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PreprintCC BY 4.0arXiv

Stellar Representation of Gottesman Kitaev Preskill States on the Double Discrete Cylinder

  • Aidan Zlotak
  • Nicolas Fabre
  • Romain Murenzi
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Abstract

Covariant integral quantization is developed on the double discrete cylinder phase space, with the torus as configuration space, and yields the Wigner distribution and the stellar representation. This phase space is particularly well suited to translationally invariant states, such as the Gottesman Kitaev Preskill (GKP) states. These states are central to fault-tolerant quantum computing architectures, yet their quantum resources are still under investigation. The stellar representations of ideal GKP logical states, which behave as phase eigenstates of the double discrete cylinder, have no zeros on this phase space, whereas those of their superpositions have infinitely many. The vacuum, although Gaussian, has zeros on this phase space, and the zeros of finitely squeezed GKP states move with the widths of the peaks and of the envelope, and reach this phase space for fine-tuned widths. These features echo the role of the vacuum as the resource that makes GKP-based architectures hard to simulate.

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Cite

BibTeXRIS
BibTeX
@misc{zlotak2026stellar,
  title = {{Stellar Representation of Gottesman Kitaev Preskill States on the Double Discrete Cylinder}},
  author = {Aidan Zlotak and Nicolas Fabre and Romain Murenzi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37831},
  eprint = {2610.37831},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37831},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stellar Representation of Gottesman Kitaev Preskill States on the Double Discrete Cylinder
AU  - Aidan Zlotak
AU  - Nicolas Fabre
AU  - Romain Murenzi
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37831
UR  - https://arxiv.org/abs/2610.37831
AB  - Covariant integral quantization is developed on the double discrete cylinder phase space, with the torus as configuration space, and yields the Wigner distribution and the stellar representation. This phase space is particularly well suited to translationally invariant states, such as the Gottesman Kitaev Preskill (GKP) states. These states are central to fault-tolerant quantum computing architectures, yet their quantum resources are still under investigation. The stellar representations of ideal GKP logical states, which behave as phase eigenstates of the double discrete cylinder, have no zeros on this phase space, whereas those of their superpositions have infinitely many. The vacuum, although Gaussian, has zeros on this phase space, and the zeros of finitely squeezed GKP states move with the widths of the peaks and of the envelope, and reach this phase space for fine-tuned widths. These features echo the role of the vacuum as the resource that makes GKP-based architectures hard to simulate.
ER  -