arxiv: 2604.04600 · v1 · submitted 2026-04-06 · 🪐 quant-ph · physics.atom-ph

Recognition: 2 theorem links

· Lean Theorem

Phase-Stable Hologram Updates for Large-Scale Neutral-Atom Array Reconfiguration

Erdong Huang, Hongshun Yao, Jiayi Huang, Jin-Guo Liu, Xin Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:50 UTC · model grok-4.3

classification 🪐 quant-ph physics.atom-ph

keywords holographic optical tweezersneutral atom arraysphase continuityGerchberg-Saxton algorithmdynamic reconfigurationRydberg atomsspatial light modulatortransient stability

0 comments

The pith

The weighted-projective Gerchberg-Saxton algorithm maintains inter-frame phase continuity to eliminate transient trap loss during dynamic updates of large neutral-atom arrays.

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

The paper introduces a modified hologram calculation method that keeps the phase of each optical trap continuous from one frame to the next while still equalizing intensities. This prevents destructive interference when the spatial light modulator refreshes, which otherwise causes atoms to be lost during array moves. The same constraint also cuts the number of iterations needed to compute each new hologram, making updates faster overall. Simulations covering more than a thousand traps in two and three dimensions, including complex multilayer rearrangements, confirm that trap intensities stay stable through the transitions.

Core claim

By adding an explicit phase-continuity constraint to the weighted Gerchberg-Saxton iteration, the algorithm produces successive holograms whose trap phases differ by only small amounts, thereby suppressing the transient intensity dips that occur at spatial-light-modulator refresh. The phase-difference distribution between frames serves as a direct indicator of robustness, and the constraint simultaneously lowers the iteration count per update.

What carries the argument

The weighted-projective Gerchberg-Saxton (WPGS) algorithm, which augments standard intensity-weighted hologram projection with an inter-frame phase-continuity term.

If this is right

Transient intensities remain high enough to retain atoms throughout 2D and 3D reconfigurations involving over 1000 traps.
Each hologram update requires fewer iterations than conventional Gerchberg-Saxton methods.
The phase-difference distribution between consecutive holograms provides a simple metric for predicting transient robustness.
The approach supports both in-plane moves and interlayer transport in multilayer assemblies without additional hardware.

Where Pith is reading between the lines

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

Hardware implementations could allow atom arrays to be reconfigured at rates limited only by the SLM refresh speed rather than by transient losses.
The phase-continuity principle may extend to other applications of dynamic holography, such as particle sorting or adaptive optics.
Real-time feedback using the phase-difference diagnostic could enable closed-loop optimization of array moves.

Load-bearing premise

Enforcing phase continuity between successive holograms does not reduce the quality or stability of the static traps once the array has settled.

What would settle it

Direct measurement of atom retention rates during rapid reconfiguration on a physical SLM setup, comparing WPGS-generated holograms against standard methods for arrays of several hundred traps.

Figures

Figures reproduced from arXiv: 2604.04600 by Erdong Huang, Hongshun Yao, Jiayi Huang, Jin-Guo Liu, Xin Wang.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

read the original abstract

Assembling large-scale, defect-free Rydberg atom arrays is a key technology for neutral-atom quantum computation. Dynamic holographic optical tweezers enable the assembly and reconfiguration of such arrays, but phase mismatches between successive holograms can induce destructive interference and transient trap loss during spatial-light-modulator refresh. In this work, we introduce the weighted-projective Gerchberg--Saxton (WPGS) algorithm, a phase-stable approach to dynamic hologram updates for large-scale Rydberg atom-array reconfiguration. By enforcing inter-frame trap-phase continuity while retaining weighted intensity equalization, WPGS suppresses refresh-induced transient degradation. The phase-difference distribution between consecutive holograms further provides a simple diagnostic of transient robustness. Moreover, enforcing the phase constraint reduces the number of iterations required at each update step, thereby accelerating hologram generation. Numerical simulations of 2D and 3D reconfiguration with more than $10^3$ traps, including multilayer assembly and interlayer transport, show robust transient intensities and significantly faster updates than conventional methods. These results establish inter-frame phase continuity as a practical design principle for dynamic holographic control and scalable neutral-atom array reconfiguration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adds an inter-frame phase continuity constraint to the Gerchberg-Saxton method and reports that it speeds up hologram generation while stabilizing transients in simulations of >1000-trap 2D/3D atom arrays.

read the letter

The main takeaway is that they modified the standard iterative Fourier-transform hologram algorithm to enforce phase continuity at the trap sites from one frame to the next. This is done while still using weighted intensity targets, and the result is fewer iterations per update plus reduced transient intensity fluctuations during SLM refresh. The phase-difference distribution between consecutive holograms is offered as a quick diagnostic for how safe the update will be. They test this on 2D and 3D reconfiguration tasks with more than 10^3 traps, including multilayer assembly and interlayer transport, and the numerics show stable transients and faster convergence than plain Gerchberg-Saxton. That combination of phase continuity with weighted equalization appears to be the new piece. The simulations are run at relevant scales and the basic idea is straightforward to understand. The phase constraint does not seem to force a visible trade-off in final trap quality within the models they used. The soft spots are all on the experimental side. There are no lab results, only numerical propagation, so we do not yet know how pixel crosstalk, phase quantization, or finite SLM response time will interact with the added constraint. The abstract also gives no quantitative numbers on iteration reduction or transient suppression, which makes it difficult to judge the size of the practical gain. The central assumption that phase continuity can be enforced without degrading steady-state performance holds in their runs, but the paper would be stronger with explicit error metrics and direct comparisons. This work is aimed at groups doing large-scale neutral-atom experiments who already use holographic tweezers for atom movement. Anyone trying to reconfigure arrays of several hundred to a few thousand sites without losing atoms during updates would find the algorithm description and the simulation results useful. It deserves peer review because the problem is real, the proposed fix is simple, and the simulations are at the right scale, even if more validation is needed before it changes practice.

Referee Report

3 major / 2 minor

Summary. The paper introduces the weighted-projective Gerchberg-Saxton (WPGS) algorithm as a phase-stable method for updating holograms in dynamic optical tweezers used for neutral-atom array reconfiguration. It claims that enforcing inter-frame trap-phase continuity (via a phase-difference diagnostic) while retaining weighted intensity equalization suppresses refresh-induced transient degradation, reduces the number of iterations per update, and yields faster hologram generation. Numerical simulations of 2D and 3D reconfigurations with >10^3 traps, including multilayer assembly and interlayer transport, are reported to demonstrate robust transient intensities and significant speedups relative to conventional methods.

Significance. If the numerical results are borne out, the work would be significant for scalable neutral-atom quantum computing by addressing a practical bottleneck in dynamic holographic control. It establishes inter-frame phase continuity as a design principle and shows that the added constraint can accelerate computation. The large-scale ( >10^3 traps) 2D/3D simulations including multilayer transport are a strength, as is the provision of a simple diagnostic. However, the significance remains conditional on the unverified assumption that the phase constraint introduces no measurable trade-off in steady-state trap quality.

major comments (3)

Abstract: The central claim that WPGS 'retains weighted intensity equalization' without compromising final trap depths or uniformities is load-bearing for the 'robust transient intensities' conclusion, yet no quantitative metrics (e.g., RMS uniformity, minimum trap intensity, or depth histograms) comparing WPGS to standard GS are provided for the >10^3-trap simulations.
Simulations section (implied by abstract claims): The statements of 'robust transient intensities' and 'significantly faster updates' for 2D/3D multilayer cases lack specific numbers such as transient intensity minima during refresh, iteration reduction factors, or error bars, leaving the magnitude of improvement and robustness unquantified.
Algorithm description: The implicit assumption that the added phase-continuity constraint can be enforced via the phase-difference diagnostic without forcing a trade-off in steady-state solution quality or requiring SLM hardware capabilities beyond current devices is tested only at the level of numerical propagation models; no explicit verification (e.g., final vs. target intensity fidelity with/without the constraint) is shown.

minor comments (2)

Abstract: The phrase 'significantly faster updates than conventional methods' would benefit from naming the baseline algorithms (e.g., standard GS or other variants) used for comparison.
General: Consider adding a brief discussion of the numerical model's assumptions regarding SLM pixel crosstalk, phase quantization, and temporal dynamics, as mismatches with real hardware could affect the transient-robustness conclusions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of our numerical results. We address each major point below and will revise the manuscript to include the requested quantitative metrics and clarifications.

read point-by-point responses

Referee: Abstract: The central claim that WPGS 'retains weighted intensity equalization' without compromising final trap depths or uniformities is load-bearing for the 'robust transient intensities' conclusion, yet no quantitative metrics (e.g., RMS uniformity, minimum trap intensity, or depth histograms) comparing WPGS to standard GS are provided for the >10^3-trap simulations.

Authors: We agree that explicit quantitative comparisons strengthen the claims. The full manuscript contains figures showing final trap intensities for WPGS, but we will add a new table (or supplementary panels) in the revised version reporting RMS uniformity, minimum trap intensity, and fidelity metrics for both WPGS and standard GS across the >10^3-trap 2D and 3D cases. These will confirm no degradation in steady-state quality. revision: yes
Referee: Simulations section (implied by abstract claims): The statements of 'robust transient intensities' and 'significantly faster updates' for 2D/3D multilayer cases lack specific numbers such as transient intensity minima during refresh, iteration reduction factors, or error bars, leaving the magnitude of improvement and robustness unquantified.

Authors: We will incorporate specific numbers into the revised text and figure captions, including measured transient intensity minima (e.g., >0.8 of target during refresh), average iteration reductions (with factors), and error bars or statistics from repeated simulations for the multilayer and interlayer transport cases. This quantifies the robustness and speedups. revision: yes
Referee: Algorithm description: The implicit assumption that the added phase-continuity constraint can be enforced via the phase-difference diagnostic without forcing a trade-off in steady-state solution quality or requiring SLM hardware capabilities beyond current devices is tested only at the level of numerical propagation models; no explicit verification (e.g., final vs. target intensity fidelity with/without the constraint) is shown.

Authors: The simulations already demonstrate comparable final fidelities through the reported uniformities, but we will add an explicit side-by-side comparison of intensity fidelity (with vs. without the phase constraint) in the algorithm/results section. The method operates within standard 0-2π phase modulation of current SLMs and imposes no additional hardware requirements; we will state this explicitly. revision: partial

Circularity Check

0 steps flagged

No circularity detected in WPGS algorithm derivation or claims

full rationale

The paper introduces the weighted-projective Gerchberg-Saxton (WPGS) algorithm as an independent design choice that adds inter-frame phase continuity enforcement to the standard weighted intensity equalization of the Gerchberg-Saxton method. No equations, steps, or performance claims in the abstract or description reduce by construction to fitted parameters, self-definitions, or self-citation chains; the phase-difference diagnostic is presented as a derived output rather than an input, and the reported speed/robustness gains are attributed to numerical simulations of >10^3 traps rather than tautological redefinitions. The derivation chain remains self-contained against external benchmarks with no load-bearing self-citations or ansatzes imported from prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5504 in / 932 out tokens · 41618 ms · 2026-05-10T19:50:12.990437+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
min_ϕ,s,W J(ϕ,s,W) := ||WE(ϕ)−sEtar||²₂ ... alternating updates of the three variable blocks (W,s,ϕ)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
Numerical simulations of 2D and 3D reconfiguration with more than 10³ traps... robust transient intensities

Reference graph

Works this paper leans on

60 extracted references · 13 canonical work pages · 1 internal anchor

[1]

Altman, K

E. Altman, K. R. Brown, G. Carleo, L. D. Carr, E. Demler, C. Chin, B. DeMarco, S. E. Economou, M. A. Eriksson, K.- M. C. Fu, M. Greiner, K. R. Hazzard, R. G. Hulet, A. J. Kol- lár, B. L. Lev, M. D. Lukin, R. Ma, X. Mi, S. Misra, C. Mon- roe, K. Murch, Z. Nazario, K.-K. Ni, A. C. Potter, P. Roushan, M. Saffman, M. Schleier-Smith, I. Siddiqi, R. Simmonds, M...

2021
[2]

W. Tian, W. J. Wee, A. Qu, B. J. M. Lim, P. R. Datla, V . P. W. Koh, and H. Loh, Parallel assembly of arbitrary defect-free atom arrays with a multitweezer algorithm, Phys. Rev. Appl. 19, 034048 (2023)

2023
[3]

Pichard, D

G. Pichard, D. Lim, E. Bloch, J. Vaneecloo, L. Bourachot, G.-J. Both, G. Mériaux, S. Dutartre, R. Hostein, J. Paris, B. Ximenez, A. Signoles, A. Browaeys, T. Lahaye, and D. Dreon, Rearrange- ment of individual atoms in a 2000-site optical-tweezer array at cryogenic temperatures, Phys. Rev. Appl.22, 024073 (2024)

2000
[4]

Schymik, V

K.-N. Schymik, V . Lienhard, D. Barredo, P. Scholl, H. Williams, A. Browaeys, and T. Lahaye, Enhanced atom-by- atom assembly of arbitrary tweezer arrays, Phys. Rev. A102, 063107 (2020)

2020
[5]

H. J. Manetsch, G. Nomura, E. Bataille, X. Lv, K. H. Leung, and M. Endres, A tweezer array with 6,100 highly coherent atomic qubits, Nature647, 60–67 (2025)

2025
[6]

Pecorari, S

L. Pecorari, S. Jandura, and G. Pupillo, Low-depth quantum error correction via three-qubit gates in rydberg atom arrays, Phys. Rev. Lett.135, 240602 (2025)

2025
[7]

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, Nature626, 58 (2024)

2024
[8]

A. M. Kaufman and K.-K. Ni, Quantum science with opti- cal tweezer arrays of ultracold atoms and molecules, Nature Physics17, 1324 (2021)

2021
[9]

Browaeys and T

A. Browaeys and T. Lahaye, Many-body physics with individu- ally controlled Rydberg atoms, Nature Physics16, 132 (2020)

2020
[10]

Babbush, D

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, Physical Review Letters121, 10.1103/phys- revlett.121.123603 (2018)

work page doi:10.1103/phys- 2018
[11]

Bernien, S

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V . Vuleti´c, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature551, 579– (2017)

2017
[12]

Ebadi, T

S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V . Vuleti´c, and M. D. Lukin, Quantum phases of matter on a 256-atom programmable quan- tum simulator, Nature595, 227–232 (2021)

2021
[13]

Semeghini, H

G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Sama- jdar,et al., Probing topological spin liquids on a programmable quantum simulator, Science374, 1242 (2021)

2021
[14]

Levine, A

H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V . Vuleti ´c, H. Pichler, and M. D. Lukin, Parallel implementation of high-fidelity multi- qubit gates with neutral atoms, Phys. Rev. Lett.123, 170503 (2019)

2019
[15]

Henriet, L

L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.- O. Reymond, and C. Jurczak, Quantum computing with neutral atoms, Quantum4, 327 (2020)

2020
[16]

S. J. Evered, D. Bluvstein, M. Kalinowski,et al., High-fidelity parallel entangling gates on a neutral-atom quantum computer, Nature622, 268 (2023)

2023
[17]

N.-C. Chiu, E. C. Trapp, J. Guo, M. H. Abobeih, L. M. Stewart, S. Hollerith, P. L. Stroganov, M. Kalinowski, A. A. Geim, S. J. Evered, S. H. Li, X. Lyu, L. M. Peters, D. Bluvstein, T. T. Wang, M. Greiner, V . Vuleti´c, and M. D. Lukin, Continuous operation of a coherent 3,000-qubit system, Nature646, 1075 (2025)

2025
[18]

Manovitz, S

T. Manovitz, S. H. Li, S. Ebadi,et al., Quantum coarsening and collective dynamics on a programmable simulator, Nature638, 86 (2025)

2025
[19]

S. J. Evered, M. Kalinowski, A. A. Geim,et al., Probing the kitaev honeycomb model on a neutral-atom quantum computer, Nature645, 341 (2025)

2025
[20]

Bluvstein, A

D. Bluvstein, A. A. Geim, S. H. Li,et al., A fault-tolerant neutral-atom architecture for universal quantum computation, Nature649, 39 (2026)

2026
[21]

Barredo, S

D. Barredo, S. de Léséleuc, V . Lienhard, T. Lahaye, and A. Browaeys, An atom-by-atom assembler of defect-free arbi- trary two-dimensional atomic arrays, Science354, 1021–1023 (2016)

2016
[22]

M. O. Brown, T. Thiele, C. Kiehl, T.-W. Hsu, and C. A. Re- gal, Gray-molasses optical-tweezer loading: Controlling colli- sions for scaling atom-array assembly, Phys. Rev. X9, 011057 (2019)

2019
[23]

A. L. Shaw, P. Scholl, R. Finklestein, I. S. Madjarov, B. Grinke- meyer, and M. Endres, Dark-state enhanced loading of an opti- cal tweezer array, Phys. Rev. Lett.130, 193402 (2023)

2023
[24]

Lin, H.-S

R. Lin, H.-S. Zhong, Y . Li, Z.-R. Zhao, L.-T. Zheng, T.-R. Hu, H.-M. Wu, Z. Wu, W.-J. Ma, Y . Gao, Y .-K. Zhu, Z.-F. Su, W.- L. Ouyang, Y .-C. Zhang, J. Rui, M.-C. Chen, C.-Y . Lu, and J.-W. Pan, Ai-enabled rapid assembly of thousands of defect- free neutral atom arrays with constant-time-overhead, Physical Review Letters135, 060602 (2025), arXiv:2412.14...

work page arXiv 2025
[25]

Pause, L

L. Pause, L. Sturm, M. Mittenbühler, S. Amann, T. Preuschoff, D. Schäffner, M. Schlosser, and G. Birkl, Supercharged two- dimensional tweezer array with more than 1000 atomic qubits, Optica11, 222 (2024)

2024
[26]

Gyger, M

F. Gyger, M. Ammenwerth, R. Tao, H. Timme, S. Snigirev, I. Bloch, and J. Zeiher, Continuous operation of large-scale atom arrays in optical lattices, Phys. Rev. Res.6, 033104 (2024)

2024
[27]

Nogrette, H

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geome- tries, Phys. Rev. X4, 021034 (2014)

2014
[28]

Tamura, T

H. Tamura, T. Unakami, J. He, Y . Miyamoto, and K. Nakagawa, Highly uniform holographic microtrap arrays for single atom trapping using a feedback optimization of in-trap fluorescence measurements, Opt. Express24, 8132 (2016)

2016
[29]

Y . T. Chew, M. Poitrinal, T. Tomita, S. Kitade, J. Mauricio, K. Ohmori, and S. de Léséleuc, Ultraprecise holographic opti- cal tweezer array, Phys. Rev. A110, 053518 (2024)

2024
[30]

Schlosser, S

M. Schlosser, S. Tichelmann, D. Schäffner, D. O. de Mello, M. Hambach, J. Schütz, and G. Birkl, Scalable multilayer ar- chitecture of assembled single-atom qubit arrays in a three- dimensional talbot tweezer lattice, Physical Review Letters130, 10.1103/physrevlett.130.180601 (2023). 8

work page doi:10.1103/physrevlett.130.180601 2023
[31]

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y . Song, and J. Ahn, In situ single-atom array synthesis using dynamic holographic optical tweezers, Nature Communications7, 13317 (2016)

2016
[32]

W. Lee, H. Kim, and J. Ahn, Three-dimensional rearrangement of single atoms using actively controlled optical microtraps, Optics Express24, 9816 (2016)

2016
[33]

R. W. Gerchberg, A practical algorithm for the determination of phase from image and diffraction plane pictures, Optik35, 237 (1972)

1972
[35]

I. H. A. Knottnerus, Y . C. Tseng, A. Urech, R. J. C. Spreeuw, and F. Schreck, Parallel assembly of neutral atom arrays with an SLM using linear phase interpolation, SciPost Phys.19, 118 (2025)

2025
[36]

J. You, J. M. Doyle, Z. Liu, S. S. Yu, and A. Periwal, Control of dipolar dynamics by geometrical programming, Phys. Rev. Lett.135, 253002 (2025)

2025
[37]

Machu, G

Y . Machu, G. Creutzer, C. Sayrin, and M. Brune, Full-field-of- view aberration correction for large arrays of focused beams (2025), arXiv:2512.15967 [physics.optics]

work page arXiv 2025
[38]

Bergamini, B

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, Holographic generation of mi- crotrap arrays for single atoms by use of a programmable phase modulator, J. Opt. Soc. Am. B21, 1889 (2004)

2004
[39]

Y . Cai, S. Yan, Z. Wang, R. Li, Y . Liang, Y . Zhou, X. Li, X. Yu, M. Lei, and B. Yao, Rapid tilted-plane gerchberg-saxton algo- rithm for holographic optical tweezers, Opt. Express28, 12729 (2020)

2020
[40]

R. D. Leonardo, F. Ianni, and G. Ruocco, Computer generation of optimal holograms for optical trap arrays, Opt. Express15, 1913 (2007)

1913
[41]

H. W. Kuhn, The hungarian method for the assignment prob- lem, Naval Research Logistics Quarterly2, 83 (1955)

1955
[42]

Kusano, Y

T. Kusano, Y . Nakamura, R. Yokoyama, N. Ozawa, K. Shibata, T. Takano, Y . Takasu, and Y . Takahashi, Plane-selective manip- ulations of nuclear spin qubits in a three-dimensional optical tweezer array, Physical Review Research7, L022045 (2025)

2025
[43]

M. A. Norcia, W. B. Cairncross, K. Barnes, P. Battaglino, A. Brown, M. O. Brown, K. Cassella, C.-A. Chen, R. Coxe, D. Crow, J. Epstein, C. Griger, A. M. W. Jones, H. Kim, J. M. Kindem, J. King, S. S. Kondov, K. Kotru, J. Lauigan, M. Li, M. Lu, E. Megidish, J. Marjanovic, M. McDonald, T. Mittiga, J. A. Muniz, S. Narayanaswami, C. Nishiguchi, R. Notermans, ...

2023
[44]

J. A. Muniz, D. Crow, H. Kim, J. M. Kindem, W. B. Cairn- cross, A. Ryou, T. C. Bohdanowicz, C.-A. Chen, Y . Ji, A. M. W. Jones, E. Megidish, C. Nishiguchi, M. Urbanek, L. Wadleigh, T. Wilkason, D. Aasen, K. Barnes, J. M. Bello-Rivas, I. Bloom- field, G. Booth, A. Brown, M. O. Brown, K. Cassella, G. Cowan, J. Epstein, M. Feldkamp, C. Griger, Y . Has- san, ...

2025
[45]

D. Kim, A. Keesling, A. Omran, H. Levine, H. Bernien, M. Greiner, M. D. Lukin, and D. R. Englund, Large-scale uni- form optical focus array generation with a phase spatial light modulator, Opt. Lett.44, 3178 (2019)

2019
[46]

Shor, Fault-tolerant quantum computation, inProceedings of 37th Conference on Foundations of Computer Science(IEEE Comput

P. Shor, Fault-tolerant quantum computation, inProceedings of 37th Conference on Foundations of Computer Science(IEEE Comput. Soc. Press, 1996) pp. 56–65, arXiv:9605011 [quant- ph]

1996
[47]

Georgescu, 25 years of quantum error correction, Nature Re- views Physics2, 519 (2020)

I. Georgescu, 25 years of quantum error correction, Nature Re- views Physics2, 519 (2020)

2020
[48]

B. Zhao, M. Jing, L. Zhang, X. Zhao, Y .-A. Chen, K. Wang, and X. Wang, Retrieving Nonlinear Features from Noisy Quantum States, PRX Quantum5, 020357 (2024)

2024
[49]

Correcting quantum errors using a classical code and one additional qubit

T. Araki, J. F. Goodwin, and Z. Cai, Correcting quantum errors using a classical code and one additional qubit, arXiv preprint arXiv:2510.05008 (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[50]

K. He, C. Zhu, H. Yao, J. Liu, Y . Li, and X. Wang, No-Go The- orems for Universal Quantum State Purification via Classically Simulable Operations, Physical Review Letters136, 090204 (2026), arXiv:2504.10516

work page arXiv 2026
[51]

A. M. Dalzell, S. McArdle, M. Berta, P. Bienias, C.-F. Chen, A. Gilyén, C. T. Hann, M. J. Kastoryano, E. T. Khabiboulline, A. Kubica, G. Salton, S. Wang, and F. G. S. L. Brandão,arXiv preprint arXiv:2310.03011(Cambridge University Press, 2025) arXiv:2310.03011

work page arXiv 2025
[52]

A. M. Childs and W. van Dam, Quantum algorithms for alge- braic problems, Reviews of Modern Physics82, 1 (2010)

2010
[53]

Quantum singular value trans- formation and beyond: exponential improvements for quantum matrix arithmetics

A. Gilyén, Y . Su, G. H. Low, and N. Wiebe, Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics, inProceedings of the 51st An- nual ACM SIGACT Symposium on Theory of Computing(ACM, New York, NY , USA, 2019) pp. 193–204, arXiv:1806.01838

work page arXiv 2019
[54]

Y . Wang, L. Zhang, Z. Yu, and X. Wang, Quantum phase pro- cessing and its applications in estimating phase and entropies, Physical Review A108, 062413 (2023), arXiv:2209.14278

work page arXiv 2023
[55]

Y .-A. Chen, Y . Mo, Y . Liu, L. Zhang, and X. Wang, Quan- tum algorithm for reversing unknown unitary evolutions, arXiv preprint arXiv:2403.04704 (2024)

work page arXiv 2024
[56]

Miessen, P

A. Miessen, P. J. Ollitrault, F. Tacchino, and I. Tavernelli, Quan- tum algorithms for quantum dynamics, Nature Computational Science3, 25 (2023)

2023
[57]

C. Zhu, L. Zhang, and X. Wang, A quest toward comprehen- sive benchmarking of quantum computing software: Quantum computing, Nature Computational Science5, 363 (2025)

2025
[58]

C. Zhu, X. Wu, Z. Yang, J. Wang, A. Wu, S. Zheng, and X. Wang, Quantum compiler design for qubit mapping and routing: A cross-architectural survey of superconduct- ing, trapped-ion, and neutral atom systems, arXiv preprint arXiv:2505.16891 (2025)

work page arXiv 2025
[59]

M. Cain, Q. Xu, R. King, L. R. B. Picard, H. Levine, M. Endres, J. Preskill, H.-Y . Huang, and D. Bluvstein, Shor’s algorithm is possible with as few as 10,000 reconfigurable atomic qubits, arXiv preprint arXiv:2603.28627 (2026)

work page arXiv 2026
[60]

Labropoulou, T

D. Labropoulou, T. Labropoulos, P. Vafeas, and D. M. Manias, On the generalizations of the cauchy-schwarz- bunyakovsky inequality with applications to elasticity (2023), arXiv:2312.03478 [math.FA]

work page arXiv 2023
[61]

1 + (1−a 2)∆ϕ2 j 6 # +O(∆ϕ 4 j),(S9) sin[(1−a)∆ϕ j] sin(∆ϕj) = (1−a)

J. R. Fienup, Phase retrieval algorithms: a comparison, Appl. Opt.21, 2758 (1982). 9 Supplemental Material for Phase-Stable Hologram Updates for Large-Scale Neutral-Atom Array Reconfiguration I. PROPAGATION MATRIX DERIV ATION We consider an optical system in which a phase-only spatial light modulator (SLM) occupies the front focal plane of a thin lens wit...

1982