Lifts of quantum CSS codes

• URL: http://arxiv.org/abs/2404.16736v1
• Date: Thu, 25 Apr 2024 16:44:45 GMT
• Title: Lifts of quantum CSS codes
• Authors: Virgile Guemard,
• Abstract summary: We propose a notion of lift for quantum CSS codes, inspired by the geometrical construction of Freedman and Hastings. It is based on the existence of a canonical complex associated to any CSS code, that we introduce under the name of Tanner cone-complex.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a notion of lift for quantum CSS codes, inspired by the geometrical construction of Freedman and Hastings. It is based on the existence of a canonical complex associated to any CSS code, that we introduce under the name of Tanner cone-complex, and over which we generate covering spaces. As a first application, we describe the classification of lifts of hypergraph product codes (HPC) and demonstrate the equivalence with the lifted product code (LPC) of Panteleev and Kalachev, including when the linear codes, factors of the HPC, are Tanner codes. As a second application, we report several new non-product constructions of quantum CSS codes, and we apply the prescription to generate their lifts which, for certain selected covering maps, are codes with improved relative parameters compared to the initial one.

Related papers

• 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)
• Equivalence Classes of Quantum Error-Correcting Codes [49.436750507696225]
  Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. We represent QECC's in a form called a ZX diagram, consisting of a tensor network.
  arXiv  Detail & Related papers  (2024-06-17T20:48:43Z)
• Uncovering LLM-Generated Code: A Zero-Shot Synthetic Code Detector via Code Rewriting [78.48355455324688]
  We propose a novel zero-shot synthetic code detector based on the similarity between the code and its rewritten variants. Our results demonstrate a notable enhancement over existing synthetic content detectors designed for general texts.
  arXiv  Detail & Related papers  (2024-05-25T08:57:28Z)
• Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma [0.5461938536945721]
  We develop a Steane-type decoder using only data from the two underlying classical codes. We show that any subsystem stabilizer code can be "doubled" to yield a subsystem CSS code with twice the number of physical, logical, and gauge qudits and up to twice the code distance.
  arXiv  Detail & Related papers  (2023-11-29T19:00:04Z)
• Dihedral Quantum Codes [0.0]
  We present the code construction and give a formula for the code dimension, depending on the two classical codes that the CSS code is based on. We also give a lower bound on the code distance and construct an example of short dihedral quantum codes.
  arXiv  Detail & Related papers  (2023-10-23T16:55:34Z)
• Spatially-Coupled QDLPC Codes [3.6622737533847936]
  We describe toric codes as quantum counterparts of classical spatially-coupled (2D-SC) codes. We introduce spatially-coupled quantum LDPC (SC-QLDPC) codes as a class of convolutional LDPC codes. This paper focuses on QLDPC codes with rate less than 1/10, but we construct 2D-SC HGP codes with small memories, higher rates (about 1/3), and superior thresholds.
  arXiv  Detail & Related papers  (2023-04-29T00:57:57Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [51.9157257936691]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code. We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• 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)
• CSS code surgery as a universal construction [51.63482609748332]
  We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes. We describe code surgery between such codes using a specific colimit in the category of chain complexes.
  arXiv  Detail & Related papers  (2023-01-31T16:17:25Z)
• Classical product code constructions for quantum Calderbank-Shor-Steane codes [1.4699455652461726]
  We introduce a new product code construction which is a natural generalisation of classical product codes to quantum codes. We show that built-in redundancies in the parity checks result in so-called meta-checks which can be exploited to correct syndrome read-out errors.
  arXiv  Detail & Related papers  (2022-09-27T15:48:37Z)
• Quantum XYZ Product Codes [0.3222802562733786]
  We study a three-fold variant of the hypergraph product code construction, differing from the standard homological product of three classical codes. When instantiated with 3 classical LDPC codes, this "XYZ product" yields a non CSS quantum LDPC code which might display a large minimum distance.
  arXiv  Detail & Related papers  (2020-11-19T09:50:08Z)

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.