Floquet Codes from Derived Semi-Regular Hyperbolic Tessellations on Orientable and Non-Orientable Surfaces

• URL: http://arxiv.org/abs/2603.29811v1
• Date: Tue, 31 Mar 2026 14:39:35 GMT
• Title: Floquet Codes from Derived Semi-Regular Hyperbolic Tessellations on Orientable and Non-Orientable Surfaces
• Abstract summary: We construct several new quantum Floquet codes on compact, orientable, as well as non-orientable surfaces.<n>A performance analysis and an investigation of the behavior of these codes are also presented.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we construct several new quantum Floquet codes on compact, orientable, as well as non-orientable surfaces. In order to obtain such codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on such surfaces. The method of construction presented here generalizes similar constructions concerning hyperbolic Floquet codes on connected and compact surfaces with genus $g \geq 2$. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.

Related papers

• P2Voxel: Pyramid Pivot Voxelization for 3D Mesh Tokenization [60.385793205570046]
  We introduce textbfP2Voxel, a pyramid pivot voxelization framework for compact and reconstruction-aware mesh tokenization.<n>Under the textitSpatial Complexity assumption, Pyramid Pivot Voxelization exploits the spatial non-uniformity of real surfaces.<n>Under the textitBlock Reconstructability assumption, a Pyramid VAE learns compact multi-resolution latent codes over locally reconstructable pivot blocks.
  arXiv  Detail & Related papers  (2026-08-01T13:04:29Z)
• Fragmented Topological Excitations in Generalized Hypergraph Product Codes [13.310044694105075]
  In this work, we investigate the fracton topological orders in a family of codes obtained by a recently proposed general construction.<n>We term the corresponding exactly solvable spin models textitorthoplex models, based on the geometry of the stabilizers.
  arXiv  Detail & Related papers  (2026-01-14T20:14:46Z)
• Untangling Surface Codes: Bridging Braids and Lattice Surgery [51.748182660642776]
  We present a systematic method for translating fault-tolerant quantum circuits between their braiding and lattice surgery representations within the surface code.<n>Our framework provides a foundation for the automated verification, compilation, and benchmarking of large-scale surface code computations.
  arXiv  Detail & Related papers  (2025-11-27T10:12:38Z)
• Geometry Distributions [51.4061133324376]
  We propose a novel geometric data representation that models geometry as distributions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity.
  arXiv  Detail & Related papers  (2024-11-25T04:06:48Z)
• Quantized topological phases beyond square lattices in Floquet synthetic dimensions [0.0]
  We show that non-square lattice Hamiltonians can be implemented using Floquet synthetic dimensions. Our construction uses dynamically modulated ring resonators and provides the capacity for direct $k$-space engineering of lattice Hamiltonians.
  arXiv  Detail & Related papers  (2024-11-04T17:50:48Z)
• Tessellation codes: encoded quantum gates by geometric rotation [4.1533777499443305]
  We show that tessellation codes exhibit decent error correction properties by analysis via geometric considerations.<n>This formalism sheds a new light on quantum code and logical operation construction.
  arXiv  Detail & Related papers  (2024-10-24T13:17:56Z)
• Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models [44.99833362998488]
  Topological subsystem codes allow for quantum error correction with no time overhead, even in the presence of measurement noise. We provide a systematic construction of a class of codes in three dimensions built from abelian quantum double models in one fewer dimension. Our construction not only generalizes the recently introduced subsystem toric code, but also provides a new perspective on several aspects of the original model.
  arXiv  Detail & Related papers  (2023-05-10T18:00:01Z)
• Asymmetric quantum codes on non-orientable surfaces [0.0]
  We prove that if the genus $g$ of a non-orientable surface is even $(g=2h)$, the parameters of the corresponding AQSC are equal to the parameters of a surface code obtained from an orientable surface of genus $h$. We also show that the new surface code constructed on a $p, q$ tessellation over $S$ has the ratio $k/n$ better than the ratio of an AQSC constructed on the same $p, q$ tessellation over an orientable surface of genus $g$.
  arXiv  Detail & Related papers  (2023-03-26T19:44:12Z)
• Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion [71.52576837870166]
  We present Minimal Neural Atlas, a novel atlas-based explicit neural surface representation. At its core is a fully learnable parametric domain, given by an implicit probabilistic occupancy field defined on an open square of the parametric space. Our reconstructions are more accurate in terms of the overall geometry, due to the separation of concerns on topology and geometry.
  arXiv  Detail & Related papers  (2022-07-29T16:55:06Z)
• A Level Set Theory for Neural Implicit Evolution under Explicit Flows [102.18622466770114]
  Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. We present a framework that allows applying deformation operations defined for triangle meshes onto such implicit surfaces. We show that our approach exhibits improvements for applications like surface smoothing, mean-curvature flow, inverse rendering and user-defined editing on implicit geometry.
  arXiv  Detail & Related papers  (2022-04-14T17:59:39Z)
• A graph-based formalism for surface codes and twists [0.7673339435080445]
  We provide a rigorous formalism for constructing surface codes with twists. We associate a surface code to any graph $G$ embedded on any 2D-manifold. We calculate and bound various code properties such as the rate and distance.
  arXiv  Detail & Related papers  (2021-01-22T22:08:56Z)
• SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS [55.41644538483948]
  Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projectedangled Pair States (PEPS) Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence.
  arXiv  Detail & Related papers  (2019-12-31T16:30:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.