Quantum Constacyclic BCH Codes over Qudits: A Spectral-Domain Approach

• URL: http://arxiv.org/abs/2407.16814v1
• Date: Tue, 23 Jul 2024 19:48:12 GMT
• Title: Quantum Constacyclic BCH Codes over Qudits: A Spectral-Domain Approach
• Authors: Shikha Patel, Shayan Srinivasa Garani,
• Abstract summary: We characterize constacyclic codes in the spectral domain using the finite field Fourier transform (FFFT) We also consider repeated-root constacyclic codes and characterize them in terms of symmetric and asymmetric $q$-cyclotomic cosets. quantum encoders and decoders are also proposed in the transform domain for Calderbank-Shor-Steane CSS-based quantum codes.
• Score: 2.3940819037450987
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We characterize constacyclic codes in the spectral domain using the finite field Fourier transform (FFFT) and propose a reduced complexity method for the spectral-domain decoder. Further, we also consider repeated-root constacyclic codes and characterize them in terms of symmetric and asymmetric $q$-cyclotomic cosets. Using zero sets of classical self-orthogonal and dual-containing codes, we derive quantum error correcting codes (QECCs) for both constacyclic Bose-Chaudhuri-Hocquenghem (BCH) codes and repeated-root constacyclic codes. We provide some examples of QECCs derived from repeated-root constacyclic codes and show that constacyclic BCH codes are more efficient than repeated-root constacyclic codes. Finally, quantum encoders and decoders are also proposed in the transform domain for Calderbank-Shor-Steane CSS-based quantum codes. Since constacyclic codes are a generalization of cyclic codes with better minimum distance than cyclic codes with the same code parameters, the proposed results are practically useful.

Related papers

• Pruning qLDPC codes: Towards bivariate bicycle codes with open boundary conditions [1.6385815610837167]
  Quantum low-density parity-check codes are promising candidates for quantum error correcting codes. We introduce the concept of pruning quantum codes. We investigate fault-tolerant quantum computation using the constructed pruned codes by describing fold-transversal gates.
  arXiv  Detail & Related papers  (2024-12-05T14:20:44Z)
• 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)
• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• Quantum Margulis Codes [3.3148826359547514]
  Recently, Lin and Pryadko presented the quantum two-block group algebra codes. We show how to modify the construction of Margulis to get a two-block algebra code.
  arXiv  Detail & Related papers  (2024-09-15T19:08:34Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [47.52324012811181]
  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)
• Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices [60.02503434201552]
  We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
  arXiv  Detail & Related papers  (2022-12-20T13:41:27Z)
• New Binary Quantum Codes Constructed from Quasi-Cyclic Codes [6.718184400443239]
  It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be symplectic dual-containing. As an application, we construct 8 binary quantum codes that exceed the best-known results.
  arXiv  Detail & Related papers  (2021-12-14T03:22:16Z)
• Dense Coding with Locality Restriction for Decoder: Quantum Encoders vs. Super-Quantum Encoders [67.12391801199688]
  We investigate dense coding by imposing various locality restrictions to our decoder. In this task, the sender Alice and the receiver Bob share an entangled state.
  arXiv  Detail & Related papers  (2021-09-26T07:29:54Z)
• Pseudocodeword-based Decoding of Quantum Color Codes [17.188280334580195]
  We introduce a two-stage decoder based on pseudocodewords for quantum cycle codes. Our decoder has only local or error-weight-dependent operations of low computational complexity and better decoding performance.
  arXiv  Detail & Related papers  (2020-10-21T09:10:04Z)

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.