Narain CFTs from qudit stabilizer codes

• URL: http://arxiv.org/abs/2212.07089v2
• Date: Thu, 27 Apr 2023 19:25:51 GMT
• Title: Narain CFTs from qudit stabilizer codes
• Authors: Kohki Kawabata, Tatsuma Nishioka and Takuya Okuda
• Abstract summary: We construct a subset of Narain CFTs from quantum stabilizer codes with qudit systems whose dimension is a prime number. We study qudit Calderbank-Shor-Steane codes as a special class of qudit stabilizer codes and the ensembles of the Narain code CFTs constructed from CSS codes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a discrete subset of Narain CFTs from quantum stabilizer codes with qudit (including qubit) systems whose dimension is a prime number. Our construction exploits three important relations. The first relation is between qudit stabilizer codes and classical codes. The second is between classical codes and Lorentzian lattices. The third is between Lorentzian lattices and Narain CFTs. In particular, we study qudit Calderbank-Shor-Steane (CSS) codes as a special class of qudit stabilizer codes and the ensembles of the Narain code CFTs constructed from CSS codes. We obtain exact results for the averaged partition functions over the ensembles and discuss their implications for holographic duality.

Related papers

• 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)
• 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)
• Narain CFTs from nonbinary stabilizer codes [0.0]
  We generalize the construction of Narain conformal field theories (CFTs) We propose a correspondence between a quantum stabilizer code with non-zero logical qubits and a finite set of Narain CFTs.
  arXiv  Detail & Related papers  (2023-07-20T04:48:20Z)
• 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)
• Quantum Codes, CFTs, and Defects [0.0]
  We map a boundary RCFT to an $n$-qubit quantum code and describe this gauging at the level of the code. We give CFT interpretations of the code subspace and the Hilbert space of qubits while mapping error operations to CFT defect fields.
  arXiv  Detail & Related papers  (2021-12-22T19:00:19Z)
• 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)
• KO codes: Inventing Nonlinear Encoding and Decoding for Reliable Wireless Communication via Deep-learning [76.5589486928387]
  Landmark codes underpin reliable physical layer communication, e.g., Reed-Muller, BCH, Convolution, Turbo, LDPC and Polar codes. In this paper, we construct KO codes, a computationaly efficient family of deep-learning driven (encoder, decoder) pairs. KO codes beat state-of-the-art Reed-Muller and Polar codes, under the low-complexity successive cancellation decoding.
  arXiv  Detail & Related papers  (2021-08-29T21:08:30Z)
• 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)
• Quantum stabilizer codes, lattices, and CFTs [0.0]
  We show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs. More specifically, real self-dual stabilizer codes can be associated with even self-dual Lorentzian lattices. We dub the resulting theories code CFTs and study their properties.
  arXiv  Detail & Related papers  (2020-09-02T18:00:01Z)

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.