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REVIEW 3 major objections 3 minor 53 references

First and second quantized digital quantum simulations of bosonic systems

T0 review · 3 major / 3 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read First-quantized encodings require fewer gates and qubits for bosonic simulations with fixed particle number.

desk verdict A careful, mostly reproducible resource comparison that introduces the unary first-quantized mapping; the core combinatorics check out, but the abstract overreaches with an unproven one-norm claim, and the paper's sweep is limited by seed-state symmetrization. read the letter →

arxiv 2511.10124 v2 pith:QN6HPPB3 submitted 2025-11-13 quant-ph

Mathias Mikkelsen , Hubert Okadome Valencia This is my paper · ORCID
classification quant-ph
keywords digitalquantumsimulationbosonicsystemsfirstquantizationsecondresourceestimationBose-HubbardmodelharmonicoscillatorTrotterdecomposition
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

This paper compares four ways of encoding N bosons in M modes on a qubit computer: unary and binary first quantization, and unary and binary second quantization. It argues that for particle-conserving problems, first-quantized encodings are systematically more efficient: the unary first-quantized mapping uses the fewest gates in most cases, and the binary first-quantized mapping uses exponentially fewer qubits than unary mappings while still outperforming second-quantized mappings for realistic N and M. It also shows that when M is a power of two, the binary first-quantized mapping's Trotter-step gate count is comparable to the unary first-quantized one. A sympathetic reader would care because this suggests bosonic simulations, such as Bose-Hubbard models and harmonic traps, can be run on smaller and noisier devices than previously assumed.

What carries the argument

The central objects are four qubit encodings: unary first-quantized (each boson's mode index as a one-hot qubit register), binary first-quantized (each index in binary), unary second-quantized (one qubit per occupation level per mode), and binary second-quantized (occupation in binary). The argument is carried by counting Pauli strings and their lengths for k-RDM off-diagonal terms and for Trotter steps of the two model Hamiltonians, with CNOT and Rz counts per Pauli string. The unary first-quantized mapping is singled out for having simple analytic gate formulas and a Hamiltonian form resembling the fermionic Jordan-Wigner structure.

What would settle it

Compute the full CNOT and Rz cost for a single Trotter step of the Bose-Hubbard Hamiltonian with a symmetrization circuit prepended to an arbitrary symmetric target state, and compare across all four mappings: if the symmetrization overhead dominates and reverses the ordering for realistic N and M, the paper's central claim would fail.

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Extended reading notes

Core claim

The central claim is that for a system of N bosons in M modes, first-quantized mappings are the most resource-efficient choice when particle number is conserved. The paper introduces the unary first-quantized mapping and shows it is the most gate-efficient in general, and that the binary first-quantized mapping—which uses N·ceil(log2 M) qubits rather than M·(N+1) or M·ceil(log2(N+1))—still requires fewer CNOT and Rz gates than either second-quantized mapping for realistic N and M. For the Bose-Hubbard and harmonic-oscillator Hamiltonians, one Trotter step in the binary first-quantized mapping uses within a modest factor of the unary first-quantized gate count when M=2^n; and off-diagonal k-R

Load-bearing premise

The resource counts assume the simulation starts from an easily prepared symmetric seed state (all bosons in one mode, or no mode occupied by more than one boson); the cost of symmetrizing an arbitrary bosonic input state is not included, and if that cost is large it could overturn the reported gate ranking.

Editorial extensions

If this is right

  • For particle-conserving bosonic problems, resource estimates for near-term and early fault-tolerant devices should use first-quantized encodings as the baseline; second-quantized encodings remain relevant only when particle number is not conserved.
  • Bose-Hubbard time evolution can reach larger system sizes in the early fault-tolerant era, since the first-quantized mapping requires relatively small Rz gate counts (on the order of 10^3 for moderate N and M).
  • When M is a power of two, the binary first-quantized mapping offers gate efficiency close to the unary first-quantized mapping while using far fewer qubits, making it a practical combined choice.
  • First-quantized mappings reduce the number of bitwise commuting Pauli groups for off-diagonal k-RDM terms, lowering measurement overhead in variational algorithms.
  • For qubitization-based quantum phase estimation, the binary first-quantized mapping has lower one-norms than the unary mapping, making it the overall most efficient choice among the considered encodings.

Reading between the lines

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

  • If an efficient general symmetrization procedure is found, the first-quantized advantage would extend to arbitrary initial states beyond the easily prepared seed states, potentially making first quantization dominant for nearly all particle-conserving bosonic algorithms.
  • The power-of-two condition for the binary mapping suggests that problem instances could be deliberately chosen or padded to M=2^n to unlock the gate savings; this is a testable design rule for future simulations.
  • The resource ranking assumes all-to-all qubit connectivity; on devices with limited connectivity, the ordering of encodings could shift, so hardware-specific implementations may need to revisit the comparison.
  • For processes that do not conserve boson number, first quantization is inapplicable, so the paper's conclusion is limited to the particle-conserving sector rather than to bosonic simulation in general.
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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 / 3 minor

Summary. The paper compares four qubit encodings for a bosonic system of N particles in M modes: unary and binary first-quantized (U1Q, B1Q) and unary and binary second-quantized (U2Q, B2Q) mappings. It derives Pauli-string counts for k-RDM off-diagonal terms, and then estimates CNOT, Rz, and measurement-group resources for a single Trotter step of the Bose-Hubbard model and a harmonic trap with short-range interactions. The central claims are that first-quantized mappings are more gate-efficient than second-quantized ones for particle-conserving bosonic problems, that U1Q is the most gate-efficient mapping in general, and that B1Q is both qubit-efficient and competitive with U1Q for gate counts when M=2^n. The abstract additionally asserts a one-norm advantage for B1Q in qubitization-based quantum phase estimation.

Significance. If established, this resource comparison provides useful practical guidance for digital quantum simulation of bosons. The analytic Pauli-string counts in Section II and Table I are transparent, and the numerical counts in Section III are checked against an independent implementation (quri-parts), giving a genuine cross-check. Section III reproduces the analytic ratios Eqs. (29)-(30) in Fig. 3, which strengthens confidence in the gate-count methodology. The main caveats are that the resource counts omit initial-state symmetrization for arbitrary states, and that the abstract's qubitization/one-norm claim is not supported in the body. The paper is a solid contribution but overstates the scope of its conclusions.

major comments (3)
  1. [Abstract and Section III introduction] The abstract states that the binary first-quantized mapping 'leads to lower one-norms than the unary mapping making it the overall most efficient choice for qubitization-based quantum phase estimation.' I could not find a derivation or even a definition of the one-norm anywhere in the body. Section III explicitly limits the resource analysis to Trotter exponentials, and qubitization is mentioned only through Ref. [51]. This is a load-bearing claim for the abstract's recommendation; it should either be derived with the relevant LCU/qubitization overheads, or removed.
  2. [Section IV (Discussion)] All gate counts in Section III and Figs. 1-4 count only the Hamiltonian Trotter exponentials. They presuppose that the simulation starts from a symmetric state of the restricted class |N000...>, |111...>, or |101...>. The Discussion concedes that 'finding an efficient way to symmetrize any input state is an important future research endeavor.' Thus the conclusion that first-quantized mappings are 'superior' to second-quantized ones is not established for arbitrary particle-conserving bosonic initial states: symmetrization circuits for states outside the restricted class could add a resource overhead not included in the reported gate counts and could overturn the ranking. The abstract and conclusions should explicitly state this conditionality.
  3. [Section III B, Figs. 3-4] The claim that B1Q is comparable to U1Q 'when M=2^n' is presented as a general statement, but the numerical evidence covers N ≤ 16 and M ≤ 32. The text attributes the effect to 'terms canceling out when all bit values of a certain length are represented' but provides no scaling argument. Since this M=2^n coincidence is central to the recommendation that B1Q can be simultaneously qubit- and gate-efficient, the authors should either prove the cancellation for general n or explicitly label the M=2^n performance as a numerical observation for small system sizes.
minor comments (3)
  1. [Section II C, Eq. (18)] The displayed symmetric operator is missing the overall factor 1/2: S^+_l S^-_m + S^+_m S^-_l = (1/2)(X_l X_m + Y_l Y_m). The factor does not affect the counted number of Pauli strings, but as written the equation is not an exact operator identity.
  2. [Throughout] There are several typos: 'th 1990s' should be 'the 1990s'; 'noisy intermediate-scale quantum (NISC)' should be 'NISQ'; 'BQCP groups' should be 'BWCP groups'; Eq. (3) is missing a '|' before a 'β,l⟩'; Eq. (5) has a spacing typo in 'V(x 1, x2)'; and reference [41] is empty.
  3. [Section II C and Conclusions] The resource comparisons assume all-to-all qubit connectivity, which is stated in Section II C but not repeated in the abstract or conclusions. On restricted connectivities, SWAP overhead can change the relative quantitative ordering; this should be mentioned wherever the final ranking is summarized.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the resource comparisons are explicit parameter-free gate counts, with only peripheral self-citations and a stated symmetrization scope limitation.

full rationale

The paper's derivation chain consists of explicit operator-to-Pauli mappings (U1Q, B1Q, U2Q, B2Q), followed by combinatorial Pauli-string/gate counts (Table I, Eqs. (20), (25)-(30)) and numerical counts obtained with the quri-parts software [49]. Nothing is fitted: no parameter is estimated from a subset of data and then used to 'predict' a related quantity. The claimed ~N^k advantage for off-diagonal k-RDM terms is a direct algebraic consequence of the mapping definitions (U1Q: 2^{2k} N^k strings versus U2Q: (4N)^{2k} strings), not an input to those definitions. The B1Q-vs-U1Q comparison at M=2^n is a computed property of the binary encoding, not built into the comparison. The two author-overlap citations are peripheral: [48] is a side remark identifying U1Q with an SU(N) hardcore model and is not used in any resource bound, while [38] is one of several references for the TE-QSCI algorithm and does not support the central counts. The Discussion explicitly concedes that efficient symmetrization of arbitrary bosonic input states is open; this is a scope limitation of the stated comparisons (which assume easily prepared seed states such as |N000...>, |111...>, or |101...>), not a step in which a result is equivalent to its input. The all-to-all connectivity assumption is likewise a stated scope condition, not circularity. A separate formatting defect is that reference [41] is blank, but it is not used in the derivation. I find no load-bearing reduction of the central claims to their inputs.

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

No free parameters are fitted anywhere: the reported numbers are exact combinatorial counts (Table I, Eqs. 25-30) or numerically tabulated Pauli decompositions for fixed (N, M). The load-bearing premises are scope choices: no symmetrization circuits, all-to-all connectivity, d=N+1 for second-quantized mappings, representativeness of the two Hamiltonians, and power-of-two M for the B1Q efficiency result. All are stated in the text; the first is the most consequential because the paper's own feasibility claims (NISQ/early-FTQC) depend on easily prepared symmetric seed states.

assumptions (7)
  • domain assumption Bosonic symmetry is provided by the initial state; no symmetrization circuits are included in any resource count.
    Introduction: algorithms are listed that work from |N000...> or states with ≤1 boson per mode ('For states which do not have two bosons in the same mode...'); Discussion concedes efficient general symmetrization is open. All Trotter gate counts exclude it.
  • domain assumption All-to-all qubit connectivity for CNOT counting.
    Section II C: 'For all-to-all connectivity, which is the focus of the resource comparisons in this paper, this ordering is irrelevant.' Restricted connectivity would add routing overhead to every CNOT count.
  • domain assumption Second-quantized mappings use local Hilbert space d = N+1 (full N-particle subsector).
    Section III: 'a local Hilbert space of d = N+1 is chosen... to take into account the full N-particle subsector.' Truncation to d < N+1 (hard-core) is analyzed only as a resource crossover (Eq. 21), not for accuracy.
  • standard math Pauli exponentials cost 2(p-1) CNOT and 1 Rz per length-p string (CNOT staircase); Clifford gates are free.
    Section III: 'Representing each exponential via a basic CNOT staircase, the exponential of a Pauli string of length p can be expressed using n_CNOT = 2(p-1) CNOT gates and 1 Rz(phi) gate [13].' Qiskit optimization (Appendix A) changes counts by factors 2-3 without changing rankings.
  • domain assumption Bose-Hubbard and harmonic-oscillator Hamiltonians are representative of 'realistic' bosonic problems.
    Section III B and the abstract generalize from these two models plus the k-RDM analysis; the abstract's overall-efficiency claims rest on this representativeness.
  • domain assumption B1Q efficiency at M = 2^n relies on exact Pauli-string cancellations present only when all bit patterns occur.
    Section III B: 'This is related to terms canceling out when all bit values of a certain length are represented in the lattice...' Non-power-of-two M results are shown separately and differ.
  • domain assumption U1Q is a valid bosonic encoding; its SU(N)-hardcore-boson interpretation is adopted from the authors' own preprint [48].
    Section II C references the companion preprint [48] for the SU(N) hardcore equivalence. The resource counts do not depend on this interpretation, but the 'U1Q is physically equivalent to...' claim does.

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Cite this review

Pith. "Pith review of First and second quantized digital quantum simulations of bosonic systems." pith.science (2026). https://pith.science/paper/QN6HPPB3

@misc{pith2026251110124,
  author       = {Pith},
  title        = {Pith review of: First and second quantized digital quantum simulations of bosonic systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QN6HPPB3}},
  note         = {Machine review of arXiv:2511.10124}
}
abstract

We compare the basic resource requirements for first and second quantized bosonic mappings in a system consisting of $N$ particles in $M$ modes. In addition to the standard binary first quantized mapping, we investigate the unary first quantized mapping. Our comparison focuses on the $k$-body reduced density matrix ($k$-RDM) and two standard bosonic Hamiltonians. The first quantized mappings use less resources for off-diagonal terms of the $k$-RDM by a factor of $ \sim N^k$, compared to the second quantized mappings. The number of gates for the first quantized binary mapping increases faster with $M$ compared to the other mappings. Nevertheless, a detailed numeric analysis reveals that the binary first quantized mapping still requires fewer gates than the binary and unary second quantized ones for realistic combinations of $N$ and $M$, while requiring exponentially fewer qubits than the unary mappings. Additionally, the number of CNOT and $R_z(\phi)$ gates necessary to express a single Trotter step of the Hamiltonian in the binary first quantized mapping is comparable to the (most efficient for a single Trotter step) unary first quantized one when $M = 2^n$ for both the Bose-Hubbard model and the harmonic trap with short-range interactions. Additionally the binary mapping leads to lower one-norms than the unary mapping making it the overall most efficient choice for qubitization-based quantum phase estimation.

Figures

Figures reproduced from arXiv: 2511.10124 by the authors.

Figure 1
Figure 1. FIG. 1. Resource comparisons for symmetric 1-RDM ODTs ˆa [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The same plots as in Fig.1, but for symmetric 2-RDM ODTs ˆa [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Resource comparisons for the BHM as a function of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Resource comparisons for the HO as a function of [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Comparing the number of CNOT gates required to express the exponential for (a) the 1-RDM ODTs, (b) the 2-RDM [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

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Works this paper leans on

53 extracted references · 2 canonical work pages

  1. [41]

    Sugisaki, S

    K. Sugisaki, S. Kanno, T. Itoko, R. Sakuma, and N. Yamamoto, Hamiltonian simulation-based quantum- selected configuration interaction for large-scale elec- tronic structure calculations with a quantum computer (2024), arXiv:2412.07218 [quant-ph]

    arXiv 2024

  2. [51]

    Akahoshi, K

    Y. Akahoshi, K. Maruyama, H. Oshima, S. Sato, and K. Fujii, PRX Quantum5, 010337 (2024)

    2024

  3. [1]

    As the Pauli strings only contain ˆZ, they can be measured simultaneously in both cases

    CNOT gates are required. As the Pauli strings only contain ˆZ, they can be measured simultaneously in both cases. Such on-site powers of the density are the only terms for which the U1Q mapping is less efficient. In the binary mappings, multiple terms will result in the same Pauli string and can be collected in a single term. Due to the complex nature of ...

  4. [2]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    2008

  5. [3]

    R. P. Feynman, International Journal of Theoretical Physics21, 467 (1982)

    1982

  6. [4]

    Z¨ urn, F

    G. Z¨ urn, F. Serwane, T. Lompe, A. N. Wenz, M. G. Ries, J. E. Bohn, and S. Jochim, Phys. Rev. Lett.108, 075303 (2012)

    2012

  7. [5]

    M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, and M. Rigol, Rev. Mod. Phys.83, 1405 (2011)

    2011

  8. [6]

    M. A. Nielsen and I. L. Chuang,Quantum Computa- tion and Quantum Information: 10th Anniversary Edi- tion(Cambridge University Press, 2010)

    2010

Show all 53 references
  1. [7]

    Mistakidis, A

    S. Mistakidis, A. Volosniev, R. Barfknecht, T. Fogarty, T. Busch, A. Foerster, P. Schmelcher, and N. Zinner, Physics Reports1042, 1 (2023), few-body Bose gases in low dimensions—A laboratory for quantum dynamics

    2023

  2. [8]

    Y. Wang, Z. Hu, B. C. Sanders, and S. Kais, Frontiers in Physics8, 10.3389/fphy.2020.589504 (2020)

    2020

  3. [9]

    N. P. de Leon, K. M. Itoh, D. Kim, K. K. Mehta, T. E. Northup, H. Paik, B. S. Palmer, N. Samarth, S. Sangtawesin, and D. W. Steuerman, Science372, eabb2823 (2021), https://www.science.org/doi/pdf/10.1126/science.abb2823

    2021 doi

  4. [10]

    Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. John- son, M. Kieferov´ a, I. D. Kivlichan, T. Menke, B. Per- opadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru- Guzik, Chemical Reviews119, 10856 (2019)

    2019

  5. [11]

    Ringbauer, M

    M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, and T. Monz, Nature Physics18, 1053 (2022)

    2022

  6. [12]

    R. D. Somma, G. Ortiz, E. H. Knill, and J. Gubernatis, inQuantum Information and Computation, Vol. 5105, edited by E. Donkor, A. R. Pirich, and H. E. Brandt, International Society for Optics and Photonics (SPIE,

  7. [13]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. C. Benjamin, and X. Yuan, Rev. Mod. Phys.92, 015003 (2020)

    2020

  8. [14]

    Trenev, P

    D. Trenev, P. J. Ollitrault, S. M. Harwood, T. P. Gu- jarati, S. Raman, A. Mezzacapo, and S. Mostame, Refin- ing resource estimation for the quantum computation of vibrational molecular spectra through trotter error anal- ysis (2023), arXiv:2311.03719 [quant-ph]

    2023 arXiv

  9. [15]

    N. P. D. Sawaya, T. Menke, T. H. Kyaw, S. Johri, A. Aspuru-Guzik, and G. G. Guerreschi, npj Quantum Information6, 49 (2020)

    2020

  10. [16]

    Kuwahara, T

    T. Kuwahara, T. V. Vu, and K. Saito, Nature Commu- nications15, 2520 (2024)

    2024

  11. [17]

    Majland and N

    M. Majland and N. T. Zinner, Resource-efficient encod- ing algorithm for variational bosonic quantum simula- tions (2021), arXiv:2102.11886 [quant-ph]

    2021 arXiv

  12. [18]

    McArdle, A

    S. McArdle, A. Mayorov, X. Shan, S. Benjamin, and X. Yuan, Chem. Sci.10, 5725 (2019)

    2019

  13. [19]

    B. Peng, Y. Su, D. Claudino, K. Kowalski, G. H. Low, and M. Roetteler, Quantum simulation of boson-related hamiltonians: Techniques, effective hamiltonian con- struction, and error analysis (2023), arXiv:2307.06580 [quant-ph]

    2023 arXiv

  14. [20]

    L¨ otstedt, K

    E. L¨ otstedt, K. Yamanouchi, T. Tsuchiya, and Y. Tachikawa, Phys. Rev. A103, 062609 (2021)

    2021

  15. [21]

    N. P. D. Sawaya and J. Huh, The Journal of Physical Chemistry Letters10, 3586 (2019)

    2019

  16. [22]

    N. P. D. Sawaya, G. G. Guerreschi, and A. Holmes, in 2020 IEEE International Conference on Quantum Com- puting and Engineering (QCE)(2020) pp. 180–190

    2020

  17. [23]

    N. P. D. Sawaya, F. Paesani, and D. P. Tabor, Phys. Rev. A104, 062419 (2021)

    2021

  18. [24]

    J. Liu, Z. Li, H. Zheng, X. Yuan, and J. Sun, Machine Learning: Science and Technology3, 045030 (2022)

    2022

  19. [25]

    Bahrami and N

    S. Bahrami and N. Sawaya, Particle-conserving quantum circuit ansatz with applications in variational simulation of bosonic systems (2024), arXiv:2402.18768 [quant-ph]

    2024 arXiv

  20. [26]

    Y. Wang, L. M. Sager-Smith, and D. A. Mazziotti, New Journal of Physics25, 103005 (2023)

    2023

  21. [27]

    Tudorovskaya and D

    M. Tudorovskaya and D. Mu˜ noz Ramo, Phys. Rev. A 109, 032612 (2024)

    2024

  22. [28]

    Y. Su, D. W. Berry, N. Wiebe, N. Rubin, and R. Bab- bush, PRX Quantum2, 040332 (2021)

    2021

  23. [29]

    D. S. Abrams and S. Lloyd, Phys. Rev. Lett.79, 2586 (1997)

    1997

  24. [30]

    N. C. Rubin, D. W. Berry, F. D. Malone, A. F. White, T. Khattar, A. E. DePrince, S. Sicolo, M. K¨ uehn, M. Kaicher, J. Lee, and R. Babbush, PRX Quantum4, 040303 (2023)

    2023

  25. [31]

    Delgado, P

    A. Delgado, P. A. M. Casares, R. dos Reis, M. S. Zini, R. Campos, N. Cruz-Hern´ andez, A.-C. Voigt, A. Lowe, S. Jahangiri, M. A. Martin-Delgado, J. E. Mueller, and J. M. Arrazola, Phys. Rev. A106, 032428 (2022)

    2022

  26. [32]

    D. W. Berry, N. C. Rubin, A. O. Elnabawy, G. Ahlers, A. E. D. III, J. Lee, C. Gogolin, and R. Bab- bush, Quantum simulation of realistic materials in first quantization using non-local pseudopotentials (2024), arXiv:2312.07654 [quant-ph]

    2024

  27. [33]

    Shokrian Zini, A

    M. Shokrian Zini, A. Delgado, R. dos Reis, P. A. Moreno Casares, J. E. Mueller, A.-C. Voigt, and J. M. Arrazola, Quantum7, 1049 (2023)

    2023

  28. [34]

    D. W. Berry, M. Kieferov´ a, A. Scherer, Y. R. Sanders, G. H. Low, N. Wiebe, C. Gidney, and R. Babbush, npj Quantum Information4, 22 (2018)

    2018

  29. [35]

    T. N. Georges, M. Bothe, C. S¨ underhauf, B. K. Berntson, R. Izs´ ak, and A. V. Ivanov, Quantum simulations of chemistry in first quantization with any basis set (2024), arXiv:2408.03145 [quant-ph]

    2024 arXiv

  30. [36]

    G. H. Low and I. L. Chuang, Quantum3, 163 (2019)

    2019

  31. [37]

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

    1995 arXiv

  32. [38]

    Mikkelsen and Y

    M. Mikkelsen and Y. O. Nakagawa, Quantum-selected configuration interaction with time-evolved state (2024), arXiv:2412.13839 [quant-ph]

    2024

  33. [39]

    I. D. Kivlichan, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, W. Sun, Z. Jiang, N. Rubin, A. Fowler, A. Aspuru-Guzik, H. Neven, and R. Babbush, Quantum 4, 296 (2020)

    2020

  34. [40]

    J. Yu, J. R. Moreno, J. T. Iosue, L. Bertels, D. Claudino, B. Fuller, P. Groszkowski, T. S. Humble, P. Jurce- vic, W. Kirby, T. A. Maier, M. Motta, B. Pokharel, A. Seif, A. Shehata, K. J. Sung, M. C. Tran, V. Tripathi, 13 A. Mezzacapo, and K. Sharma, Quantum-centric algo- rith...

    2025

  35. [42]

    Veis and J

    L. Veis and J. Pittner, The Jour- nal of Chemical Physics140, 214111 (2014), https://pubs.aip.org/aip/jcp/article- pdf/doi/10.1063/1.4880755/15480639/214111 1 online.pdf

    2014 doi

  36. [43]

    S. Lee, J. Lee, H. Zhai, Y. Tong, A. M. Dalzell, A. Ku- mar, P. Helms, J. Gray, Z.-H. Cui, W. Liu, M. Kasto- ryano, R. Babbush, J. Preskill, D. R. Reichman, E. T. Campbell, E. F. Valeev, L. Lin, and G. K.-L. Chan, Na- ture Communications14, 1952 (2023)

    1952

  37. [44]

    L. S. Cederbaum, O. E. Alon, and A. I. Streltsov, Phys- ical Review A73, 10.1103/physreva.73.043609 (2006)

    2006 doi

  38. [45]

    Tilly, H

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, and J. Tennyson, Physics Reports986, 1 (2022), the Vari- ational Quantum Eigensolver: a review of methods and best practices

    2022

  39. [46]

    Anand, P

    A. Anand, P. Schleich, S. Alperin-Lea, P. W. K. Jensen, S. Sim, M. D ´ ıaz-Tinoco, J. S. Kottmann, M. Degroote, A. F. Izmaylov, and A. Aspuru-Guzik, Chem. Soc. Rev. 51, 1659 (2022)

    2022

  40. [47]

    Horiba, S

    T. Horiba, S. Shirai, and H. Hirai, Construction of an- tisymmetric variational quantum states with real-space representation (2023), arXiv:2306.08434 [quant-ph]

    2023 arXiv

  41. [48]

    Mikkelsen and I

    M. Mikkelsen and I. Danshita, Entanglement-enhanced correlation propagation in the one-dimensional su(n) fermi-hubbard model (2025), arXiv:2510.25358 [cond- mat.quant-gas]

    2025 arXiv

  42. [49]

    QURI Parts (2022),https://github.com/QunaSys/ quri-parts

    2022

  43. [50]

    where larger systems sizes are therefore more within reach. In Fig. 4 the number of CNOT andR z(ϕ) gates re- quired to express the exponential of the HO Hamiltonian as well as the number of BWCP groups required to mea- 9 U1Q B1Q min. ham. B1Q max. ham. U2Q B2Q a) N = 3 n CNOT ...

    2000

  44. [52]

    J. Lee, D. W. Berry, C. Gidney, W. J. Huggins, J. R. McClean, N. Wiebe, and R. Babbush, PRX Quantum2, 030305 (2021)

    2021

  45. [53]

    Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023). Appendix A: Comparing with optimized CNOT gate counts In the main text we considered CNOT gates based on the basic CNOT staircase approach without further sim- plifications applied to the circu...

    2023

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Reviewed August 3, 2026 · model on record in the stance chip above.