Non-rational Narain CFTs from codes over $F_4$

• URL: http://arxiv.org/abs/2107.02816v1
• Date: Tue, 6 Jul 2021 18:00:06 GMT
• Title: Non-rational Narain CFTs from codes over $F_4$
• Authors: Anatoly Dymarsky and Adar Sharon
• Abstract summary: We construct a map between a class of codes over $F_4$ and a family of non-rational Narain CFTs. This construction is complementary to a recently introduced relation between quantum stabilizer codes and a class of rational Narain theories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We construct a map between a class of codes over $F_4$ and a family of non-rational Narain CFTs. This construction is complementary to a recently introduced relation between quantum stabilizer codes and a class of rational Narain theories. From the modular bootstrap point of view we formulate a polynomial ansatz for the partition function which reduces modular invariance to a handful of algebraic easy-to-solve constraints. For certain small values of central charge our construction yields optimal theories, i.e. those with the largest value of the spectral gap.

Related papers

• Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields [0.0]
  We identify Narain conformal field theories (CFTs) that correspond to code lattices for quantum error-correcting codes (QECC) over integers of cyclotomic fields $Q(zeta_p)$ $(zeta_p=efrac2pi ip)$ for general prime $pgeq 3$.
  arXiv  Detail & Related papers  (2024-10-16T12:08:04Z)
• 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)
• 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)
• Classical Codes and Chiral CFTs at Higher Genus [0.0]
  We derive explicit expressions for the higher genus partition functions of a specific class of CFTs: code CFTs. This work provides a step towards a full understanding of the constraints from higher genus modular invariance on 2d CFTs.
  arXiv  Detail & Related papers  (2021-12-09T19:00:04Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Permutation Compressors for Provably Faster Distributed Nonconvex Optimization [68.8204255655161]
  We show that the MARINA method of Gorbunov et al (2021) can be considered as a state-of-the-art method in terms of theoretical communication complexity. Theory of MARINA to support the theory of potentially em correlated compressors, extends to the method beyond the classical independent compressors setting.
  arXiv  Detail & Related papers  (2021-10-07T09:38:15Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• Near-Optimal Regret Bounds for Contextual Combinatorial Semi-Bandits with Linear Payoff Functions [53.77572276969548]
  We show that the C$2$UCB algorithm has the optimal regret bound $tildeO(dsqrtkT + dk)$ for the partition matroid constraints. For general constraints, we propose an algorithm that modifies the reward estimates of arms in the C$2$UCB algorithm.
  arXiv  Detail & Related papers  (2021-01-20T04:29:18Z)
• On Function Approximation in Reinforcement Learning: Optimism in the Face of Large State Spaces [208.67848059021915]
  We study the exploration-exploitation tradeoff at the core of reinforcement learning. In particular, we prove that the complexity of the function class $mathcalF$ characterizes the complexity of the function. Our regret bounds are independent of the number of episodes.
  arXiv  Detail & Related papers  (2020-11-09T18:32:22Z)
• 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)
• Free Energy Wells and Overlap Gap Property in Sparse PCA [81.64027805404483]
  We study a variant of the sparse PCA (principal component analysis) problem in the "hard" regime. We show bounds on the depth of free energy wells for various Gibbs measures naturally associated to the problem. We prove that the Overlap Gap Property (OGP) holds in a significant part of the hard regime.
  arXiv  Detail & Related papers  (2020-06-18T17:18:02Z)

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.