, H. Neven, and G. K.-L. Chan, Low Depth Quantum Simulation of Electronic Structure, Physical Review X 8, 011044 (2018)

    2018

  6. [15]

    Babbush, D

    R. Babbush, D. W. Berry, J. R. McClean, and H. Neven, Quantum simulation of chemistry with sublinear scaling in basis size, npj Quantum Information 5, 92 (2019)

    2019

  7. [16]

    J. R. McClean, F. M. Faulstich, Q. Zhu, B. O’Gorman, Y. Qiu, S. R. White, R. Babbush, and L. Lin, Discon- tinuous Galerkin discretization for quantum simulation of chemistry, New Journal of Physics22, 093015 (2020)

    2020

  8. [17]

    Motta, E

    M. Motta, E. Ye, J. R. McClean, Z. Li, A. J. Minnich, R. Babbush, and G. K.-L. Chan, Low rank represen- tations for quantum simulation of electronic structure, npj Quantum Information 7, 83 (2021)

    2021

  9. [18]

    Campbell, Random Compiler for Fast Hamilto- nian Simulation, Physical Review Letters 123, 070503 (2019)

    E. Campbell, Random Compiler for Fast Hamilto- nian Simulation, Physical Review Letters 123, 070503 (2019)

    2019

  10. [19]

    D. W. Berry, C. Gidney, M. Motta, J. R. McClean, and R. Babbush, Qubitization of arbitrary basis quantum chemistry leveraging sparsity and low rank factoriza- tion, Quantum 3, 208 (2019)

    2019

  11. [20]

    I. D. Kivlichan, C. E. Granade, and N. Wiebe, Phase estimation with randomized Hamiltonians (2019)

    2019

  12. [21]

    V. v. Burg, G. H. Low, T. H¨ aner, D. S. Steiger, M. Rei- her, M. Roetteler, and M. Troyer, Quantum computing enhanced computational catalysis, Physical Review Re- search 3, 033055 (2021)

    2021

  13. [22]

    J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. Mc- Clean, N. Wiebe, and R. Babbush, Even More Efficient Quantum Computations of Chemistry Through Tensor 7 Hypercontraction, PRX Quantum 2, 030305 (2021)

    2021

  14. [23]

    Y. Su, D. W. Berry, N. Wiebe, N. Rubin, and R. Bab- bush, Fault-tolerant quantum simulations of chemistry in first quantization, PRX Quantum 2, 040332 (2021)

    2021

  15. [24]

    K. Wan, M. Berta, and E. T. Campbell, Random- ized quantum algorithm for statistical phase estimation, Physical Review Letters 129, 030503 (2022)

    2022

  16. [25]

    M. S. Zini, A. Delgado, R. d. Reis, P. A. M. Casares, J. E. Mueller, A.-C. Voigt, and J. M. Arrazola, Quan- tum simulation of battery materials using ionic pseu- dopotentials, Quantum 7, 1049 (2023)

    2023

  17. [26]

    D. W. Berry, N. C. Rubin, A. O. Elnabawy, G. Ahlers, A. E. DePrince, J. Lee, C. Gogolin, and R. Babbush, Quantum simulation of realistic materials in first quan- tization using non-local pseudopotentials, npj Quantum Information 10, 130 (2024)

    2024

  18. [27]

    Oumarou, M

    O. Oumarou, M. Scheurer, R. M. Parrish, E. G. Hohen- stein, and C. Gogolin, Accelerating Quantum Compu- tations of Chemistry Through Regularized Compressed Double Factorization, Quantum 8, 1371 (2024)

    2024

  19. [28]

    N. C. Rubin, D. W. Berry, A. Kononov, F. D. Malone, T. Khattar, A. White, J. Lee, H. Neven, R. Babbush, and A. D. Baczewski, Quantum computation of stop- ping power for inertial fusion target design, Proceedings of the National Academy of Sciences 121, e2317772121 (2024)

    2024

  20. [29]

    T. N. Georges, M. Bothe, C. S¨ underhauf, B. K. Berntson, R. Izs´ ak, and A. V. Ivanov, Quantum simu- lations of chemistry in first quantization with any basis set, npj Quantum Information 11, 55 (2025)

    2025

  21. [30]

    Koizumi, K

    Y. Koizumi, K. Wada, W. Mizukami, and N. Yosh- ioka, Faster quantum algorithm for multiple observ- ables estimation in fermionic problems, arXiv preprint arXiv:2505.00697 (2025)

    2025 arXiv

  22. [31]

    G. H. Low, R. King, D. W. Berry, Q. Han, A. E. De- Prince III, A. White, R. Babbush, R. D. Somma, and N. C. Rubin, Fast quantum simulation of electronic structure by spectrum amplification, arXiv preprint arXiv:2502.15882 (2025)

    2025

  23. [32]

    Babbush, D

    R. Babbush, D. W. Berry, R. Kothari, R. D. Somma, and N. Wiebe, Exponential quantum speedup in simu- lating coupled classical oscillators, Physical Review X 13, 041041 (2023)

    2023

  24. [33]

    R. D. Somma, R. King, R. Kothari, T. E. O’Brien, and R. Babbush, Shadow hamiltonian simulation, Nature Communications 16, 2690 (2025)

    2025

  25. [34]

    Stroeks, D

    M. Stroeks, D. Lenterman, B. Terhal, and Y. Herasy- menko, Solving Free Fermion Problems on a Quantum Computer (2024)

    2024

  26. [35]

    Chen and G

    J. Chen and G. K. Chan, Quantum linear algebra for disordered electrons, arXiv preprint arXiv:2411.00434 (2024)

    2024 arXiv

  27. [36]

    Shavitt and R

    I. Shavitt and R. J. Bartlett, Many-body methods in chemistry and physics: MBPT and coupled-cluster the- ory (Cambridge university press, 2009)

    2009

  28. [37]

    Typically the triples are treated with additional approx- imations [36]

  29. [38]

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

    2007

  30. [39]

    Sch¨ utz and H.-J

    M. Sch¨ utz and H.-J. Werner, Low-order scaling lo- cal electron correlation methods. iv. linear scaling lo- cal coupled-cluster (lccsd), The Journal of Chemical Physics 114, 661 (2001)

    2001

  31. [40]

    Merkel and F

    K. Merkel and F. Ortmann, Linear scaling approach for optical excitations using maximally localized wan- nier functions, Journal of Physics: Materials 7, 015001 (2023)

    2023

  32. [41]

    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, in Pro- ceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing(2019) pp. 193–204

    2019

  33. [42]

    Technically, the matrix elements are summation of poly(m) terms with magnitude O(1), but throughout the paper we focus on m ≤ 3 so we drop this factor

  34. [43]

    Szabo and N

    A. Szabo and N. S. Ostlund, Modern quantum chem- istry: introduction to advanced electronic structure the- ory (Courier Corporation, 1996)

    1996

  35. [44]

    K. E. Shulenberger, S. C. Coppieters ‘t Wallant, M. D. Klein, A. R. McIsaac, T. Goldzak, D. B. Berkinsky, H. Utzat, U. Barotov, T. Van Voorhis, and M. G. Bawendi, Resolving the triexciton recombination path- way in cdse/cds nanocrystals through state-specific cor- relation mea...

    2021

  36. [45]

    J. J. Pijpers, R. Ulbricht, K.-J. Tielrooij, A. Osherov, Y. Golan, C. Delerue, G. Allan, and M. Bonn, Assess- ment of carrier-multiplication efficiency in bulk pbse and pbs, Nature Physics 5, 811 (2009)

    2009

  37. [46]

    Steinhoff, M

    A. Steinhoff, M. Florian, A. Singh, K. Tran, M. Ko- larczik, S. Helmrich, A. W. Achtstein, U. Woggon, N. Owschimikow, F. Jahnke, et al., Biexciton fine struc- ture in monolayer transition metal dichalcogenides, Na- ture Physics 14, 1199 (2018)

    2018

  38. [47]

    S. C. Kuhn and M. Richter, Combined tensor net- work/cluster expansion method using logic gates: Il- lustrated for (bi) excitons by a single-layer mos 2 model system, Physical Review B 99, 241301 (2019)

    2019

  39. [48]

    A. L. Fetter and J. D. Walecka, Quantum theory of many-particle systems (Courier Corporation, 2012)

    2012

  40. [49]

    Blase, I

    X. Blase, I. Duchemin, D. Jacquemin, and P.-F. Loos, The bethe–salpeter equation formalism: From physics to chemistry, The Journal of Physical Chemistry Letters 11, 7371 (2020)

    2020

  41. [50]

    Assuming quasi-particle hops, the factor ( dRc)2mD can be computed by estimating the number of sites reached by a walker on a 2mD dimensional lattice after d steps

  42. [51]

    Saad, On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods, SIAM Journal on Nu- merical Analysis 17, 687 (1980)

    Y. Saad, On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods, SIAM Journal on Nu- merical Analysis 17, 687 (1980)

    1980

  43. [52]

    Saad, Numerical Methods for Large Eigenvalue Prob- lems (Manchester University Press, 1992)

    Y. Saad, Numerical Methods for Large Eigenvalue Prob- lems (Manchester University Press, 1992)

    1992

  44. [53]

    A. Y. Kitaev, Quantum measurements and the abelian stabilizer problem (1995), arXiv:quant-ph/9511026 [quant-ph]

    1995 arXiv

  45. [54]

    R. D. Somma, Quantum eigenvalue estimation via time series analysis, New Journal of Physics 21, 123025 (2019)

    2019

  46. [55]

    T. E. O’Brien, B. Tarasinski, and B. M. Terhal, Quan- tum phase estimation of multiple eigenvalues for small- scale (noisy) experiments, New Journal of Physics 21, 023022 (2019)

    2019

  47. [56]

    Dutkiewicz, B

    A. Dutkiewicz, B. M. Terhal, and T. E. O’Brien, Heisenberg-limited quantum phase estimation of mul- tiple eigenvalues with few control qubits, Quantum 6, 830 (2022)

    2022

  48. [57]

    Ding and L

    Z. Ding and L. Lin, Simultaneous estimation of mul- tiple eigenvalues with short-depth quantum circuit on 8 early fault-tolerant quantum computers, Quantum 7, 1136 (2023)

    2023

  49. [58]

    H. Li, H. Ni, and L. Ying, On adaptive low-depth quan- tum algorithms for robust multiple-phase estimation (2023)

    2023

  50. [59]

    G. Wang, D. S. Fran¸ ca, R. Zhang, S. Zhu, and P. D. Johnson, Quantum algorithm for ground state energy estimation using circuit depth with exponentially im- proved dependence on precision, Quantum 7, 1167 (2023)

    2023

  51. [60]

    D. W. Berry, M. Kieferov´ a, A. Scherer, Y. R. Sanders, G. H. Low, N. Wiebe, C. Gidney, and R. Babbush, Im- proved techniques for preparing eigenstates of fermionic hamiltonians, npj Quantum Information 4, 22 (2018)

    2018

  52. [61]

    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. X 8, 041015 (2018)

    2018

  53. [62]

    G. H. Low, V. Kliuchnikov, and L. Schaeffer, Trading t gates for dirty qubits in state preparation and unitary synthesis, Quantum 8, 1375 (2024)

    2024

  54. [63]

    S. Lee, J. Lee, H. Zhai, Y. Tong, A. M. Dalzell, A. Ku- mar, P. Helms, J. Gray, Z.-H. Cui, W. Liu, et al., Eval- uating the evidence for exponential quantum advantage in ground-state quantum chemistry, Nature communi- cations 14, 1952 (2023)

    1952

  55. [64]

    Y. Guo, C. Riplinger, U. Becker, D. G. Liakos, Y. Mi- nenkov, L. Cavallo, and F. Neese, Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [dlpno-ccsd (t)], ...

    2018

  56. [65]

    A. G. Taube and R. J. Bartlett, Rethinking linearized coupled-cluster theory, The Journal of chemical physics 130 (2009)

    2009

  57. [66]

    Further the work in Ref

    For completeness, we note that the term linearized CC theory has to our knowledge appeared once before in the context of quantum simulation [99], but the equa- tions used in that work contain an important error as they mistakenly replace the commutator [ ˆH, ˆOν ] by ( ˆH − E)...

  58. [67]

    Saebo and P

    S. Saebo and P. Pulay, Local treatment of electron cor- relation, Annual Review of Physical Chemistry 44, 213 (1993)

    1993

  59. [68]

    Pinski, C

    P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, Sparse maps—a systematic infrastructure for reduced- scaling electronic structure methods. i. an efficient and simple linear scaling local mp2 method that uses an in- termediate basis of pair natural orbitals, The Journal of...

    2015

  60. [69]

    A. W. Harrow, A. Hassidim, and S. Lloyd, Quantum Al- gorithm for Linear Systems of Equations, Physical Re- view Letters 103, 150502 (2009)

    2009

  61. [70]

    Ambainis, Variable time amplitude amplification and a faster quantum algorithm for solving systems of linear equations (2010)

    A. Ambainis, Variable time amplitude amplification and a faster quantum algorithm for solving systems of linear equations (2010)

    2010

  62. [71]

    A. M. Childs, R. Kothari, and R. D. Somma, Quantum Algorithm for Systems of Linear Equations with Ex- ponentially Improved Dependence on Precision, SIAM Journal on Computing 46, 1920 (2017)

    1920

  63. [72]

    Suba¸ sı, R

    Y. Suba¸ sı, R. D. Somma, and D. Orsucci, Quantum Al- gorithms for Systems of Linear Equations Inspired by Adiabatic Quantum Computing, Physical Review Let- ters 122, 060504 (2019)

    2019

  64. [73]

    Lin and Y

    L. Lin and Y. Tong, Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems, Quantum 4, 361 (2020)

    2020

  65. [74]

    P. C. S. Costa, D. An, Y. R. Sanders, Y. Su, R. Bab- bush, and D. W. Berry, Optimal scaling quantum linear systems solver via discrete adiabatic theorem (2021)

    2021

  66. [75]

    An and L

    D. An and L. Lin, Quantum Linear System Solver Based on Time-optimal Adiabatic Quantum Computing and Quantum Approximate Optimization Algorithm, ACM Transactions on Quantum Computing 3, 5:1 (2022)

    2022

  67. [76]

    A. M. Dalzell, A shortcut to an optimal quantum linear system solver (2024)

    2024

  68. [77]

    Jennings, M

    D. Jennings, M. Lostaglio, S. Pallister, A. T. Sorn- borger, and Y. Suba¸ sı, Randomized adiabatic quantum linear solver algorithm with optimal complexity scaling and detailed running costs (2025)

    2025

  69. [78]

    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 (2025), arXiv:2411.02522 [quant-ph]

    2025 arXiv

  70. [79]

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

    2000

  71. [80]

    Grover and T

    L. Grover and T. Rudolph, Creating superpositions that correspond to efficiently integrable probability distribu- tions (2002)

    2002

  72. [81]

    Plesch and ˇC

    M. Plesch and ˇC. Brukner, Quantum-state preparation with universal gate decompositions, Physical Review A 83, 032302 (2011)

    2011

  73. [82]

    Y. R. Sanders, G. H. Low, A. Scherer, and D. W. Berry, Black-box quantum state preparation without arith- metic, Phys. Rev. Lett. 122, 020502 (2019)

    2019

  74. [83]

    Zhang, T

    X.-M. Zhang, T. Li, and X. Yuan, Quantum State Preparation with Optimal Circuit Depth: Implemen- tations and Applications, Physical Review Letters 129, 230504 (2022)

    2022

  75. [84]

    X. Sun, G. Tian, S. Yang, P. Yuan, and S. Zhang, Asymptotically Optimal Circuit Depth for Quan- tum State Preparation and General Unitary Synthesis (2023)

    2023

  76. [85]

    Yuan and S

    P. Yuan and S. Zhang, Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits, Quantum 7, 956 (2023)

    2023

  77. [86]

    K. Gui, A. M. Dalzell, A. Achille, M. Suchara, and F. T. Chong, Spacetime-Efficient Low-Depth Quantum State Preparation with Applications, Quantum 8, 1257 (2024)

    2024

  78. [87]

    Lemieux, M

    J. Lemieux, M. Lostaglio, S. Pallister, W. Pol, K. Seetharam, S. Sim, and B. S ¸ahino˘ glu, Quantum sam- pling algorithms for quantum state preparation and ma- trix block-encoding (2024)

    2024

  79. [88]

    McArdle, A

    S. McArdle, A. Gily´ en, and M. Berta, Quantum state preparation without coherent arithmetic (2025), arXiv:2210.14892 [quant-ph]

    2025 arXiv

  80. [89]

    Brassard, P

    G. Brassard, P. Hoyer, M. Mosca, and A. Tapp, Quan- tum Amplitude Amplification and Estimation (2002) 9 pp. 53–74

    2002

  81. [90]

    Aaronson and P

    S. Aaronson and P. Rall, Quantum Approximate Count- ing, Simplified, in 2020 Symposium on Simplicity in Al- gorithms (SOSA), Proceedings (Society for Industrial and Applied Mathematics, 2019) pp. 24–32

    2020

  82. [91]

    Grinko, J

    D. Grinko, J. Gacon, C. Zoufal, and S. Woerner, It- erative quantum amplitude estimation, npj Quantum Information 7, 52 (2021)

    2021

  83. [92]

    Fukuzawa, C

    S. Fukuzawa, C. Ho, S. Irani, and J. Zion, Modified It- erative Quantum Amplitude Estimation is Asymptoti- cally Optimal, in 2023 Proceedings of the Symposium on Algorithm Engineering and Experiments (ALENEX), Proceedings (Society for Industrial and Applied Math- ematics, 2023...

    2023

  84. [93]

    Rall and B

    P. Rall and B. Fuller, Amplitude Estimation from Quan- tum Signal Processing, Quantum 7, 937 (2023)

    2023

  85. [94]

    A. W. Harrow and A. Y. Wei, Adaptive Quantum Simu- lated Annealing for Bayesian Inference and Estimating Partition Functions, in Proceedings of the 2020 ACM- SIAM Symposium on Discrete Algorithms (SODA) , Proceedings (Society for Industrial and Applied Math- ematics, 2019) pp. 193–212

    2020

  86. [95]

    Cornelissen and Y

    A. Cornelissen and Y. Hamoudi, A Sublinear-Time Quantum Algorithm for Approximating Partition Func- tions, in Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Proceed- ings (Society for Industrial and Applied Mathematics,

    2023

  87. [96]

    A. M. Dalzell, S. McArdle, M. Berta, P. Bienias, C.- F. Chen, A. Gily´ en, C. T. Hann, M. J. Kastoryano, E. T. Khabiboulline, A. Kubica, G. Salton, S. Wang, and F. G. S. L. Brand˜ ao, Quantum algorithms: A survey of applications and end-to-end complexities (2023)

    2023

  88. [97]

    R. C. Farrell, N. A. Zemlevskiy, M. Illa, and J. Preskill, Digital quantum simulations of scattering in quan- tum field theories using w states, arXiv preprint arXiv:2505.03111 (2025)

    2025

  89. [98]

    Shenvi, H

    N. Shenvi, H. Van Aggelen, Y. Yang, W. Yang, C. Schw- erdtfeger, and D. Mazziotti, The tensor hypercontracted parametric reduced density matrix algorithm: Coupled- cluster accuracy with O(r4) scaling, The Journal of Chemical Physics 139 (2013)

    2013

  90. [99]

    Baskaran, A

    N. Baskaran, A. S. Rawat, A. Jayashankar, D. Chakravarti, K. Sugisaki, S. Roy, S. B. Man- dal, D. Mukherjee, and V. Prasannaa, Adapting the harrow-hassidim-lloyd algorithm to quantum many- body theory, Physical Review Research 5, 043113 (2023)

    2023

  91. [100]

    Camps and R

    D. Camps and R. V. Beeumen, F ABLE: Fast Approx- imate Quantum Circuits for Block-Encodings, in 2022 IEEE International Conference on Quantum Comput- ing and Engineering (QCE)(2022) pp. 104–113

    2022

  92. [101]

    Camps, L

    D. Camps, L. Lin, R. V. Beeumen, and C. Yang, Ex- plicit Quantum Circuits for Block Encodings of Certain Sparse Matrices (2023)

    2023

  93. [102]

    S¨ underhauf, E

    C. S¨ underhauf, E. Campbell, and J. Camps, Block- encoding structured matrices for data input in quantum computing, Quantum 8, 1226 (2024)

    2024

  94. [103]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Quantum Random Access Memory, Physical Review Letters 100, 160501 (2008)

    2008

  95. [104]

    Aaronson, Read the fine print, Nature Physics 11, 291 (2015)

    S. Aaronson, Read the fine print, Nature Physics 11, 291 (2015)

    2015

  96. [105]

    Arunachalam, V

    S. Arunachalam, V. Gheorghiu, T. Jochym-O’Connor, M. Mosca, and P. V. Srinivasan, On the robustness of bucket brigade quantum RAM, New Journal of Physics 17, 123010 (2015)

    2015

  97. [106]

    O. D. Matteo, V. Gheorghiu, and M. Mosca, Fault- Tolerant Resource Estimation of Quantum Random- Access Memories, IEEE Transactions on Quantum En- gineering 1, 1 (2020)

    2020

  98. [107]

    C. T. Hann, G. Lee, S. M. Girvin, and L. Jiang, Re- silience of quantum random access memory to generic noise, PRX Quantum 2, 020311 (2021)

    2021

  99. [108]

    Z.-Y. Chen, C. Xue, Y.-J. Wang, T.-P. Sun, H.-Y. Liu, X.-N. Zhuang, M.-H. Dou, T.-R. Zou, Y. Fang, Y.-C. Wu, and G.-P. Guo, Efficient and Error-Resilient Data Access Protocols for a Limited-Sized Quantum Random Access Memory (2023). Appendix A: Effective Hamiltonians We presen...

    2023

  100. [109]

    (A3) where |a i ⟩ denotes the configuration of an electron promoted from an occupied orbital i to an unoccupied orbital a

    Multi-exciton In the Tamm–Dancoff approximation (TDA) to the Bethe–Salpeter equation (BSE), a single-exciton ( m = 1) state is expanded in the basis of electron–hole excitations, |ψSE ⟩ = X ia cia |a i ⟩ . (A3) where |a i ⟩ denotes the configuration of an electron promoted fro...

  101. [110]

    = P µ tµOµ

    Linearized coupled cluster The coupled cluster method assumes the exponential ansatz |Ψ⟩ = eT |0⟩, where |0⟩ is a mean-field Slater determi- nant and T = T1 + T2 + . . .= P µ tµOµ. Here, Oµ excites to determinant |µ⟩, and Tm contains the subset in the µ sum corresponding to m-...

  102. [111]

    Using the procedure in Ref

    Gate complexity of Hartree-F ock state preparation in the distinguishable particle basis As described in the multi-exciton section, we may wish to prepare a Hartree-Fock initial state. Using the procedure in Ref. [60], the gate complexity of the antisymmetrizer is m × polylog ...

  103. [112]

    sparse-access oracles

    QROM versus QRAM in block-encoding In our block-encoding, we make extensive use of quantum read-only memory. For example, when loading the one- electron integrals, this allow us to access |i⟩ |j⟩ |0⟩ → |i⟩ |j⟩ |fij⟩ as an oracle (and similarly for two-electron integrals). The ...

  104. [113]

    Initial state overlap In the discussion of the multi-exciton problem, quantum algorithms to determine specific eigenvalues contain a 1/γ dependence where γ is the initial state overlap. In Ref. [63] which discussed the standard quantum simulation problem, it was argued that th...

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