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arxiv: 2605.18622 · v1 · pith:AEAYF3UPnew · submitted 2026-05-18 · 🪐 quant-ph

Fibonacci many-body scars in a decorated Rule-54 quantum cellular automaton

Han-Ze Li , Jian-Xin Zhong This is my paper

Pith reviewed 2026-05-20 10:05 UTC · model grok-4.3

classification 🪐 quant-ph
keywords many-body scarsRule-54quantum cellular automatonFibonacciFloquet eigenstatesweak ergodicity breakinghard-core dimerssoliton structures
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The pith

Decorations on the Rule-54 automaton reduce its hard-core dimer dynamics to finite translation orbits whose Fourier modes are exact scars.

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

The paper constructs exact many-body scars by adding local projector-controlled decorations to the Rule-54 quantum cellular automaton. A hard-core dimer sector acts as a protected skeleton that translates exactly under the evolution, while the decorations leave this skeleton untouched and act only on states outside it. Consequently the protected dynamics collapses onto finite translation orbits whose Fourier modes become exact Floquet eigenstates carrying sub-volume-law entanglement. The number of these scars grows according to Fibonacci combinatorics, yet they occupy an exponentially small fraction of the full qubit Hilbert space. Finite-size simulations confirm that the remaining states thermalize, displaying Page-like entanglement, rapid growth, and circular unitary ensemble statistics.

Core claim

A hard-core dimer sector of Rule 54 supplies an exactly translatable protected skeleton, while local projector-controlled decorations are invisible on this skeleton and nontrivial outside it. The protected dynamics is therefore reducible to finite translation orbits, whose Fourier modes form exact Floquet eigenstates with sub-volume-law entanglement. The number of exact scars grows with Fibonacci combinatorics, whereas their fraction in the full qubit Hilbert space remains exponentially small.

What carries the argument

Local projector-controlled decorations that remain invisible to the hard-core dimer skeleton of the Rule-54 automaton

If this is right

  • The exact scars possess sub-volume-law entanglement.
  • The complement of the scarred subspace exhibits thermalizing dynamics with Page-like eigenstate entanglement.
  • Quasienergy statistics in the complement follow the circular unitary ensemble.
  • The construction supplies a concrete starting point for digital quantum simulation of scarred cellular-automaton dynamics.

Where Pith is reading between the lines

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

  • The same decoration strategy could be applied to other reversible automata that possess native finite-orbit or soliton structures.
  • Fibonacci scaling of the scar count may link this model to combinatorial objects appearing in other scarred or integrable systems.
  • The approach offers a route to engineer controllable weak ergodicity breaking directly in hardware-native quantum cellular-automaton circuits.

Load-bearing premise

The local projector-controlled decorations stay invisible on the hard-core dimer skeleton under the full unitary evolution.

What would settle it

A numerical or analytical check showing that decorated states escape the finite translation orbits or develop volume-law entanglement under time evolution would falsify the exact-scar construction.

Figures

Figures reproduced from arXiv: 2605.18622 by Han-Ze Li, Jian-Xin Zhong.

Figure 1
Figure 1. Figure 1: Circuit architecture of the bare and decorated Rule￾54 quantum cellular automaton. (a) Bare Rule-54 QCA. The evolution is generated by alternating layers of three-site re￾versible Rule-54 gates. The green blocks denote local up￾dates Rj arranged in the even and odd layers Ue and Uo, and one Floquet period is U54 =UoUe. The vertical direction represents discrete Floquet time, while the horizontal direc￾tion… view at source ↗
Figure 2
Figure 2. Figure 2: Analytic structure of the Fibonacci-dimensional scar sector. (a) Number of exact scar eigenstates as a function of system size. For a chain of N = 2L qubits, the protected hard-core soliton sector has dimension Nscar = FL−1 + FL+1, the Fibonacci count of hard-core configurations on a cycle of length L. The exponential growth Nscar ∼ φ L is shown together with the exponentially small Hilbert-space fraction … view at source ↗
Figure 3
Figure 3. Figure 3: Numerical signatures of exact scars in representative projector-decorated Rule-54 circuits. The top row shows a construction protecting the vacuum orbit, while the bottom row shows a construction protecting the one-soliton translation orbit generated by |1100 · · · 0⟩ for N = 10. (a,d) Half-chain entanglement entropy SN/2 of Floquet eigenstates versus quasienergy eigenphase ϕ. The bulk eigenstates concentr… view at source ↗
Figure 4
Figure 4. Figure 4: Bulk quasienergy spacing statistics after remov￾ing the exact scar sector. We diagonalize the decorated Flo￾quet unitary, remove the protected scar subspace, and com￾pute the normalized nearest-neighbor quasienergy spacing s=∆θ/⟨∆θ⟩ from the remaining bulk eigenphases on the unit circle. The histogram is compared with the β = 2 random￾matrix prediction appropriate for a Floquet unitary without a time-rever… view at source ↗
Figure 5
Figure 5. Figure 5: Digital-circuit realization of the projector-decorated Rule-54 QCA. (a) The local Rule-54 update Rj is imple￾mented by two CNOT gates and one Toffoli gate, giving y ′ =y ⊕ x ⊕ z ⊕ xz. (b) The most general local decoration is a projected three-qubit unitary d µ c . (c) A hardware-friendly diagonal realization decomposes d µ c into pattern-controlled phase gates Cτ (θc,τ ) acting only on forbidden local patt… view at source ↗
read the original abstract

Quantum many-body scars provide a controlled form of weak ergodicity breaking, in which structured nonthermal eigenstates coexist with a thermalizing many-body spectrum. We introduce a qubit-level route to exact scars based on the intrinsic soliton structure of the Rule-54 quantum cellular automaton. A hard-core dimer sector of Rule 54 supplies an exactly translatable protected skeleton, while local projector-controlled decorations are invisible on this skeleton and nontrivial outside it. The protected dynamics is therefore reducible to finite translation orbits, whose Fourier modes form exact Floquet eigenstates with sub-volume-law entanglement. The number of exact scars grows with Fibonacci combinatorics, whereas their fraction in the full qubit Hilbert space remains exponentially small. Finite-size simulations show Page-like eigenstate entanglement, rapid entanglement growth, fidelity decay, and circular unitary ensemble quasienergy statistics in the decorated complement. This construction demonstrates that exact many-body scars can be engineered from native finite-orbit structures of an interacting reversible automaton, and provides a direct starting point for digital quantum simulation of scarred cellular-automaton dynamics.

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.

Referee Report

1 major / 1 minor

Summary. The paper introduces a construction for exact many-body scars in a decorated Rule-54 quantum cellular automaton. A hard-core dimer sector supplies an exactly translatable protected skeleton, while local projector-controlled decorations are invisible on this skeleton and nontrivial outside it. The protected dynamics reduce to finite translation orbits whose Fourier modes form exact Floquet eigenstates with sub-volume-law entanglement. The number of scars grows with Fibonacci combinatorics while their fraction in the full Hilbert space remains exponentially small. Finite-size simulations are reported to show Page-like entanglement, rapid growth, fidelity decay, and circular unitary ensemble statistics in the complement.

Significance. If the invariance of the dimer skeleton under the full unitary is established, the work supplies a parameter-free route to exact scars engineered directly from the finite-orbit structure of a reversible interacting automaton. The Fibonacci scaling and explicit reduction to translation orbits are distinctive, and the construction is positioned for digital quantum simulation. These features would strengthen the link between cellular-automaton models and controlled weak ergodicity breaking.

major comments (1)
  1. [Abstract and construction description] Abstract and construction description: the reduction to finite translation orbits and exact Floquet eigenstates rests on the claim that local projector-controlled decorations are invisible on the hard-core dimer skeleton under the full unitary evolution. No explicit commutation relation between the skeleton update and the decorations, nor an inductive verification that the protected sector remains closed for all times, is supplied. If cross terms permit leakage even when the skeleton is in a valid dimer configuration, the orbits cease to be closed and the eigenstates are no longer exact.
minor comments (1)
  1. [Abstract] The abstract states that simulations exhibit 'Page-like eigenstate entanglement' without specifying the system sizes, the precise quantity compared to the Page curve, or error bars; this makes it difficult to assess how closely the numerics support the sub-volume-law claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the positive evaluation of the construction, its Fibonacci scaling, and its relevance to digital quantum simulation. We address the single major comment below and will incorporate the requested clarification into the revised version.

read point-by-point responses

  1. Referee: the reduction to finite translation orbits and exact Floquet eigenstates rests on the claim that local projector-controlled decorations are invisible on the hard-core dimer skeleton under the full unitary evolution. No explicit commutation relation between the skeleton update and the decorations, nor an inductive verification that the protected sector remains closed for all times, is supplied. If cross terms permit leakage even when the skeleton is in a valid dimer configuration, the orbits cease to be closed and the eigenstates are no longer exact.

    Authors: We agree that an explicit verification of sector closure is required to rigorously establish the exactness of the scars. The manuscript argues that the decorations are invisible on valid hard-core dimer configurations because the local projectors annihilate any deviation from the skeleton and the Rule-54 update on the skeleton itself is a pure translation. However, we acknowledge that a formal commutation relation between the skeleton evolution operator and the decoration projectors, together with an inductive argument over multiple time steps, was not supplied. In the revised manuscript we will add a dedicated subsection (and supporting appendix) that (i) defines the skeleton projector and the decoration operators, (ii) proves the commutation relation [U_skeleton, P_decoration] = 0 on the protected subspace, and (iii) supplies a short induction showing that any initial state in the hard-core dimer sector remains in that sector under the full unitary for all times, with no leakage from cross terms. This addition will confirm that the finite translation orbits are closed and that their Fourier modes are exact Floquet eigenstates. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation follows from explicit construction

full rationale

The paper defines the protected skeleton via the hard-core dimer sector of Rule 54 and states that projector-controlled decorations are invisible on this sector. The reduction to finite translation orbits and exact Floquet eigenstates is presented as a direct consequence of this construction and the resulting closed orbits under the automaton dynamics. The Fibonacci combinatorics is identified as arising from the enumeration of those orbits rather than from any fitted parameter or self-referential definition. No equation is shown to equate a derived quantity back to an input fit, and no load-bearing uniqueness theorem or ansatz is imported solely via self-citation. The central claims remain independent of the target scar statistics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the intrinsic soliton properties of Rule-54 and the invariance of the chosen decorations; no free parameters are introduced in the abstract description.

axioms (1)
  • domain assumption Rule-54 quantum cellular automaton possesses a hard-core dimer sector that supplies an exactly translatable protected skeleton
    Invoked in the abstract as the starting point for the protected dynamics.
invented entities (1)
  • local projector-controlled decorations no independent evidence
    purpose: To render dynamics nontrivial outside the dimer skeleton while remaining invisible on it
    Introduced to engineer the exact scars; no independent evidence supplied in abstract.

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Works this paper leans on

117 extracted references · 117 canonical work pages · 4 internal anchors

  1. [1]

    Quantum statistical mechanics in a closed system of particles,

    J. M. Deutsch, “Quantum statistical mechanics in a closed system of particles,” Phys. Rev. A43, 2046 (1991)

    work page 2046

  2. [2]

    Chaos and quantum thermalization,

    M. Srednicki, “Chaos and quantum thermalization,” Phys. Rev. E50, 888 (1994)

    work page 1994

  3. [3]

    Thermalization and its mechanism for generic isolated quantum sys- tems,

    M. Rigol, V. Dunjko, and M. Olshanii, “Thermalization and its mechanism for generic isolated quantum sys- tems,” Nature452, 854 (2008)

    work page 2008

  4. [4]

    From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,

    L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics,” Adv. Phys. 65, 239 (2016)

    work page 2016

  5. [5]

    Charac- terization of chaotic quantum spectra and universality of level fluctuation laws,

    O. Bohigas, M.-J. Giannoni, and C. Schmit, “Charac- terization of chaotic quantum spectra and universality of level fluctuation laws,” Phys. Rev. Lett.52, 1 (1984)

    work page 1984

  6. [6]

    M. L. Mehta,Random Matrices, 3rd ed. (Elsevier, Am- sterdam, 2004)

    work page 2004

  7. [7]

    Haake,Quantum Signatures of Chaos, 3rd ed

    F. Haake,Quantum Signatures of Chaos, 3rd ed. (Springer, Berlin, 2010)

    work page 2010

  8. [8]

    Distribution of the ratio of consecutive level spacings in random matrix ensembles,

    Y. Y. Atas, E. Bogomolny, O. Giraud, and G. Roux, “Distribution of the ratio of consecutive level spacings in random matrix ensembles,” Phys. Rev. Lett.110, 084101 (2013)

    work page 2013

  9. [9]

    Probing many-body dynamics on a 51-atom quantum simula- tor,

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- 11 ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, “Probing many-body dynamics on a 51-atom quantum simula- tor,” Nature551, 579 (2017)

    work page 2017

  10. [10]

    Weak ergodicity breaking from quantum many-body scars,

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Ser- byn, and Z. Papić, “Weak ergodicity breaking from quantum many-body scars,” Nat. Phys.14, 745 (2018)

    work page 2018

  11. [11]

    Quantum scarred eigenstates in a Rydbergatomchain: Entanglement, breakdownofther- malization, and stability to perturbations,

    C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Ser- byn, and Z. Papić, “Quantum scarred eigenstates in a Rydbergatomchain: Entanglement, breakdownofther- malization, and stability to perturbations,” Phys. Rev. B98, 155134 (2018)

    work page 2018

  12. [12]

    Pe- riodic orbits, entanglement, and quantum many-body scarsinconstrainedquantumsystems,

    W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, “Pe- riodic orbits, entanglement, and quantum many-body scarsinconstrainedquantumsystems,” Phys.Rev.Lett. 122, 040603 (2019)

    work page 2019

  13. [13]

    Systematic construction of counterexamples to the eigenstate thermalization hy- pothesis,

    N. Shiraishi and T. Mori, “Systematic construction of counterexamples to the eigenstate thermalization hy- pothesis,” Phys. Rev. Lett.119, 030601 (2017)

    work page 2017

  14. [14]

    Quantum many-body scars and weak breaking of ergodicity,

    M. Serbyn, D. A. Abanin, and Z. Papić, “Quantum many-body scars and weak breaking of ergodicity,” Nat. Phys.17, 675 (2021)

    work page 2021

  15. [15]

    Quan- tum many-body scars and Hilbert-space fragmentation: A review of exact results,

    S. Moudgalya, B. A. Bernevig, and N. Regnault, “Quan- tum many-body scars and Hilbert-space fragmentation: A review of exact results,” Rep. Prog. Phys.85, 086501 (2022)

    work page 2022

  16. [16]

    Quantum many-body scars: A quasiparticle per- spective,

    A. Chandran, T. Iadecola, V. Khemani, and R. Moess- ner, “Quantum many-body scars: A quasiparticle per- spective,” Annu. Rev. Condens. Matter Phys.14, 443 (2023)

    work page 2023

  17. [17]

    Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette,

    H. Bethe, “Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette,” Z. Phys.71, 205 (1931)

    work page 1931

  18. [18]

    Time evolution of lo- cal observables after quenching to an integrable model,

    J.-S. Caux and F. H. L. Essler, “Time evolution of lo- cal observables after quenching to an integrable model,” Phys. Rev. Lett.110, 257203 (2013)

    work page 2013

  19. [19]

    Absenceofdiffusionincertainrandom lattices,

    P.W.Anderson, “Absenceofdiffusionincertainrandom lattices,” Phys. Rev.109, 1492 (1958)

    work page 1958

  20. [20]

    Metal– insulator transition in a weakly interacting many- electron system with localized single-particle states,

    D. M. Basko, I. L. Aleiner, and B. L. Altshuler, “Metal– insulator transition in a weakly interacting many- electron system with localized single-particle states,” Ann. Phys.321, 1126 (2006)

    work page 2006

  21. [21]

    Many-body localiza- tion and thermalization in quantum statistical mechan- ics,

    R. Nandkishore and D. A. Huse, “Many-body localiza- tion and thermalization in quantum statistical mechan- ics,” Annu. Rev. Condens. Matter Phys.6, 15 (2015)

    work page 2015

  22. [22]

    Colloquium: Many-body localization, thermalization, and entanglement,

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, “Colloquium: Many-body localization, thermalization, and entanglement,” Rev. Mod. Phys.91, 021001 (2019)

    work page 2019

  23. [23]

    Ergodicity breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltoni- ans,

    P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Pollmann, “Ergodicity breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltoni- ans,” Phys. Rev. X10, 011047 (2020)

    work page 2020

  24. [24]

    Local- ization from Hilbert space shattering: From theory to physical realizations,

    V. Khemani, M. Hermele, and R. Nandkishore, “Local- ization from Hilbert space shattering: From theory to physical realizations,” Phys. Rev. B101, 174204 (2020)

    work page 2020

  25. [25]

    Emer- gent SU(2) dynamics and perfect quantum many-body scars,

    S. Choi, D. A. Abanin, and M. D. Lukin, “Emer- gent SU(2) dynamics and perfect quantum many-body scars,” Phys. Rev. Lett.122, 220603 (2019)

    work page 2019

  26. [26]

    Sig- natures of integrability in the dynamics of Rydberg- blockaded chains,

    V. Khemani, C. R. Laumann, and A. Chandran, “Sig- natures of integrability in the dynamics of Rydberg- blockaded chains,” Phys. Rev. B99, 161101(R) (2019)

    work page 2019

  27. [27]

    Exact quantum many- body scar states in the Rydberg-blockaded spin chain,

    C.-J. Lin and O. I. Motrunich, “Exact quantum many- body scar states in the Rydberg-blockaded spin chain,” Phys. Rev. Lett.124, 120603 (2020)

    work page 2020

  28. [28]

    Slow quantum thermalization and many-body revivals from mixed phase space,

    A. A. Michailidis, C. J. Turner, Z. Papić, D. A. Abanin, and M. Serbyn, “Slow quantum thermalization and many-body revivals from mixed phase space,” Phys. Rev. X10, 011055 (2020)

    work page 2020

  29. [29]

    Quantum many- body scars and quantum criticality,

    Z. Yao, L. Pan, S. Liu, and H. Zhai, “Quantum many- body scars and quantum criticality,” Phys. Rev. B105, 125123 (2022)

    work page 2022

  30. [30]

    Taking the temperature of quantum many-body scars,

    P. C. Burke and S. Dooley, “Taking the temperature of quantum many-body scars,” Phys. Rev. Research7, 043054 (2025)

    work page 2025

  31. [31]

    Un- covering quantum many-body scars with quantum ma- chine learning,

    J.-J. Feng, B. Zhang, Z.-C. Yang, and Q. Zhuang, “Un- covering quantum many-body scars with quantum ma- chine learning,” npj Quantum Inf.11, 42 (2025)

    work page 2025

  32. [32]

    Preparing quantum many-body scar states on quantum computers,

    E. J. Gustafson, A. C. Y. Li, A. Khan, J. Kim, D. M. Kurkcuoglu, M. S. Alam, P. P. Orth, A. Rah- mani, and T. Iadecola, “Preparing quantum many-body scar states on quantum computers,” Quantum7, 1171 (2023)

    work page 2023

  33. [33]

    On one-dimensional quantum cellular au- tomaton,

    J. Watrous, “On one-dimensional quantum cellular au- tomaton,” inProceedings of the 36th Annual Symposium on Foundations of Computer Science(IEEE, 1995), p. 528

    work page 1995

  34. [34]

    Reversible quantum cellular automata

    B. Schumacher and R. F. Werner, “Reversible quantum cellular automaton,” arXiv:quant-ph/0405174 (2004)

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  35. [35]

    Index theory of one dimensional quantum walks and cellular automata,

    D. Gross, V. Nesme, H. Vogts, and R. F. Werner, “Index theory of one dimensional quantum walks and cellular automata,” Commun. Math. Phys.310, 419 (2012)

    work page 2012

  36. [36]

    An overview of quantum cellular automa- ton,

    P. Arrighi, “An overview of quantum cellular automa- ton,” Nat. Comput.18, 885 (2019)

    work page 2019

  37. [37]

    A review of quantum cellular automaton,

    T. Farrelly, “A review of quantum cellular automaton,” Quantum4, 368 (2020)

    work page 2020

  38. [38]

    Universal quantum simulators,

    S. Lloyd, “Universal quantum simulators,” Science273, 1073 (1996)

    work page 1996

  39. [39]

    Quantum cellular automaton for uni- versal quantum computation,

    R. Raussendorf, “Quantum cellular automaton for uni- versal quantum computation,” Phys. Rev. A72, 022301 (2005)

    work page 2005

  40. [40]

    Quantum computing in the NISQ era and beyond,

    J. Preskill, “Quantum computing in the NISQ era and beyond,” Quantum2, 79 (2018)

    work page 2018

  41. [41]

    Qiskit: An open-source framework for quantum computing,

    M. S. Aniset al., “Qiskit: An open-source framework for quantum computing,”https://qiskit.org(2021)

    work page 2021

  42. [42]

    Simulating quantum many-body dynamics on a cur- rent digital quantum computer,

    A. Smith, M. S. Kim, F. Pollmann, and J. Knolle, “Simulating quantum many-body dynamics on a cur- rent digital quantum computer,” npj Quantum Inf.5, 106 (2019)

    work page 2019

  43. [43]

    Quantum supremacy using a pro- grammable superconducting processor,

    F. Aruteet al., “Quantum supremacy using a pro- grammable superconducting processor,” Nature574, 505 (2019)

    work page 2019

  44. [44]

    Quan- tum entanglement growth under random unitary dy- namics,

    A. Nahum, J. Ruhman, S. Vijay, and J. Haah, “Quan- tum entanglement growth under random unitary dy- namics,” Phys. Rev. X7, 031016 (2017)

    work page 2017

  45. [45]

    Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws,

    C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, “Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws,” Phys. Rev. X8, 021013 (2018)

    work page 2018

  46. [46]

    Coarse-grained dynamics of operator and state entanglement

    C. Jonay, D. A. Huse, and A. Nahum, “Coarse- grained dynamics of operator and state entanglement,” arXiv:1803.00089 (2018)

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  47. [47]

    Emergentstatisticalmechanics of entanglement in random unitary circuits,

    T.ZhouandA.Nahum, “Emergentstatisticalmechanics of entanglement in random unitary circuits,” Phys. Rev. B99, 174205 (2019)

    work page 2019

  48. [48]

    On two-dimensional integrable cellular automata,

    A. Bobenko, M. Bordemann, C. Gunn, and U. Pinkall, “On two-dimensional integrable cellular automata,” Commun. Math. Phys.158, 127 (1993)

    work page 1993

  49. [49]

    Integrability of a 12 deterministic cellular automaton driven by stochastic boundaries,

    T. Prosen and C. Mejía-Monasterio, “Integrability of a 12 deterministic cellular automaton driven by stochastic boundaries,” J. Phys. A49, 185003 (2016)

    work page 2016

  50. [50]

    Exact matrix product eigen- vectors of the open rule 54 cellular automaton,

    T. Prosen and B. Buča, “Exact matrix product eigen- vectors of the open rule 54 cellular automaton,” J. Phys. A50, 395002 (2017)

    work page 2017

  51. [51]

    Exact large deviation statistics and trajectory phase transition of a deterministic boundary-driven cellular automaton,

    B. Buča, J. P. Garrahan, T. Prosen, and M. Vanicat, “Exact large deviation statistics and trajectory phase transition of a deterministic boundary-driven cellular automaton,” Phys. Rev. E100, 020103(R) (2019)

    work page 2019

  52. [52]

    Rule 54: Exactly solvable model of nonequilibrium statistical mechanics,

    B. Buča, K. Klobas, and T. Prosen, “Rule 54: Exactly solvable model of nonequilibrium statistical mechanics,” J. Stat. Mech.2021, 074001 (2021)

    work page 2021

  53. [53]

    Exact thermal- ization dynamics in the ‘Rule 54’ quantum cellular au- tomaton,

    K. Klobas, B. Bertini, and L. Piroli, “Exact thermal- ization dynamics in the ‘Rule 54’ quantum cellular au- tomaton,” Phys. Rev. Lett.126, 160602 (2021)

    work page 2021

  54. [54]

    Entanglement dynamics in Rule 54: Exact results and quasiparticle picture,

    K. Klobas and B. Bertini, “Entanglement dynamics in Rule 54: Exact results and quasiparticle picture,” Sci- Post Phys.11, 106 (2021)

    work page 2021

  55. [55]

    Integrability breaking in the Rule 54 cellular automa- ton,

    J. López-Piqueres, S. Gopalakrishnan, and R. Vasseur, “Integrability breaking in the Rule 54 cellular automa- ton,” J. Phys. A: Math. Theor.55, 234005 (2022)

    work page 2022

  56. [56]

    On the integrability struc- ture of the deformed rule-54 reversible cellular automa- ton,

    C. Paletta and T. Prosen, “On the integrability struc- ture of the deformed rule-54 reversible cellular automa- ton,” arXiv:2603.25424 (2026)

    work page arXiv 2026

  57. [57]

    En- tanglement of exact excited states of Affleck-Kennedy- Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hy- pothesis,

    S. Moudgalya, N. Regnault, and B. A. Bernevig, “En- tanglement of exact excited states of Affleck-Kennedy- Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hy- pothesis,” Phys. Rev. B98, 235156 (2018)

    work page 2018

  58. [58]

    Weak ergodicity breaking and quantum many-body scars in spin-1 XY magnets,

    M. Schecter and T. Iadecola, “Weak ergodicity breaking and quantum many-body scars in spin-1 XY magnets,” Phys. Rev. Lett.123, 147201 (2019)

    work page 2019

  59. [59]

    Exact eigenstates in the PXP model from the forward scatter- ing approximation,

    D. K. Mark, C.-J. Lin, and O. I. Motrunich, “Exact eigenstates in the PXP model from the forward scatter- ing approximation,” Phys. Rev. B101, 094308 (2020)

    work page 2020

  60. [60]

    Many-body scars as a group invariant sector of Hilbert space,

    K.Pakrouski, P.N.Pallegar, F.K.Popov, andI.R.Kle- banov, “Many-body scars as a group invariant sector of Hilbert space,” Phys. Rev. Lett.125, 230602 (2020)

    work page 2020

  61. [61]

    Exact spectral form factor in a minimal model of many-body quantum chaos,

    B. Bertini, P. Kos, and T. Prosen, “Exact spectral form factor in a minimal model of many-body quantum chaos,” Phys. Rev. Lett.121, 264101 (2018)

    work page 2018

  62. [62]

    Entanglement spreading in a minimal model of maximal many-body quantum chaos,

    B. Bertini, P. Kos, and T. Prosen, “Entanglement spreading in a minimal model of maximal many-body quantum chaos,” Phys. Rev. X9, 021033 (2019)

    work page 2019

  63. [63]

    Exact correlation functions for dual-unitary lattice models in one dimen- sion,

    B. Bertini, P. Kos, and T. Prosen, “Exact correlation functions for dual-unitary lattice models in one dimen- sion,” Phys. Rev. Lett.123, 210601 (2019)

    work page 2019

  64. [64]

    Exact dynamics in dual-unitary quantum circuits,

    L. Piroli, B. Bertini, J. I. Cirac, and T. Prosen, “Exact dynamics in dual-unitary quantum circuits,” Phys. Rev. B101, 094304 (2020)

    work page 2020

  65. [65]

    Exactly solv- ablequantummany-bodydynamicsfromspace-timedu- ality,

    B. Bertini, P. W. Claeys, and T. Prosen, “Exactly solv- ablequantummany-bodydynamicsfromspace-timedu- ality,” Rev. Mod. Phys.98, 025001 (2026)

    work page 2026

  66. [66]

    Quantum many-body scars in dual-unitary circuits,

    L. Logarić, S. Dooley, S. Pappalardi, and J. Goold, “Quantum many-body scars in dual-unitary circuits,” Phys. Rev. Lett.132, 010401 (2024)

    work page 2024

  67. [67]

    Average entropy of a subsystem,

    D. N. Page, “Average entropy of a subsystem,” Phys. Rev. Lett.71, 1291 (1993)

    work page 1993

  68. [68]

    Evolution of entanglement entropy in one-dimensional systems,

    P. Calabrese and J. Cardy, “Evolution of entanglement entropy in one-dimensional systems,” J. Stat. Mech. 2005, P04010 (2005)

    work page 2005

  69. [69]

    Entanglement and thermo- dynamics after a quantum quench in integrable sys- tems,

    V. Alba and P. Calabrese, “Entanglement and thermo- dynamics after a quantum quench in integrable sys- tems,” Proc. Natl. Acad. Sci. U.S.A.114, 7947 (2017)

    work page 2017

  70. [70]

    Simulation of interaction-induced chiral topological dynamics on a digital quantum computer,

    J. M. Koh, T. Tai, and C. H. Lee, “Simulation of interaction-induced chiral topological dynamics on a digital quantum computer,” Phys. Rev. Lett.129, 140502 (2022)

    work page 2022

  71. [71]

    Stabilizing multiple topological fermions on a quantum computer,

    J. M. Koh, T. Tai, Y. H. Phee, W. E. Ng, and C. H. Lee, “Stabilizing multiple topological fermions on a quantum computer,” npj Quantum Inf.8, 16 (2022)

    work page 2022

  72. [72]

    Realization of higher- order topological lattices on a quantum computer,

    J. M. Koh, T. Tai, and C. H. Lee, “Realization of higher- order topological lattices on a quantum computer,” Nat. Commun.15, 5807 (2024)

    work page 2024

  73. [73]

    Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer,

    R. Shen, T. Chen, B. Yang, and C. H. Lee, “Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer,” Nat. Commun.16, 1340 (2025)

    work page 2025

  74. [74]

    Interacting non-Hermitian edge and cluster bursts on a digital quantum processor,

    J. M.Koh, W.-T.Xue, T. Tai, D. E.Koh, andC. H.Lee, “Interacting non-Hermitian edge and cluster bursts on a digital quantum processor,” arXiv:2503.14595 (2025)

    work page arXiv 2025

  75. [75]

    Observation of feedback-directed quantum dynamics in large-scale quantum processors

    R. Shen and C. H. Lee, “Observation of feedback- directed quantum dynamics in large-scale quantum pro- cessors,” arXiv:2604.11900 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  76. [76]

    Circuit structure- preserving error mitigation for high-fidelity quantum simulations,

    R. Shen, T. Chen, and C. H. Lee, “Circuit structure- preserving error mitigation for high-fidelity quantum simulations,” arXiv:2505.17187 (2025)

    work page arXiv 2025

  77. [77]

    Benchmarking quan- tum solvers in noisy digital simulations for financial portfolio optimization,

    R. Shen, Z. Hao, and C. H. Lee, “Benchmarking quan- tum solvers in noisy digital simulations for financial portfolio optimization,” arXiv:2508.21123 (2025)

    work page arXiv 2025

  78. [78]

    Digital Simulation of Non-Hermitian Knotted Bands on Quantum Hardware

    T. Y. Ng, Y. Wang, W. J. Chan, R. Shen, T. Chen, and C. H. Lee, “Digital simulation of non-Hermitian knotted bands on quantum hardware,” arXiv:2604.26914 (2026)

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  79. [79]

    Quantum Zeno ef- fectandthe many-bodyentanglementtransition,

    Y. Li, X. Chen, and M. P. A. Fisher, “Quantum Zeno ef- fectandthe many-bodyentanglementtransition,” Phys. Rev. B98, 205136 (2018)

    work page 2018

  80. [80]

    Measurement- induced phase transitions in the dynamics of entangle- ment,

    B. Skinner, J. Ruhman, and A. Nahum, “Measurement- induced phase transitions in the dynamics of entangle- ment,” Phys. Rev. X9, 031009 (2019)

    work page 2019

Showing first 80 references.