Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary

• URL: http://arxiv.org/abs/2504.09171v1
• Date: Sat, 12 Apr 2025 10:25:26 GMT
• Title: Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary
• Authors: Vincent Steffan, Shin Ho Choe, Nikolas P. Breuckmann, Francisco Revson Fernandes Pereira, Jens Niklas Eberhardt,
• Abstract summary: Tile codes generalize the usual surface code by allowing for a bit more flexibility in terms of locality and stabilizer weight.<n>We find codes with parameters $[288, 8, 12]]$ using weight-6 stabilizers and $[[288, 8, 14]]$ using weight-8 stabilizers, outperforming all previously known constructions in this direction.
• Score: 10.159681653887237
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We introduce tile codes, a simple yet powerful way of constructing quantum codes that are local on a planar 2D-lattice. Tile codes generalize the usual surface code by allowing for a bit more flexibility in terms of locality and stabilizer weight. Our construction does not compromise on the fact that the codes are local on a lattice with open boundary conditions. Despite its simplicity, we use our construction to find codes with parameters $[[288, 8, 12]]$ using weight-6 stabilizers and $[[288, 8, 14]]$ using weight-8 stabilizers, outperforming all previously known constructions in this direction. Allowing for a slightly higher non-locality, we find a $[[512, 18, 19]]$ code using weight-8 stabilizers, which outperforms the rotated surface code by a factor of more than 12. Our approach provides a unified framework for understanding the structure of codes that are local on a 2D planar lattice and offers a systematic way to explore the space of possible code parameters. In particular, due to its simplicity, the construction naturally accommodates various types of boundary conditions and stabilizer configurations, making it a versatile tool for quantum error correction code design.

Related papers

• Planar quantum low-density parity-check codes with open boundaries [7.42725219729553]
  We construct high-performance planar quantum low-density parity-check (qLDPC) codes with open boundaries.<n>These codes achieve an efficiency metric that is an order of magnitude greater than that of the surface code.<n>We observe fractal logical operators in the form of Sierpinski triangles, with the code distances scaling proportionally to the area of the truncated fractal.
  arXiv  Detail & Related papers  (2025-04-11T18:00:05Z)
• New local stabilizer codes from local classical codes [0.0]
  We discuss new local and low-weight stabilizer codes which are obtained from the recent progress in $2D$ local classical codes.<n>We construct codes with weight and qubit use count of $5$ while being able to protect the information with high distance, or greater logical count.
  arXiv  Detail & Related papers  (2025-03-26T16:53:36Z)
• Generalized toric codes on twisted tori for quantum error correction [9.623534315687825]
  Kitaev toric code is widely considered one of the leading candidates for error correction in fault-tolerant quantum computation.<n>We introduce a ring-theoretic approach for efficiently analyzing topological CSS codes in two dimensions.
  arXiv  Detail & Related papers  (2025-03-05T19:00:05Z)
• List Decodable Quantum LDPC Codes [49.2205789216734]
  We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff. We get efficiently list decodable QLDPC codes with unique decoders.
  arXiv  Detail & Related papers  (2024-11-06T23:08:55Z)
• Wire Codes [0.0]
  We introduce a recipe to transform any quantum stabilizer code into a subsystem code with related code parameters that has weight and degree three. We call the subsystem codes produced by our recipe "wire codes" Our results constitute a general method to construct low-overhead subsystem codes on general graphs.
  arXiv  Detail & Related papers  (2024-10-14T06:27:09Z)
• SSIP: automated surgery with quantum LDPC codes [55.2480439325792]
  We present Safe Surgery by Identifying Pushouts (SSIP), an open-source lightweight Python package for automating surgery between qubit CSS codes. Under the hood, it performs linear algebra over $mathbbF$ governed by universal constructions in the category of chain complexes. We show that various logical measurements can be performed cheaply by surgery without sacrificing the high code distance.
  arXiv  Detail & Related papers  (2024-07-12T16:50:01Z)
• Improved rate-distance trade-offs for quantum codes with restricted connectivity [34.95121779484252]
  We study how the connectivity graph associated with a quantum code constrains the code parameters. We establish a tighter dimension-distance trade-off as a function of the size of separators in the connectivity graph.
  arXiv  Detail & Related papers  (2023-07-06T20:38:34Z)
• Quantum spherical codes [55.33545082776197]
  We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat codes that can outperform previous constructions.
  arXiv  Detail & Related papers  (2023-02-22T19:00:11Z)
• Quantum computation on a 19-qubit wide 2d nearest neighbour qubit array [59.24209911146749]
  This paper explores the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds. We engineer an error bias at the lowest level of encoding using the surface code. We then address this bias at a higher level of encoding using a lattice-surgery surface code bus.
  arXiv  Detail & Related papers  (2022-12-03T06:16:07Z)
• Morphing quantum codes [77.34726150561087]
  We morph the 15-qubit Reed-Muller code to obtain the smallest known stabilizer code with a fault-tolerant logical $T$ gate. We construct a family of hybrid color-toric codes by morphing the color code.
  arXiv  Detail & Related papers  (2021-12-02T17:43:00Z)
• Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks [0.0]
  We represent complex code constructions as tensor networks built from the tensors of simple codes or states. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes. We lay out some examples where we glue together simple stabilizer codes to construct non-trivial codes.
  arXiv  Detail & Related papers  (2021-09-16T18:00:00Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians [7.092674229752723]
  We introduce a framework that takes it any classical code and explicitly constructs the corresponding QEC code. A concrete advantage is that the desirable properties of a classical code are automatically incorporated in the design of the resulting quantum code.
  arXiv  Detail & Related papers  (2020-12-02T19:00:19Z)

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.