Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 19 min ago
PreprintCC BY 4.0HAL

Aperiodicity in Quantum Wang Tilings

  • Titouan Carette
  • Etienne Moutot
Open at sourcePDFDOICite

Abstract

By reformulating Wang tiles with tensors, we propose a natural generalization to the probabilistic and quantum setting. In this new framework, we introduce notions of tilings and periodicity directly extending their classical counterparts. In the one dimensional case, we recover the decidability of the generalized domino problem by linking it to the trace characterization of nilpotent matrices. In the two-dimensional case, we provide extension of weak and strong aperiodicity respectively and show the equivalence of those generalized notions, extending the well known equivalence in the classical case. We also exhibit a quantum tile set being aperiodic while its underlying classical tile set is not, proving that quantum interference can suppress periodic patterns and paving the way to the investigation of a new kind of aperiodicity. Finally, we highlight the many new research directions opened by this generalization of Wang tiles, related to (quantum) cellular automata, condensed matter physics, symbolic dynamics and more.

Related

  1. Tiling, spectrality and aperiodicity of connected sets
    Rachel Greenfeld, Mihail N. Kolountzakis
    Israel Journal of MathematicsPeer-reviewedLicence not statedFull text16 citedGeneral mathematicsOpenAlex
  2. Aperiodicity and subword complexity in the binary expansion of powers of three
    Ralf Stephan
    arXivPreprintCC0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Aperiodicity is sufficient for macroscopic thermalization
    Amit Vikram
    arXivPreprintarXiv licenceFull textMathematical physicsHigh-energy & particle physicsarXiv
  4. C*-irreducible regular inclusions, Galois correspondence and aperiodicity
    B. K. Kwaśniewski, R. Meyer
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. The Work of Hong Wang
    Christopher D. Sogge
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{carette2026aperiodicity,
  title = {{Aperiodicity in Quantum Wang Tilings}},
  author = {Titouan Carette and Etienne Moutot},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.1016/j.tcs.2026.116159},
  eprint = {2302.04503},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-04776560v2},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Aperiodicity in Quantum Wang Tilings
AU  - Titouan Carette
AU  - Etienne Moutot
PY  - 2026
DA  - 2026/09/02
PB  - HAL
DO  - 10.1016/j.tcs.2026.116159
UR  - https://hal.science/hal-04776560v2
AB  - By reformulating Wang tiles with tensors, we propose a natural generalization to the probabilistic and quantum setting. In this new framework, we introduce notions of tilings and periodicity directly extending their classical counterparts. In the one dimensional case, we recover the decidability of the generalized domino problem by linking it to the trace characterization of nilpotent matrices. In the two-dimensional case, we provide extension of weak and strong aperiodicity respectively and show the equivalence of those generalized notions, extending the well known equivalence in the classical case. We also exhibit a quantum tile set being aperiodic while its underlying classical tile set is not, proving that quantum interference can suppress periodic patterns and paving the way to the investigation of a new kind of aperiodicity. Finally, we highlight the many new research directions opened by this generalization of Wang tiles, related to (quantum) cellular automata, condensed matter physics, symbolic dynamics and more.
ER  -