Pith. sign in

REVIEW 2 major objections 4 minor 2 cited by

The kicked-Ising model at its self-dual point gives an exactly solvable quantum battery whose stored energy after any number of kicks takes only three values—0, half, or full capacity—and reaches full charge at predictable kick counts.

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 20:54 UTC pith:EQFRXSD5

load-bearing objection The exact charging classification is real and useful; the paper's own equations contradict its GHZ/entanglement claims, so read it for the energy formula and treat the state-preparation story with suspicion. the 2 major comments →

arxiv 2511.17835 v2 pith:EQFRXSD5 submitted 2025-11-21 quant-ph cond-mat.stat-mechnlin.CD

Kicked-Ising Quantum Battery

Sebasti\'an V. Romero , Xi Chen , Yue Ban This is my paper
classification quant-ph cond-mat.stat-mechnlin.CD
keywords quantum batterykicked-Ising modelself-dual pointClifford quantum cellular automataFloquet dynamicsenergy injectiondisorder robustnessspin chain
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.

This paper proposes using the kicked-Ising spin chain, a standard periodically driven many-body model, as a quantum battery. At a special parameter point—the self-dual regime where the Ising coupling and the transverse-field kick strength are both π/4—the charging dynamics become exactly solvable for any system size. The authors prove that the injected energy after m kicks follows a simple sine formula, so the battery's stored energy is always 0, 50%, or 100% of its capacity, with full charge achieved at specific Floquet cycles. They argue that this protocol is stable against disorder and timing imperfections, and show that non-uniform kick sequences within a fixed time window accelerate charging toward the continuous-driving limit. If correct, this gives a scalable, analytically tractable testbed for quantum batteries on existing spin-chain hardware.

Core claim

At the self-dual point (J = b = π/4), the Floquet operator of the kicked-Ising chain becomes a Clifford circuit, equivalent to a Clifford quantum cellular automaton. Using this structure—or, equivalently, momentum-space diagonalization plus the Cayley-Hamilton theorem—the authors obtain exact expressions for the energy injected into a battery of N spins prepared in the ground state of H0. With the H_xx charger under periodic boundary conditions and N even, the normalized injected energy EN/N equals 1 at m = (q+1/2)N kicks, 0 at m = qN, and 1/2 at all other times, with Floquet period N; the H_zz charger under open boundary conditions gives full charge at m = (2+4q)N and period 4N. The authors

What carries the argument

The central object is the self-dual operator regime of the kicked-Ising chain, J = b = π/4, where the Floquet operator U = e^{-iH_K} e^{-iH_I} is a Clifford unitary. In this regime the evolution is captured by a Clifford quantum cellular automaton (CQCA), a discrete-time linear map on Pauli operators that tracks exactly how each spin operator spreads; equivalently, a Jordan-Wigner plus Bogoliubov momentum-space analysis gives a 2×2 Floquet matrix per mode, whose m-th power is computed by the Cayley-Hamilton theorem using Chebyshev polynomials. The energy formula EN(m) = ω0 Σ_k sin²(mk) (after zeroing the ground-state energy) is the identity that carries the proof: the sum over pseudomomenta

Load-bearing premise

The claim that open-boundary chains follow the same charging pattern as the odd-N periodic case—on which the OBC figures, the GHZ-preparation statements, and the entanglement-entropy formulas rest—is assumed, not derived; the exact momentum-space method works only under periodic boundary conditions.

What would settle it

Simulate or run on hardware the H_zz charger with open boundary conditions for, say, N = 10 or N = 12 and track the injected energy for m up to 4N, beyond the sizes reported by tensor-network checks; the central claim fails if the normalized energy deviates from the predicted 0 / 0.5 / 1 staircase at any kick, or if the OBC pattern diverges from the PBC odd-N prediction.

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

If this is right

  • The battery can be exactly and fully charged at prescribed numbers of kicks, with stored energy pinned to 0, 50%, or 100% between those times, so charging and discharging schedules are deterministic.
  • Fluctuations in the stored energy, a known practical obstacle in quantum batteries, are absent in the ideal dynamics.
  • Disorder in the exchange couplings up to σJ ≈ 0.2 leaves the charging curve essentially unchanged, and stronger disorder saturates the mean injected energy at half capacity rather than destroying it.
  • Non-uniform kicks in a unit time window approach the continuously driven transverse-field Ising result, so fewer than about 10 kicks reproduce the regular Ising battery's saturation energy, and the strict π/4-per-kick timing constraint is relaxed.
  • The protocol admits a constant-depth circuit implementation on platforms with RZZ and RX gates, demonstrated on a 104-qubit superconducting processor.

Where Pith is reading between the lines

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

  • Inference: The three-valued energy quantization is a direct consequence of the self-dual Clifford structure; one testable extension is to probe whether couplings slightly away from π/4 produce a smooth crossover or a sharp breakdown, revealing whether the exactness is structurally necessary for the plateau stability.
  • Inference: Because the maximal-charge kicks coincide with the preparation of GHZ-type states (for H_zz under open boundary conditions), the paper implicitly offers a byproduct: the same protocol can serve as a deterministic GHZ-state factory, and a separate experiment measuring entanglement witnesses at those kicks would test that reading.
  • Inference: The authors' OBC equivalence, if it holds generally, implies that open chains—more practical in most experimental platforms—enjoy the same exact charging properties as a special periodic case; this is worth a dedicated proof, since the paper itself notes that the exact momentum-space method does not cover OBC.
  • Inference: The light-cone/spin-correlator analysis suggests that charging rate is tied to operator-spreading speed; a quantitative link between the butterfly velocity and the energy-injection rate at non-saturating kicks could turn scrambling into a design parameter for future protocols.

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 / 4 minor

Summary. The manuscript proposes the kicked-Ising model at the self-dual point as a quantum battery charger. It claims an exact analytical solution for the injected energy after m kicks, EN(m) = ω0 Σ_k sin²(mk) (up to a constant shift), obtained independently via Clifford quantum cellular automata and momentum-space Floquet analysis combined with the Cayley–Hamilton theorem. Depending on boundary conditions and system-size parity, the normalized charging EN/N is claimed to take only the discrete values 0, 1/2, and 1, with Floquet periods N or 4N. The paper further claims robustness against disorder, a non-uniform kick protocol that approaches the continuously driven transverse-field Ising limit, and verification on IBM quantum hardware. It also makes prominent claims that maximal entanglement growth yields maximal energy injection, including GHZ-state preparation at specific kick numbers.

Significance. The central technical result — the exact energy-injection formula and the discrete EN/N ∈ {0, 1/2, 1} structure — appears sound and is a valuable contribution. Two independent derivations (CQCA and momentum space) agree, the Lagrange identity explains the flat plateaus, and MPS and IBM data support the first cycles. The paper also provides source code and detailed supplementary derivations, which are strengths. If the OBC extension and the robustness claims survive revision, the model would be a simple, exactly solvable, and experimentally accessible quantum-battery testbed. However, the advertised connection between maximal entanglement and maximal energy injection is incorrect as stated, and the GHZ preparation claims are contradicted by the paper's own exact solution.

major comments (2)
  1. [Abstract; main text 'Spin localization in time domain' and Fig. 3d] The claim that 'maximal entanglement growth yields maximal energy injection' is contradicted by the exact CQCA solution reported in Supplementary Section I B2. For the H_zz charger under OBC (and PBC with odd N), Eq. (S42)/(S46) gives σy_i(2N) = −σy_i(0). Since the initial state is |−i⟩^⊗N and EN(2N)/N = 1, the state at m = 2N is forced to be |+i⟩^⊗N, a product state with zero von Neumann entropy across every cut. The GHZ±i state (|0⟩^⊗N ± i|1⟩^⊗N)/√2 has ⟨σy_i⟩ = 0 and fidelity 2^{−N/2} with |+i⟩^⊗N, so it is not prepared at m = 2N. The statements in Fig. 3d ('GHZ-like state ... prepared at kicks 2(1+q)N and 2(1+3q)N') and in the spin-correlator section are therefore inconsistent with the exact solution. The energy results do not require this interpretation, but the abstract, Fig. 6a, and the conclusion use it as a headline. This must be corrected or removed.
  2. [Supplementary I C final remarks; main text 'Charging dynamics of uniform KIC'] The OBC results are presented as analytical (Figs. 2b,d; 3b,d; 5; and entanglement-entropy formulas S91–S95), but Supplementary Section I C states that the momentum-space method 'can only be applied when PBC are considered' and that OBC requires diagonalizing a 2N×2N matrix. The claimed equivalence — 'regardless the parity of the number of spins, the behavior of the energy injected for OBC evolves as the N-odd case for PBC' — is not derived; it is only verified by MPS for finite sizes and kick counts. Since the OBC maximal-charging times and the parabolic entanglement-entropy formulas rely on this unproven equivalence, the paper should either supply a proof or clearly label the OBC predictions as numerically supported conjectures.
minor comments (4)
  1. [Fig. 2 caption] Calling the OBC curves 'Analytical' is misleading given that the OBC equivalence is not proven; consider relabeling as 'Exact (PBC) / MPS-verified (OBC)' or similar.
  2. [Supplementary II A] Typo: 'power-lay-decaying' should be 'power-law-decaying'.
  3. [Equation (9)] The variance V[EN] uses EN both as the expectation value and as the random variable; clarify notation to distinguish the estimator from the true injected energy.
  4. [Throughout] IBM hardware name is inconsistently formatted ('ibm torino' vs. 'IBM Torino'); also, the abstract contains a grammatical issue ('characterizing the charging process, featuring...').

Circularity Check

0 steps flagged

No significant circularity: the KIC charging profile is derived parameter-free; the OBC/GHZ issues are extrapolation/consistency caveats, not circularity.

full rationale

The central result, EN(m) = ω0 Σ_k sin²(mk) with EN/N ∈ {0, 0.5, 1}, is not an input to the paper's argument: it is obtained by two independent, parameter-free derivations (Clifford quantum cellular automata conjugation of Pauli operators, and momentum-space Floquet diagonalization with the Cayley-Hamilton theorem), and it is benchmarked against MPS/TEBD simulations and, for early cycles, IBM hardware data. The only self-citations, refs. [38] (binomial spectrum of H0) and [42] (disorder model), supply standard inputs rather than the central claim; removing them would not alter the derivation, so they are not load-bearing. The OBC=PBC-odd assertion does rest on an extrapolation in the sense that the momentum-space method 'can only be applied when PBC are considered' and the paper states that the OBC equivalence was 'verified via tensor network simulations' rather than proved; however, that is an independent numerical check, not a fitted target built into the derivation, so it is a completeness/correctness caveat rather than circularity. Separately, the GHZ/maximal-entanglement interpretation in Fig. 3d and Fig. 6a appears inconsistent with the paper's own exact Pauli evolution (e.g., at m=2N, Eqs. (S42)/(S46) reduce to −σ_y, implying a product state), but an internal contradiction is not a self-referential reduction, so it is outside the scope of the circularity pass.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 1 invented entities

The derivation is remarkably lean: given the self-dual point (J=b=π/4), the energy-injection formulas follow from standard free-fermion and Clifford machinery with no fitted constants. What the reader pays for upstream: (i) the fine-tuned operating point that makes everything solvable, (ii) the battery-performance identification (mean internal energy, no ergotropy), (iii) the numerically-verified-not-derived OBC equivalence, (iv) the ideal kick idealization. The GHZ-state claim adds an invented interpretive layer that conflicts with the CQCA result.

free parameters (1)
  • Self-dual operating point J = b = π/4 (mod 2π) = π/4
    Chosen by hand, from prior literature [21], because at this point the Floquet operator is Clifford and the model is exactly solvable; the EN/N ∈ {0, 0.5, 1} patterns exist only here. Not fitted to data, but the paper's entire analytical tower depends on it.
axioms (4)
  • domain assumption Self-dual kicked-Ising Floquet operator is a Clifford unitary (CQCA) and the chain is exactly solvable via Jordan-Wigner/free fermions
    Imported from refs [21] and standard Kitaev-chain results; invoked in Methods step 1 and SI Section I; the paper's exact solutions live at this point.
  • domain assumption Battery Hamiltonian H0 = (ω0/2)Σσ^{α}_i with equally spaced spectrum ϵk = kω0 (binomial multiplicity) and product ground state; ⟨H0⟩ is the measure of charging performance
    Standard QB setup (refs [5],[38]); the paper does not analyze ergotropy/extractable work, so 'stored energy' is implicitly equated with 'battery performance'.
  • ad hoc to paper OBC charging dynamics equals PBC-odd-N dynamics for arbitrary system size and kick count
    Asserted in main text and SI I C; only verified by MPS, not derived ('this method can only be applied when PBC are considered').
  • domain assumption Instantaneous kicks (Dirac deltas) and step-function switching λ(t); finite-width pulses and slow quenches are checked only numerically (SI II B, II C)
    The exact patterns require δ-function kicks; quasikicks with δt > 0.08 already degrade the profile (Fig S3).
invented entities (1)
  • Quasikick (finite-width kick envelope with Blackman window) no independent evidence
    purpose: Regularize the ideal Dirac-delta kicks to model realistic pulses (SI II B, Eq S85-S87)
    A modeling device, not a new physical object; no falsifiable prediction attached. Its main role is to bound when the KIC nature survives (δt ≤ ~0.08).

pith-pipeline@v1.3.0-alltime-deepseek · 52648 in / 30509 out tokens · 274139 ms · 2026-08-03T20:54:26.093522+00:00 · methodology

0 comments
read the original abstract

Entanglement has been identified as a key resource for enhancing charging performance in quantum batteries. We show that the kicked-Ising model at the self-dual point provides an explicit charging mechanism, where maximal entanglement growth yields maximal energy injection. Identifying the Floquet dynamics as a Clifford quantum cellular automata and considering exact diagonalization in momentum space, we analytically characterize the charging process, featuring a stable performance while achieving maximal charging. We further propose a fixed time window protocol that accelerates charging toward the continuously driven transverse-field limit. Spin-correlator analysis reveals that scrambling and light-cone spreading govern charging performance. The protocols remain compatible with diverse platforms, underscoring their scalability and practical feasibility.

Figures

Figures reproduced from arXiv: 2511.17835 by Sebasti\'an V. Romero, Xi Chen, Yue Ban.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum resonance-enhanced performance of quantum battery

    quant-ph 2026-07 conditional novelty 6.0

    At quantum resonance, kicked-rotor and kicked-top quantum batteries charge with power growing linearly in time and near-unity extractable-energy efficiency.

  2. Impact of thermal and dissipative effects in a periodically-kicked quantum battery

    quant-ph 2026-04 unverdicted novelty 4.0

    Quantum batteries using periodically kicked Ising models maintain robust charging under finite temperature and dissipation in identified parameter regimes.

Reference graph

Works this paper leans on

82 extracted references · 24 canonical work pages · cited by 2 Pith papers

  1. [1]

    author author K. V. \ Hovhannisyan , author M. Perarnau-Llobet , author M. Huber ,\ and\ author A. Ac\' n ,\ https://doi.org/10.1103/PhysRevLett.111.240401 journal journal Phys. Rev. Lett. \ volume 111 ,\ pages 240401 ( year 2013 ) NoStop

    doi:10.1103/physrevlett.111.240401 2013

  2. [2]

    Campaioli et al

    author author F. Campaioli et al. ,\ https://doi.org/10.1103/PhysRevLett.118.150601 journal journal Phys. Rev. Lett. \ volume 118 ,\ pages 150601 ( year 2017 ) NoStop

    doi:10.1103/physrevlett.118.150601 2017

  3. [3]

    author author F. C. \ Binder , author S. Vinjanampathy , author K. Modi ,\ and\ author J. Goold ,\ https://doi.org/10.1088/1367-2630/17/7/075015 journal journal New J. Phys. \ volume 17 ,\ pages 075015 ( year 2015 ) NoStop

    doi:10.1088/1367-2630/17/7/075015 2015

  4. [4]

    Alicki \ and\ author M

    author author R. Alicki \ and\ author M. Fannes ,\ https://doi.org/10.1103/PhysRevE.87.042123 journal journal Phys. Rev. E \ volume 87 ,\ pages 042123 ( year 2013 ) NoStop

    doi:10.1103/physreve.87.042123 2013

  5. [5]

    Campaioli , author S

    author author F. Campaioli , author S. Gherardini , author J. Q. \ Quach , author M. Polini ,\ and\ author G. M. \ Andolina ,\ https://doi.org/10.1103/RevModPhys.96.031001 journal journal Rev. Mod. Phys. \ volume 96 ,\ pages 031001 ( year 2024 ) NoStop

    doi:10.1103/revmodphys.96.031001 2024

  6. [6]

    Rossini , author G

    author author D. Rossini , author G. M. \ Andolina , author D. Rosa , author M. Carrega ,\ and\ author M. Polini ,\ https://doi.org/10.1103/PhysRevLett.125.236402 journal journal Phys. Rev. Lett. \ volume 125 ,\ pages 236402 ( year 2020 ) NoStop

    doi:10.1103/physrevlett.125.236402 2020

  7. [7]

    author author G. M. \ Andolina , author V. Stanzione , author V. Giovannetti ,\ and\ author M. Polini ,\ https://doi.org/10.1103/kzvn-dj7v journal journal Phys. Rev. Lett. \ volume 134 ,\ pages 240403 ( year 2025 ) NoStop

    doi:10.1103/kzvn-dj7v 2025

  8. [8]

    Ebadi et al

    author author S. Ebadi et al. ,\ https://doi.org/10.1038/s41586-021-03582-4 journal journal Nature \ volume 595 ,\ pages 227–232 ( year 2021 ) NoStop

    doi:10.1038/s41586-021-03582-4 2021

  9. [9]

    Kim et al

    author author Y. Kim et al. ,\ https://doi.org/10.1038/s41586-023-06096-3 journal journal Nature \ volume 618 ,\ pages 500–505 ( year 2023 ) NoStop

    doi:10.1038/s41586-023-06096-3 2023

  10. [10]

    author author A. D. \ King et al. ,\ https://doi.org/10.1126/science.ado6285 journal journal Science \ volume 388 ,\ pages 199 ( year 2025 ) NoStop

    doi:10.1126/science.ado6285 2025

  11. [11]

    author author T. P. \ Le , author J. Levinsen , author K. Modi , author M. M. \ Parish ,\ and\ author F. A. \ Pollock ,\ https://doi.org/10.1103/PhysRevA.97.022106 journal journal Phys. Rev. A \ volume 97 ,\ pages 022106 ( year 2018 ) NoStop

    doi:10.1103/physreva.97.022106 2018

  12. [12]

    Rossini , author G

    author author D. Rossini , author G. M. \ Andolina ,\ and\ author M. Polini ,\ https://doi.org/10.1103/PhysRevB.100.115142 journal journal Phys. Rev. B \ volume 100 ,\ pages 115142 ( year 2019 ) NoStop

    doi:10.1103/physrevb.100.115142 2019

  13. [13]

    author author M. B. \ Arjmandi , author H. Mohammadi , author A. Saguia , author M. S. \ Sarandy ,\ and\ author A. C. \ Santos ,\ https://doi.org/10.1103/PhysRevE.108.064106 journal journal Phys. Rev. E \ volume 108 ,\ pages 064106 ( year 2023 ) NoStop

    work page doi:10.1103/physreve.108.064106 2023

  14. [14]

    author author E. B. \ Rozenbaum , author S. Ganeshan ,\ and\ author V. Galitski ,\ https://doi.org/10.1103/PhysRevLett.118.086801 journal journal Phys. Rev. Lett. \ volume 118 ,\ pages 086801 ( year 2017 ) NoStop

    work page doi:10.1103/physrevlett.118.086801 2017

  15. [15]

    \ Lin \ and\ author O

    author author C.-J. \ Lin \ and\ author O. I. \ Motrunich ,\ https://doi.org/10.1103/PhysRevB.97.144304 journal journal Phys. Rev. B \ volume 97 ,\ pages 144304 ( year 2018 ) NoStop

    work page doi:10.1103/physrevb.97.144304 2018

  16. [16]

    author author M. K. \ Joshi et al. ,\ https://doi.org/10.1103/PhysRevLett.124.240505 journal journal Phys. Rev. Lett. \ volume 124 ,\ pages 240505 ( year 2020 ) NoStop

    doi:10.1103/physrevlett.124.240505 2020

  17. [17]

    Santhanam , author S

    author author M. Santhanam , author S. Paul ,\ and\ author J. B. \ Kannan ,\ https://doi.org/https://doi.org/10.1016/j.physrep.2022.01.002 journal journal Phys. Rep. \ volume 956 ,\ pages 1 ( year 2022 ) NoStop

    doi:10.1016/j.physrep.2022.01.002 2022

  18. [18]

    Anand , author J

    author author A. Anand , author J. Davis ,\ and\ author S. Ghose ,\ https://doi.org/10.1103/PhysRevResearch.6.023120 journal journal Phys. Rev. Res. \ volume 6 ,\ pages 023120 ( year 2024 ) NoStop

    work page doi:10.1103/physrevresearch.6.023120 2024

  19. [19]

    author author S. P. G. , author J. B. \ Kannan , author S. H. \ Tekur ,\ and\ author M. S. \ Santhanam ,\ https://doi.org/10.1103/PhysRevB.111.054314 journal journal Phys. Rev. B \ volume 111 ,\ pages 054314 ( year 2025 ) NoStop

    work page doi:10.1103/physrevb.111.054314 2025

  20. [20]

    Waltner \ and\ author P

    author author D. Waltner \ and\ author P. Braun ,\ https://doi.org/10.1103/PhysRevB.104.054432 journal journal Phys. Rev. B \ volume 104 ,\ pages 054432 ( year 2021 ) NoStop

    doi:10.1103/physrevb.104.054432 2021

  21. [21]

    Bertini , author P

    author author B. Bertini , author P. Kos ,\ and\ author T. Prosen ,\ https://doi.org/10.1103/PhysRevX.9.021033 journal journal Phys. Rev. X \ volume 9 ,\ pages 021033 ( year 2019 ) NoStop

    doi:10.1103/physrevx.9.021033 2019

  22. [22]

    Colmenarez \ and\ author D

    author author L. Colmenarez \ and\ author D. J. \ Luitz ,\ https://doi.org/10.1103/PhysRevResearch.2.043047 journal journal Phys. Rev. Res. \ volume 2 ,\ pages 043047 ( year 2020 ) NoStop

    work page doi:10.1103/physrevresearch.2.043047 2020

  23. [23]

    Kim et al

    author author K. Kim et al. ,\ https://doi.org/10.1038/nature09071 journal journal Nature \ volume 465 ,\ pages 590–593 ( year 2010 ) NoStop

    doi:10.1038/nature09071 2010

  24. [24]

    author author J. W. \ Britton et al. ,\ https://doi.org/10.1038/nature10981 journal journal Nature \ volume 484 ,\ pages 489–492 ( year 2012 ) NoStop

    doi:10.1038/nature10981 2012

  25. [25]

    Jurcevic et al

    author author P. Jurcevic et al. ,\ https://doi.org/10.1103/PhysRevLett.119.080501 journal journal Phys. Rev. Lett. \ volume 119 ,\ pages 080501 ( year 2017 ) NoStop

    doi:10.1103/physrevlett.119.080501 2017

  26. [26]

    Zhang et al

    author author J. Zhang et al. ,\ https://doi.org/10.1038/nature24654 journal journal Nature \ volume 551 ,\ pages 601–604 ( year 2017 ) NoStop

    doi:10.1038/nature24654 2017

  27. [27]

    author author T. A. \ Johnson et al. ,\ https://doi.org/10.1103/PhysRevLett.100.113003 journal journal Phys. Rev. Lett. \ volume 100 ,\ pages 113003 ( year 2008 ) NoStop

    work page doi:10.1103/physrevlett.100.113003 2008

  28. [28]

    B\'eguin , author A

    author author L. B\'eguin , author A. Vernier , author R. Chicireanu , author T. Lahaye ,\ and\ author A. Browaeys ,\ https://doi.org/10.1103/PhysRevLett.110.263201 journal journal Phys. Rev. Lett. \ volume 110 ,\ pages 263201 ( year 2013 ) NoStop

    work page doi:10.1103/physrevlett.110.263201 2013

  29. [29]

    Hermann-Avigliano et al

    author author C. Hermann-Avigliano et al. ,\ https://doi.org/10.1103/PhysRevA.90.040502 journal journal Phys. Rev. A \ volume 90 ,\ pages 040502 ( year 2014 ) NoStop

    work page doi:10.1103/physreva.90.040502 2014

  30. [30]

    Ebert , author M

    author author M. Ebert , author M. Kwon , author T. G. \ Walker ,\ and\ author M. Saffman ,\ https://doi.org/10.1103/PhysRevLett.115.093601 journal journal Phys. Rev. Lett. \ volume 115 ,\ pages 093601 ( year 2015 ) NoStop

    work page doi:10.1103/physrevlett.115.093601 2015

  31. [31]

    Labuhn et al

    author author H. Labuhn et al. ,\ https://doi.org/10.1038/nature18274 journal journal Nature \ volume 534 ,\ pages 667–670 ( year 2016 ) NoStop

    doi:10.1038/nature18274 2016

  32. [32]

    Guardado-Sanchez et al

    author author E. Guardado-Sanchez et al. ,\ https://doi.org/10.1103/PhysRevX.8.021069 journal journal Phys. Rev. X \ volume 8 ,\ pages 021069 ( year 2018 ) NoStop

    work page doi:10.1103/physrevx.8.021069 2018

  33. [33]

    Keesling et al

    author author A. Keesling et al. ,\ https://doi.org/10.1038/s41586-019-1070-1 journal journal Nature \ volume 568 ,\ pages 207–211 ( year 2019 ) NoStop

    doi:10.1038/s41586-019-1070-1 2019

  34. [34]

    author author T. M. \ Graham et al. ,\ https://doi.org/10.1103/PhysRevLett.123.230501 journal journal Phys. Rev. Lett. \ volume 123 ,\ pages 230501 ( year 2019 ) NoStop

    doi:10.1103/physrevlett.123.230501 2019

  35. [35]

    Egorova , author G

    author author E. Egorova , author G. Fedorov , author I. Tsitsilin , author I. Besedin ,\ and\ author A. Ustinov ,\ https://doi.org/10.1063/5.0011812 journal journal AIP Conf. Proc. \ volume 2241 ,\ pages 020013 ( year 2020 ) NoStop

    work page doi:10.1063/5.0011812 2020

  36. [36]

    Stehlik et al

    author author J. Stehlik et al. ,\ https://doi.org/10.1103/PhysRevLett.127.080505 journal journal Phys. Rev. Lett. \ volume 127 ,\ pages 080505 ( year 2021 ) NoStop

    doi:10.1103/physrevlett.127.080505 2021

  37. [37]

    Greenaway , author A

    author author S. Greenaway , author A. Smith , author F. Mintert ,\ and\ author D. Malz ,\ https://doi.org/10.22331/q-2024-02-22-1263 journal journal Quantum \ volume 8 ,\ pages 1263 ( year 2024 ) NoStop

    work page doi:10.22331/q-2024-02-22-1263 2024

  38. [38]

    author author S. V. \ Romero , author Y. Ding , author X. Chen ,\ and\ author Y. Ban ,\ https://doi.org/10.1007/JHEP05(2025)021 journal journal J. High Energ. Phys \ volume 2025 ,\ pages 21 ( year 2025 ) NoStop

    doi:10.1007/jhep05(2025)021 2025

  39. [39]

    \ Schlingemann , author H

    author author D.-M. \ Schlingemann , author H. Vogts ,\ and\ author R. F. \ Werner ,\ https://doi.org/10.1063/1.3005565 journal journal J. Math. Phys. \ volume 49 ,\ pages 112104 ( year 2008 ) NoStop

    doi:10.1063/1.3005565 2008

  40. [40]

    author author IBM Quantum ,\ @noop howpublished https://quantum.cloud.ibm.com/ ( year 2025 ) NoStop

    2025

  41. [41]

    author author A. C. \ Santos , author B. C akmak , author S. Campbell ,\ and\ author N. T. \ Zinner ,\ https://doi.org/10.1103/PhysRevE.100.032107 journal journal Phys. Rev. E \ volume 100 ,\ pages 032107 ( year 2019 ) NoStop

    doi:10.1103/physreve.100.032107 2019

  42. [42]

    author author S. V. \ Romero , author X. Chen , author G. Platero ,\ and\ author Y. Ban ,\ https://doi.org/10.1103/PhysRevApplied.21.034033 journal journal Phys. Rev. Appl. \ volume 21 ,\ pages 034033 ( year 2024 ) NoStop

    work page doi:10.1103/physrevapplied.21.034033 2024

  43. [43]

    Lorenzo et al

    author author S. Lorenzo et al. ,\ https://doi.org/10.1103/PhysRevB.98.054302 journal journal Phys. Rev. B \ volume 98 ,\ pages 054302 ( year 2018 ) NoStop

    work page doi:10.1103/physrevb.98.054302 2018

  44. [44]

    Gyawali et al

    author author G. Gyawali et al. ,\ https://arxiv.org/abs/2410.06557 title Observation of disorder-free localization using a (2+1)D lattice gauge theory on a quantum processor ( year 2025 ),\ https://arxiv.org/abs/2410.06557 arXiv:2410.06557 [quant-ph] NoStop

    Pith/arXiv arXiv 2025

  45. [45]

    Koch et al

    author author J. Koch et al. ,\ https://doi.org/10.1103/PhysRevA.76.042319 journal journal Phys. Rev. A \ volume 76 ,\ pages 042319 ( year 2007 ) NoStop

    doi:10.1103/physreva.76.042319 2007

  46. [46]

    Paik et al

    author author H. Paik et al. ,\ https://doi.org/10.1103/PhysRevLett.107.240501 journal journal Phys. Rev. Lett. \ volume 107 ,\ pages 240501 ( year 2011 ) NoStop

    doi:10.1103/physrevlett.107.240501 2011

  47. [47]

    author author J. S. \ Douglas et al. ,\ https://doi.org/10.1038/nphoton.2015.57 journal journal Nat. Photonics \ volume 9 ,\ pages 326–331 ( year 2015 ) NoStop

    doi:10.1038/nphoton.2015.57 2015

  48. [48]

    \ Hung , author A

    author author C.-L. \ Hung , author A. González-Tudela , author J. I. \ Cirac ,\ and\ author H. J. \ Kimble ,\ https://doi.org/10.1073/pnas.1603777113 journal journal Proc. Natl. Acad. Sci. U.S.A. \ volume 113 ,\ pages E4946 ( year 2016 ) NoStop

    doi:10.1073/pnas.1603777113 2016

  49. [49]

    Pita-Vidal et al

    author author M. Pita-Vidal et al. ,\ https://doi.org/10.1038/s41567-024-02497-x journal journal Nat. Phys. \ volume 20 ,\ pages 1158–1163 ( year 2024 ) NoStop

    doi:10.1038/s41567-024-02497-x 2024

  50. [50]

    Pita-Vidal , author J

    author author M. Pita-Vidal , author J. J. \ Wesdorp ,\ and\ author C. K. \ Andersen ,\ https://doi.org/10.1103/PRXQuantum.6.010308 journal journal PRX Quantum \ volume 6 ,\ pages 010308 ( year 2025 ) NoStop

    work page doi:10.1103/prxquantum.6.010308 2025

  51. [51]

    Fishman , author S

    author author M. Fishman , author S. R. \ White ,\ and\ author E. M. \ Stoudenmire ,\ https://doi.org/10.21468/SciPostPhysCodeb.4 journal journal SciPost Phys. Codebases \ ,\ pages 4 ( year 2022 ) NoStop

    doi:10.21468/scipostphyscodeb.4 2022

  52. [52]

    Jordan \ and\ author E

    author author P. Jordan \ and\ author E. Wigner ,\ https://doi.org/10.1007/BF01331938 journal journal Z. Phys. \ volume 47 ,\ pages 631–651 ( year 1928 ) NoStop

    doi:10.1007/bf01331938 1928

  53. [53]

    Dziarmaga ,\ https://doi.org/10.1103/PhysRevLett.95.245701 journal journal Phys

    author author J. Dziarmaga ,\ https://doi.org/10.1103/PhysRevLett.95.245701 journal journal Phys. Rev. Lett. \ volume 95 ,\ pages 245701 ( year 2005 ) NoStop

    doi:10.1103/physrevlett.95.245701 2005

  54. [54]

    Damski \ and\ author M

    author author B. Damski \ and\ author M. M. \ Rams ,\ https://doi.org/10.1088/1751-8113/47/2/025303 journal journal J. Phys. A: Math. Theor. \ volume 47 ,\ pages 025303 ( year 2013 ) NoStop

    work page doi:10.1088/1751-8113/47/2/025303 2013

  55. [55]

    author author D. J. \ Griffiths \ and\ author C. A. \ Steinke ,\ https://doi.org/10.1119/1.1308266 journal journal Am. J. Phys. \ volume 69 ,\ pages 137 ( year 2001 ) NoStop

    doi:10.1119/1.1308266 2001

  56. [56]

    Das \ and\ author A

    author author P. Das \ and\ author A. Dutta ,\ https://doi.org/10.1103/PhysRevB.111.045159 journal journal Phys. Rev. B \ volume 111 ,\ pages 045159 ( year 2025 ) NoStop

    work page doi:10.1103/physrevb.111.045159 2025

  57. [57]

    author author IBM Quantum ,\ @noop title New fractional gates reduce circuit depth for utility-scale workloads ,\ howpublished https://www.ibm.com/quantum/blog/fractional-gates ( year 2024 ) NoStop

    2024

  58. [58]

    Bravyi ,\ https://dl.acm.org/doi/abs/10.5555/2011637.2011640 journal journal Quantum Info

    author author S. Bravyi ,\ https://dl.acm.org/doi/abs/10.5555/2011637.2011640 journal journal Quantum Info. Comput. \ volume 5 ,\ pages 216–238 ( year 2005 ) NoStop

    arXiv 2005

  59. [59]

    author author C. F. \ Gauss ,\ title Congruences of the first degree ,\ in\ https://doi.org/10.1007/978-1-4939-7560-0_2 booktitle Disquisitiones Arithmeticae \ ( publisher Springer New York ,\ address New York, NY ,\ year 1986 )\ pp.\ pages 5--28 NoStop

    work page doi:10.1007/978-1-4939-7560-0_2 1986

  60. [60]

    author author R. P. \ Feynman ,\ https://doi.org/10.1007/BF02650179 journal journal Int. J. Theor. Phys. \ volume 21 ,\ pages 467–488 ( year 1982 ) NoStop

    doi:10.1007/bf02650179 1982

  61. [61]

    Watrous ,\ in\ https://doi.org/10.1109/SFCS.1995.492583 booktitle Proceedings of IEEE 36th Annual Foundations of Computer Science \ ( year 1995 )\ pp.\ pages 528--537 NoStop

    author author J. Watrous ,\ in\ https://doi.org/10.1109/SFCS.1995.492583 booktitle Proceedings of IEEE 36th Annual Foundations of Computer Science \ ( year 1995 )\ pp.\ pages 528--537 NoStop

    arXiv 1995

  62. [62]

    Schumacher \ and\ author R

    author author B. Schumacher \ and\ author R. F. \ Werner ,\ https://arxiv.org/abs/quant-ph/0405174 title Reversible quantum cellular automata ( year 2004 ),\ https://arxiv.org/abs/quant-ph/0405174 arXiv:quant-ph/0405174 [quant-ph] NoStop

    Pith/arXiv arXiv 2004

  63. [63]

    Gross , author V

    author author D. Gross , author V. Nesme , author H. Vogts ,\ and\ author R. F. \ Werner ,\ https://doi.org/10.1007/s00220-012-1423-1 journal journal Commun. Math. Phys. \ volume 310 ,\ pages 419–454 ( year 2012 ) NoStop

    doi:10.1007/s00220-012-1423-1 2012

  64. [64]

    Farrelly ,\ https://doi.org/10.22331/q-2020-11-30-368 journal journal Quantum \ volume 4 ,\ pages 368 ( year 2020 ) NoStop

    author author T. Farrelly ,\ https://doi.org/10.22331/q-2020-11-30-368 journal journal Quantum \ volume 4 ,\ pages 368 ( year 2020 ) NoStop

    work page doi:10.22331/q-2020-11-30-368 2020

  65. [65]

    author author A. Y. \ Kitaev ,\ https://doi.org/10.1070/1063-7869/44/10S/S29 journal journal Phys.-Usp. \ volume 44 ,\ pages 131 ( year 2001 ) NoStop

    doi:10.1070/1063-7869/44/10s/s29 2001

  66. [66]

    Lieb , author T

    author author E. Lieb , author T. Schultz ,\ and\ author D. Mattis ,\ https://doi.org/https://doi.org/10.1016/0003-4916(61)90115-4 journal journal Ann. Phys. \ volume 16 ,\ pages 407 ( year 1961 ) NoStop

    doi:10.1016/0003-4916(61)90115-4 1961

  67. [67]

    Katsura ,\ https://doi.org/10.1103/PhysRev.127.1508 journal journal Phys

    author author S. Katsura ,\ https://doi.org/10.1103/PhysRev.127.1508 journal journal Phys. Rev. \ volume 127 ,\ pages 1508 ( year 1962 ) NoStop

    doi:10.1103/physrev.127.1508 1962

  68. [68]

    author author C. W. \ Clenshaw \ and\ author A. R. \ Curtis ,\ https://doi.org/10.1007/BF01386223 journal journal Numer. Math. \ volume 2 ,\ pages 197–205 ( year 1960 ) NoStop

    doi:10.1007/bf01386223 1960

  69. [69]

    Akila , author D

    author author M. Akila , author D. Waltner , author B. Gutkin ,\ and\ author T. Guhr ,\ https://doi.org/10.1088/1751-8113/49/37/375101 journal journal J. Phys. A: Math. Theor. \ volume 49 ,\ pages 375101 ( year 2016 ) NoStop

    doi:10.1088/1751-8113/49/37/375101 2016

  70. [70]

    author author R. B. \ Blackman \ and\ author J. W. \ Tukey ,\ https://doi.org/10.1002/j.1538-7305.1958.tb01530.x journal journal Bell Labs Tech. J. \ volume 37 ,\ pages 485 ( year 1958 ) NoStop

    arXiv 1958

  71. [71]

    author author R. P. \ Kanwal ,\ title Additional properties of distributions ,\ in\ https://doi.org/10.1007/978-1-4684-0035-9_3 booktitle Generalized Functions Theory and Technique \ ( publisher Birkh \"a user Boston ,\ address Boston, MA ,\ year 1998 )\ pp.\ pages 49--70 NoStop

    work page doi:10.1007/978-1-4684-0035-9_3 1998

  72. [72]

    Schollw\"ock ,\ https://doi.org/https://doi.org/10.1016/j.aop.2010.09.012 journal journal Ann

    author author U. Schollw\"ock ,\ https://doi.org/https://doi.org/10.1016/j.aop.2010.09.012 journal journal Ann. Phys. \ volume 326 ,\ pages 96 ( year 2011 ) NoStop

    doi:10.1016/j.aop.2010.09.012 2010

  73. [73]

    Calabrese \ and\ author J

    author author P. Calabrese \ and\ author J. Cardy ,\ https://doi.org/10.1088/1742-5468/2005/04/P04010 journal journal J. Stat. Mech. Theory Exp. \ volume 2005 ,\ pages P04010 ( year 2005 ) NoStop

    doi:10.1088/1742-5468/2005/04/p04010 2005

  74. [74]

    Liu \ and\ author S

    author author H. Liu \ and\ author S. J. \ Suh ,\ https://doi.org/10.1103/PhysRevLett.112.011601 journal journal Phys. Rev. Lett. \ volume 112 ,\ pages 011601 ( year 2014 ) NoStop

    doi:10.1103/physrevlett.112.011601 2014

  75. [75]

    Kim \ and\ author D

    author author H. Kim \ and\ author D. A. \ Huse ,\ https://doi.org/10.1103/PhysRevLett.111.127205 journal journal Phys. Rev. Lett. \ volume 111 ,\ pages 127205 ( year 2013 ) NoStop

    doi:10.1103/physrevlett.111.127205 2013

  76. [76]

    Nahum , author J

    author author A. Nahum , author J. Ruhman , author S. Vijay ,\ and\ author J. Haah ,\ https://doi.org/10.1103/PhysRevX.7.031016 journal journal Phys. Rev. X \ volume 7 ,\ pages 031016 ( year 2017 ) NoStop

    doi:10.1103/physrevx.7.031016 2017

  77. [77]

    author author C. W. \ von Keyserlingk , author T. Rakovszky , author F. Pollmann ,\ and\ author S. L. \ Sondhi ,\ https://doi.org/10.1103/PhysRevX.8.021013 journal journal Phys. Rev. X \ volume 8 ,\ pages 021013 ( year 2018 ) NoStop

    doi:10.1103/physrevx.8.021013 2018

  78. [78]

    author author S. K. \ Mishra , author A. Lakshminarayan ,\ and\ author V. Subrahmanyam ,\ https://doi.org/10.1103/PhysRevA.91.022318 journal journal Phys. Rev. A \ volume 91 ,\ pages 022318 ( year 2015 ) NoStop

    work page doi:10.1103/physreva.91.022318 2015

  79. [79]

    Chan , author A

    author author A. Chan , author A. De Luca ,\ and\ author J. T. \ Chalker ,\ https://doi.org/10.1103/PhysRevX.8.041019 journal journal Phys. Rev. X \ volume 8 ,\ pages 041019 ( year 2018 ) NoStop

    doi:10.1103/physrevx.8.041019 2018

  80. [80]

    author author A. R. \ Brown et al. ,\ https://doi.org/10.1103/PRXQuantum.4.010320 journal journal PRX Quantum \ volume 4 ,\ pages 010320 ( year 2023 ) NoStop

    work page doi:10.1103/prxquantum.4.010320 2023

Showing first 80 references.