Pith. sign in

REVIEW 3 major objections 4 minor 58 references

Pulse-based optimization of quantum many-body states with Rydberg atoms in optical tweezer arrays

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read Randomly segmented laser pulses can prepare ground states of Rydberg spin models with up to ten qubits.

desk verdict A genuine numerical study of adaptive linear-ramp PVQE with a useful hybrid measurement scheme, but the Heisenberg N=6,10 claims lean on an undemonstrated q=pi initial state; referee should require the claim to be narrowed. read the letter →

arxiv 2507.19153 v1 pith:PL4BC4XD submitted 2025-07-25 quant-ph cond-mat.quant-gascond-mat.stat-mech

Kazuma Nagao , Sergi Julià-Farré , Joseph Vovrosh , Alexandre Dauphin , Seiji Yunoki This is my paper · ORCID
classification quant-phcond-mat.quant-gascond-mat.stat-mech
keywords pulse-basedvariationalquantumeigensolverRydbergatomsopticaltweezerarraysHeisenbergmodelmixed-fieldIsinganalogsimulationadaptivepulsesegmentationmany-bodystatepreparation
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 argues that a variational quantum eigensolver can run entirely at the pulse level on Rydberg atoms in optical tweezer arrays, without decomposing the computation into digital gates. The algorithm represents the candidate state as the output of a time-dependent laser pulse and improves that state by randomly splitting the pulse into more segments and re-optimizing the Rabi frequency and detuning at each new boundary. Numerical simulations show this prepares accurate ground states for the one-dimensional antiferromagnetic Heisenberg model and the mixed-field Ising model with up to ten qubits, and that the optimized states reproduce the models' spin correlations. A hybrid measurement scheme, in which digital gates are approximated by optimized analog pulses, keeps the entire protocol within the hardware coherence time. If correct, this offers a practical route to small many-body ground-state preparation and energy measurement on current neutral-atom devices.

What carries the argument

The key machinery is the adaptive random time-splitting of a single global pulse. The variational state is $|\Psi[\Omega,\Delta,R]\rangle = \mathcal{T}\exp\left(-\frac{i}{\hbar}\int_0^T dt\,\hat H(t)\right)|\psi_0\rangle$, where $\hat H(t)$ is the Rydberg Hamiltonian with time-dependent Rabi frequency $\Omega(t)$, detuning $\Delta(t)$, and a circular geometry of radius $R$. Starting from a one-segment linear ramp, each iteration randomly splits one time interval, interpolates the pulse values at the new boundary, and re-optimizes all boundary values to minimize the expectation value of the target Hamiltonian. This turns a small initial parameter set into a progressively richer variational ansatz while avoiding piecewise-constant discontinuities; a minimum segment duration and a hardware clock period keep the schedules physically realizable. A second component is the hybrid measurement scheme, in which the global $\pi/2$ rotations needed to measure $\hat X$ and $\hat Y$ correlations are themselves synthesized from optimized analog pulses.

What would settle it

Measure the fidelity of the $q=\pi$ state produced by the GHZ-type circuit or by a pulse realizing $U_{\mathrm{flip}}(\pi/2)$ on a Rydberg array; if the achieved overlap is too low to keep the reported energy errors, or if the preparation takes longer than the coherence time, the odd-$N/2$ Heisenberg results do not transfer to hardware.

Watch

Extended reading notes

Core claim

The central discovery is that the ground states of two prototypical spin models can be prepared by globally optimizing a continuous, piecewise-linear pulse of laser detuning and Rabi frequency, with the atom array radius as the only geometrical parameter. For Heisenberg rings with an even number of spin pairs, starting from the all-down product state, the random time-splitting procedure converges to the target ground state: the best $N=4$ run reaches a relative energy error below $1\%$ with three segments, while $N=8$ needs about fifty segments and reaches roughly $0.1\%$. For $N=6$ and $N=10$, where the ground state lives in the momentum $q=\pi$ sector, the all-down state is trapped in the $q=0$ sector; the authors show that initializing in a $q=\pi$ superposition repairs convergence, with $N=6$ errors around $0.005\%$ and $N=10$ errors around $1.7\%$. The same algorithm prepares the mixed-field Ising ground state for $N=10$ with average errors below $0.02\%$ across the tested transverse-field range. The optimized states match exact diagonalization for both energy and spin correlation functions, including the SU(2)-symmetric correlations of the Heisenberg model, even though the pulse ansatz does not enforce that symmetry.

Load-bearing premise

The load-bearing premise is that the $q=\pi$ starting state required for odd-size Heisenberg rings can be prepared with high fidelity inside the roughly six-microsecond coherence time of current Rydberg arrays.

Editorial extensions

If this is right

  • If the numerical results carry over to hardware, Rydberg tweezer arrays can prepare and measure the ground-state energy of the one-dimensional Heisenberg and mixed-field Ising models at up to ten qubits using only global pulses and one geometric parameter.
  • The optimized variational states reproduce spin correlations, so the protocol can be used to extract correlation functions of the target model, not just energies.
  • Because the optimized pulses resemble quasi-adiabatic schedules for Ising-type ground states, the method offers a way to initialize analog Rydberg simulators for subsequent quench dynamics.
  • The hybrid rotation scheme keeps the total experimental duration around $3.3\,\mu\mathrm{s}$, below the roughly $6\,\mu\mathrm{s}$ coherence time quoted for current arrays, making the measurement step feasible now.
  • For odd-$N/2$ Heisenberg rings, the results depend on an initial $q=\pi$ state, so the proposed GHZ-type or string-unitary preparation is an integral part of the claim rather than a peripheral detail.

Reading between the lines

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

  • Editorial inference: because the ansatz is a generic time-ordered unitary, the same random-segmentation optimizer could be pointed at excited-state or time-evolution cost functions, not just ground states.
  • Editorial inference: the $q=\pi$ preparation bottleneck suggests a direct experimental benchmark: synthesize the string unitary $U_{\mathrm{flip}}(\pi/2)$ as an analog pulse; success would remove the main obstacle for odd-$N/2$ rings.
  • Editorial inference: the observed restoration of SU(2) symmetry in the Heisenberg correlations may be a finite-size effect of the optimizer; enforcing the symmetry explicitly in the ansatz or measuring the symmetry violation as $N$ grows would test how the method scales.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a pulse-based variational quantum eigensolver (PVQE) for Rydberg-atom arrays, in which the global Rabi frequency and detuning are linearly ramped pulses that are adaptively refined by random time segmentation, and the array radius is treated as an additional variational parameter. The authors test this ansatz on the one-dimensional antiferromagnetic Heisenberg model (N=4, 6, 8, 10) and the mixed-field Ising model (N=10), reporting relative energy errors and spin correlation functions against exact diagonalization. They also introduce a hybrid measurement scheme in which global rotations synthesized by variational quantum gates are used to measure the XX, YY, and ZZ components of the Heisenberg Hamiltonian. The central claim is that ground states of these models can be accurately prepared for systems of up to ten qubits.

Significance. If fully supported, the work would provide a hardware-realistic, pulse-level variational method for preparing small many-body ground states on Rydberg platforms. A notable strength is that all numerical results are benchmarked against independent exact diagonalization, and the optimized states are shown to reproduce spin correlations, not only energies. The linearly varying, clock-constrained pulse model is also more experimentally credible than piecewise-constant ansätze, and the proposed variational-rotation measurement scheme addresses a practical bottleneck for evaluating generic Hamiltonians. However, the support for the headline claim is incomplete: the Heisenberg results for N=6 and N=10 rely on a q=pi initial state whose preparation within the quoted coherence time is not demonstrated, and for the larger systems the reported high accuracies are often achieved only by the best of many optimization runs rather than by typical runs.

major comments (3)
  1. [Sec. IV, Eq. (15), and Appendix B] The Heisenberg results for N=6 and N=10 depend on the unverified assumption that the q=pi state of Eq. (15) can be prepared on hardware. Because the PVQE Hamiltonian in Eq. (1) commutes with the translation operator, the momentum quantum number is conserved, and the all-down product state (q=0) cannot reach the ground-state sector with q=pi; the paper therefore initializes with |Psi_{q=pi}>. Appendix B proposes a GHZ circuit (Eq. B4) whose CNOT gates each require approximately 6.2 microseconds at Jnn/h~2.3 MHz [35], so the sequential N=6 implementation is roughly 31 microseconds, far exceeding the ~6 microsecond coherence time cited in Sec. VI; the logarithmic-depth variant is not quantified. The alternative U_flip(pi/2) in Eq. (B5) is a non-native N-body Pauli string for which no pulse sequence is given. The authors themselves concede that the GHZ implementation may be limited by the short coherence time (Appendix B). Without a demonstrated or quantified preparation protocol within coherence time, the abstract's "up to ten qubits" claim for the Heisenberg model is not supported.
  2. [Sec. IV, Fig. 3(a) and Fig. 4(b)] The reported high accuracy for larger systems is based on the best-performing runs rather than on typical behavior. For N=8, the text states that over 90 of the 100 PVQE runs converge to states with rather higher errors, and the ensemble-averaged final relative error is 2.14 +/- 0.12%, while only the best run reaches about 0.1%. For N=10 with the q=pi initial state, the best result among 92 runs is on the order of 0.1%, with an ensemble average of 1.65 +/- 0.17%. The manuscript does not report success probabilities, medians, or the full error distribution. If PVQE is claimed to accurately prepare ground states, the typical success rate must be quantified; as written, the central claim overstates the reliability of the method.
  3. [Sec. VI, Fig. 9] The fixed-radius hybrid scheme intended for measurement of the Heisenberg Hamiltonian also shows poor typical convergence: the Fig. 9 caption states that only 10 representative runs out of 100 achieved good convergence. No success probability or ensemble statistics are reported for this configuration. Since the hybrid protocol is presented as experimentally feasible, the same typical-performance concern applies here as in Fig. 3, and the manuscript should report how often the full T*=3.3 microsecond protocol actually prepares the ground state to the claimed accuracy.
minor comments (4)
  1. [Sec. VII] There is a typographical error in the Conclusions: "antiferromangnetic" should be "antiferromagnetic."
  2. [Sec. IV, Fig. 2(a)] The text says the optimization achieves high accuracy with "as few as nine time segments" and then states that the highlighted run uses "only three pulse segments"; this is confusing and should be reworded to distinguish the best run from the threshold-crossing run.
  3. [References [27] and [34]] References [27] and [34] refer to the same paper (Sherbert et al., Phys. Rev. Appl. 23, 024036); if both citations are kept, this duplication should be noted or the numbering adjusted.
  4. [Appendix B, Fig. 11] The logarithmic-depth GHZ circuit is referenced but not described; a few sentences or an explicit gate-count estimate for N=6 and N=10 would allow the reader to check whether that optimized version fits within the quoted coherence time.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction in the PVQE derivation: ground-state energies are validated against exact diagonalization. Minor self-citations appear in feasibility estimates and symmetry arguments, but they do not force the central numerical result.

full rationale

The paper's central claim is numerical state preparation via pulse optimization. The variational state (Eq. 3) is evolved under the Rydberg Ising Hamiltonian (Eq. 1), and the cost function is the expectation value of the target model Hamiltonian (Eq. 6). This is a genuine variational optimization, not an identity: the optimized state is compared with independent exact diagonalization (Figs. 5 and 7), and the paper explicitly reports failure cases (product-state initialization for odd N/2 in Fig. 4). For the mixed-field Ising model, the success is attributed by the authors themselves to the structural resemblance between the target Hamiltonian and the Rydberg pulse Hamiltonian (Sec. V); this is a physical explanation, not a circular derivation. The q=pi initial state (Eq. 15) is symmetry-informed rather than equal to the target ground state, and the pulse sequence still must reach the ground state within that sector. The only self-citations are (i) Ref. [35] for variational gate durations used in the measurement protocol and in the q=pi preparation estimate, and (ii) Ref. [40] for the momentum-sector assignment of Heisenberg ground states. These are not load-bearing for the numerical state-preparation claim: the energy optimization is validated against exact diagonalization, and the paper itself cautions that the GHZ-based q=pi preparation 'may be limited by the short coherence time' (Appendix B). Thus there is no exhibited Eq.-X-equals-Eq.-Y reduction or fitted-parameter-renamed-as-prediction. The score reflects the presence of minor self-citations in feasibility and symmetry arguments, not any circular reduction of the main result.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The main unproven inputs are the hardware model, the preparability of the q=pi state, and the imported gate fidelities from Ref. [35].

free parameters (2)
  • Per-segment pulse endpoints (Omega_i, Delta_i) = Optimized per run; example values not listed in text
    Variational parameters minimized against Eq. (6). The central claim depends on optimizing these, not on externally known constants.
  • Array radius R = Examples: 5.95 um (N=4), 11.27 um (N=8), 15.81 um (N=10)
    Single geometry parameter tuned to change Jij; treated as part of the variational ansatz.
assumptions (5)
  • domain assumption Time evolution under the global Rydberg Hamiltonian Eq. (1) with linearly interpolated pulses generates the variational manifold.
    The whole PVQE ansatz in Eq. (3) rests on this model of the analog device.
  • domain assumption Pulser's virtual simulator faithfully represents a real neutral-atom device.
    All numerical results are obtained through Pulser [36]; no hardware data are reported.
  • ad hoc to paper The q=pi state in Eq. (15) can be prepared on hardware via the Appendix B protocols.
    Appendix B proposes a GHZ circuit or a string unitary Uflip, but does not demonstrate a practical pulse sequence; the CNOT duration near coherence is a stated limitation.
  • domain assumption Global rotations for measurement can be implemented with the variational gates of Ref. [35] at about 0.9 microseconds and with sufficient fidelity.
    Sec. VI imports this result from [35], authored in part by the same group, without reproducing the fidelity for the combined protocol.
  • standard math Marshall sign rule and momentum sectors are correctly applied to choose initial states.
    Used to explain why a q=pi initial state is required for odd N/2 Heisenberg rings; standard result, but it imposes an additional preparation cost.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Pulse-based optimization of quantum many-body states with Rydberg atoms in optical tweezer arrays." pith.science (2026). https://pith.science/paper/PL4BC4XD

@misc{pith2026250719153,
  author       = {Pith},
  title        = {Pith review of: Pulse-based optimization of quantum many-body states with Rydberg atoms in optical tweezer arrays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PL4BC4XD}},
  note         = {Machine review of arXiv:2507.19153}
}
read the original abstract

We explore a pulse-based variational quantum eigensolver (VQE) algorithm for Rydberg atoms in optical tweezer arrays and evaluate its performance on prototypical quantum spin models. We numerically demonstrate that the ground states of the one-dimensional antiferromagnetic Heisenberg model and the mixed-field Ising model can be accurately prepared using an adaptive update algorithm that randomly segments pulse sequences, for systems of up to ten qubits. Furthermore, we propose and validate a hybrid scheme that integrates this pulse-level analog quantum algorithm with a variational quantum gate approach, where digital quantum gates are approximated by optimized analog pulses. This enables efficient measurement of the cost function for target many-body Hamiltonians.

Figures

Figures reproduced from arXiv: 2507.19153 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic illustration of the pulse-based vari [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Pulse-based VQE for the one-dimensional antiferromagnetic Heisenberg model with [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Pulse-based VQE for the one-dimensional antiferromagnetic Heisenberg model with [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Pulse-based VQE for the one-dimensional antifer [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Spin correlation functions of the optimized PVQE state for the one-dimensional antiferromagnetic Heisenberg model. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Pulse-based VQE results for the one-dimensional MFI model with [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Pulse-based VQE combined with the variational [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Fixed-radius pulse-based VQE for the one [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Total number of Nelder-Mead iterations accumulated up to each time segment to obtain the best-performing PVQE [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. (Top) Quantum circuit representation of the GHZ [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 35 canonical work pages

  1. [35]

    Chevallier, J

    C. Chevallier, J. Vovrosh, J. de Hond, M. Dagrada, A. Dauphin, and V. E. Elfving, Variational protocols for emulating digital gates using analog control with always- on interactions, Physical Review A 109, 062604 (2024)

    work page 2024

  2. [1]

    M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge university press, 2010)

    2010

  3. [2]

    Browaeys and T

    A. Browaeys and T. Lahaye, Many-body physics with in- dividually controlled rydberg atoms, Nature Physics 16, 132 (2020)

    2020

  4. [3]

    Foss-Feig, G

    M. Foss-Feig, G. Pagano, A. C. Potter, and N. Y. Yao, Progress in trapped-ion quantum simulation, Annual Re- view of Condensed Matter Physics 16 (2024)

    work page 2024

  5. [4]

    X. Mi, M. Ippoliti, C. Quintana, A. Greene, Z. Chen, J. Gross, F. Arute, K. Arya, J. Atalaya, R. Babbush, et al. , Time-crystalline eigenstate order on a quantum processor, Nature 601, 531 (2022)

    2022

  6. [5]

    Shinjo, K

    K. Shinjo, K. Seki, T. Shirakawa, R.-Y. Sun, and S. Yunoki, Unveiling clean two-dimensional discrete time quasicrystals on a digital quantum computer, arXiv preprint arXiv:2403.16718 (2024)

    arXiv 2024

  7. [6]

    Shtanko, D

    O. Shtanko, D. S. Wang, H. Zhang, N. Harle, A. Seif, R. Movassagh, and Z. Minev, Uncovering local integra- bility in quantum many-body dynamics, Nature Commu- nications 16, 2552 (2025)

    work page 2025

  8. [7]

    Robledo-Moreno, M

    J. Robledo-Moreno, M. Motta, H. Haas, A. Javadi- Abhari, P. Jurcevic, W. Kirby, S. Martiel, K. Sharma, S. Sharma, T. Shirakawa, et al. , Chemistry beyond the scale of exact diagonalization on a quantum-centric su- percomputer, Science Advances 11, eadu9991 (2025)

    work page 2025

Show all 58 references
  1. [8]

    K. Seki, Y. Kikuchi, T. Hayata, and S. Yunoki, Simulat- ing floquet scrambling circuits on trapped-ion quantum computers, Phys. Rev. Res. 7, 023032 (2025)

    2025

  2. [9]

    Levine, A

    H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, High-fidelity control and entanglement of rydberg-atom qubits, Phys. Rev. Lett. 121, 123603 (2018)

    2018

  3. [10]

    Scholl, M

    P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, et al. , Quantum simulation of 2d antiferromagnets with hundreds of rydberg atoms, Na- ture 595, 233 (2021)

    2021

  4. [11]

    Henriet, L

    L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.-O. Reymond, and C. Jurczak, Quantum computing with neutral atoms, Quantum 4, 327 (2020)

    2020

  5. [12]

    Lanes, M

    O. Lanes, M. Beji, A. D. Corcoles, C. Dalyac, J. M. Gam- betta, L. Henriet, A. Javadi-Abhari, A. Kandala, A. Mez- zacapo, C. Porter, et al. , A framework for quantum ad- vantage, arXiv preprint arXiv:2506.20658 (2025)

    2025 arXiv

  6. [13]

    Labuhn, D

    H. Labuhn, D. Barredo, S. Ravets, S. De L´ es´ eleuc, T. Macr` ı, T. Lahaye, and A. Browaeys, Tunable two- dimensional arrays of single rydberg atoms for realizing quantum ising models, Nature 534, 667 (2016)

    2016

  7. [14]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, et al. , Probing many-body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017)

    2017

  8. [15]

    Semeghini, H

    G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kali- nowski, R. Samajdar, et al. , Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021)

    2021

  9. [16]

    Scholl, H

    P. Scholl, H. J. Williams, G. Bornet, F. Wallner, D. Barredo, L. Henriet, A. Signoles, C. Hainaut, T. Franz, S. Geier, A. Tebben, A. Salzinger, G. Z¨ urn, T. Lahaye, M. Weidem¨ uller, and A. Browaeys, Microwave engineering of programmable xxz hamiltonians in arrays of rydberg ...

    2022

  10. [17]

    C. Chen, G. Bornet, M. Bintz, G. Emperauger, L. Leclerc, V. S. Liu, P. Scholl, D. Barredo, J. Hauschild, S. Chatterjee, et al., Continuous symmetry breaking in a two-dimensional rydberg array, Nature 616, 691 (2023)

    2023

  11. [18]

    Barredo, V

    D. Barredo, V. Lienhard, S. De Leseleuc, T. Lahaye, and A. Browaeys, Synthetic three-dimensional atomic struc- tures assembled atom by atom, Nature 561, 79 (2018)

    2018

  12. [19]

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´ c, Weak ergodicity breaking from quantum many-body scars, Nature Physics 14, 745 (2018)

    2018

  13. [20]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and hilbert space fragmentation: A review of exact results, Reports on Progress in Physics 85, 086501 (2022)

    2022

  14. [21]

    Chandran, T

    A. Chandran, T. Iadecola, V. Khemani, and R. Moess- 14 ner, Quantum many-body scars: A quasiparticle perspec- tive, Annual Review of Condensed Matter Physics 14, 443 (2023)

    2023

  15. [22]

    Y. Chew, T. Tomita, T. P. Mahesh, S. Sugawa, S. de L´ es´ eleuc, and K. Ohmori, Ultrafast energy ex- change between two single rydberg atoms on a nanosec- ond timescale, Nature Photonics 16, 724 (2022)

    2022

  16. [23]

    Bluvstein, S

    D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, et al., Logical quantum processor based on reconfigurable atom arrays, Nature 626, 58 (2024)

    2024

  17. [24]

    Parra-Rodriguez, P

    A. Parra-Rodriguez, P. Lougovski, L. Lamata, E. Solano, and M. Sanz, Digital-analog quantum computation, Physical Review A 101, 022305 (2020)

    2020

  18. [25]

    O. R. Meitei, B. T. Gard, G. S. Barron, D. P. Pappas, S. E. Economou, E. Barnes, and N. J. Mayhall, Gate-free state preparation for fast variational quantum eigensolver simulations, npj Quantum Information 7, 155 (2021)

    2021

  19. [26]

    Michel, S

    A. Michel, S. Grijalva, L. Henriet, C. Domain, and A. Browaeys, Blueprint for a digital-analog variational quantum eigensolver using rydberg atom arrays, Phys. Rev. A 107, 042602 (2023)

    2023

  20. [28]

    T. I. Andersen, N. Astrakhantsev, A. H. Karamlou, J. Berndtsson, J. Motruk, A. Szasz, J. A. Gross, A. Schuckert, T. Westerhout, Y. Zhang, et al. , Thermal- ization and criticality on an analogue–digital quantum simulator, Nature 638, 79 (2025)

    2025

  21. [29]

    Asthana, C

    A. Asthana, C. Liu, O. R. Meitei, S. E. Economou, E. Barnes, and N. J. Mayhall, Leakage reduces device coherence demands for pulse-level molecular simulations, Phys. Rev. Appl. 19, 064071 (2023)

    2023

  22. [30]

    Shingu, Y

    Y. Shingu, Y. Zhang, Y. Matsuzaki, T. Nikuni, X. Yuan, and Y. Huang, Digital-analog variational neural- simulation hybrid eigensolver with classical shadow, Japanese Journal of Applied Physics (2025)

    2025

  23. [31]

    Elben, S

    A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, The random- ized measurement toolbox, Nature Reviews Physics 5, 9 (2023)

    2023

  24. [32]

    Notarnicola, A

    S. Notarnicola, A. Elben, T. Lahaye, A. Browaeys, S. Montangero, and B. Vermersch, A randomized mea- surement toolbox for an interacting rydberg-atom quan- tum simulator, New Journal of Physics 25, 103006 (2023)

    2023

  25. [33]

    Huang, R

    H.-Y. Huang, R. Kueng, and J. Preskill, Efficient estima- tion of pauli observables by derandomization, Phys. Rev. Lett. 127, 030503 (2021)

    2021

  26. [34]

    K. M. Sherbert, H. Amer, S. E. Economou, E. Barnes, and N. J. Mayhall, Parametrization and optimizability of pulse-level variational quantum eigensolvers, Phys. Rev. Appl. 23, 024036 (2025)

    2025

  27. [36]

    Silv´ erio, S

    H. Silv´ erio, S. Grijalva, C. Dalyac, L. Leclerc, P. J. Kar- alekas, N. Shammah, M. Beji, L.-P. Henry, and L. Hen- riet, Pulser: An open-source package for the design of pulse sequences in programmable neutral-atom arrays, Quantum 6, 629 (2022)

    2022

  28. [37]

    Abramavicius, M

    V. Abramavicius, M. Math´ e, G. V. Velikova, J. P. Moutinho, M. Dagrada, V. E. Elfving, A. Dauphin, J. Vovrosh, and R. Guichard, Pulserdiff: a pulse differentiable extension for pulser, arXiv preprint arXiv:2505.16744 (2025)

    2025 arXiv

  29. [38]

    Takahashi, Thermodynamics of one-dimensional solv- able models (Cambridge university press Cambridge, 1999)

    M. Takahashi, Thermodynamics of one-dimensional solv- able models (Cambridge university press Cambridge, 1999)

    1999

  30. [39]

    Faddeev, How algebraic bethe ansatz works for inte- grable model, arXiv preprint hep-th/9605187 (1996)

    L. Faddeev, How algebraic bethe ansatz works for inte- grable model, arXiv preprint hep-th/9605187 (1996)

    1996 arXiv

  31. [40]

    K. Seki, T. Shirakawa, and S. Yunoki, Symmetry-adapted variational quantum eigensolver, Phys. Rev. A 101, 052340 (2020)

    2020

  32. [41]

    M. S. Jattana, F. Jin, H. De Raedt, and K. Michielsen, Assessment of the variational quantum eigensolver: ap- plication to the heisenberg model, Frontiers in Physics 10, 907160 (2022)

    2022

  33. [42]

    J. L. Bosse and A. Montanaro, Probing ground-state properties of the kagome antiferromagnetic heisenberg model using the variational quantum eigensolver, Phys. Rev. B 105, 094409 (2022)

    2022

  34. [43]

    Fujii, K

    K. Fujii, K. Mizuta, H. Ueda, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, Deep variational quantum eigen- solver: A divide-and-conquer method for solving a larger problem with smaller size quantum computers, PRX Quantum 3, 010346 (2022)

    2022

  35. [44]

    R.-Y. Sun, T. Shirakawa, and S. Yunoki, Efficient varia- tional quantum circuit structure for correlated topologi- cal phases, Phys. Rev. B 108, 075127 (2023)

    2023

  36. [45]

    Virtanen, R

    P. Virtanen, R. Gommers, T. E. Oliphant, M. Haber- land, T. Reddy, D. Cournapeau, E. Burovski, P. Pe- terson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, ˙I. Po- lat, Y...

    2020

  37. [46]

    J. A. Nelder and R. Mead, A simplex method for function minimization, The computer journal 7, 308 (1965)

    1965

  38. [47]

    Marshall, Antiferromagnetism, Proceedings of the Royal Society of London

    W. Marshall, Antiferromagnetism, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 232, 48 (1955)

    1955

  39. [48]

    Weinberg and M

    P. Weinberg and M. Bukov, Quspin: a python package for dynamics and exact diagonalisation of quantum many body systems part i: spin chains, SciPost Physics 2, 003 (2017)

    2017

  40. [49]

    Kitaev and C

    A. Kitaev and C. Laumann, Topological phases and quantum computation, Exact methods in low- dimensional statistical physics and quantum computing , 101 (2010)

    2010

  41. [50]

    S. B. Rutkevich, Large- n excitations in the ferromag- netic ising field theory in a weak magnetic field: Mass spectrum and decay widths, Phys. Rev. Lett. 95, 250601 (2005)

    2005

  42. [51]

    Coldea, D

    R. Coldea, D. Tennant, E. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, Quantum criticality in an ising chain: ex- perimental evidence for emergent e8 symmetry, Science 327, 177 (2010)

    2010

  43. [52]

    C. Lamb, Y. Tang, R. Davis, and A. Roy, Ising meson spectroscopy on a noisy digital quantum simulator, Na- 15 ture communications 15, 5901 (2024)

    2024

  44. [53]

    Vovrosh, J

    J. Vovrosh, J. de Hond, S. Juli` a-Farr´ e, J. Knolle, and A. Dauphin, Meson spectroscopy of exotic symmetries of ising criticality in rydberg atom arrays, arXiv preprint arXiv:2506.21299 (2025)

    2025 arXiv

  45. [54]

    Wurtz, A

    J. Wurtz, A. Bylinskii, B. Braverman, J. Amato-Grill, S. H. Cantu, F. Huber, A. Lukin, F. Liu, P. Weinberg, J. Long, et al. , Aquila: Quera’s 256-qubit neutral-atom quantum computer, arXiv preprint arXiv:2306.11727 (2023)

    2023 arXiv

  46. [55]

    Xiang, Density Matrix and Tensor Network Renor- malization (Cambridge University Press, 2023)

    T. Xiang, Density Matrix and Tensor Network Renor- malization (Cambridge University Press, 2023)

    2023

  47. [56]

    Singh, A

    J. Singh, A. Kruckenhauser, R. van Bijnen, and R. Zeier, Ground-state reachability for variational quantum eigen- solvers: a rydberg-atom case study, arXiv preprint arXiv:2506.22387 (2025)

    2025 arXiv

  48. [57]

    Facchi, G

    P. Facchi, G. Florio, S. Pascazio, and F. V. Pepe, Greenberger-horne-zeilinger states and few-body hamil- tonians, Phys. Rev. Lett. 107, 260502 (2011)

    2011

  49. [58]

    G. J. Mooney, G. A. White, C. D. Hill, and L. C. Hollenberg, Generation and verification of 27-qubit greenberger-horne-zeilinger states in a superconducting quantum computer, Journal of Physics Communications 5, 095004 (2021)

    2021

  50. [59]

    de Oliveira, L

    M. de Oliveira, L. S. Barbosa, and E. F. Galv˜ ao, Quan- tum advantage in temporally flat measurement-based quantum computation, Quantum 8, 1312 (2024)

    2024

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.