Qudit Stabilizer Codes, CFTs, and Topological Surfaces

• URL: http://arxiv.org/abs/2311.13680v1
• Date: Wed, 22 Nov 2023 20:29:40 GMT
• Title: Qudit Stabilizer Codes, CFTs, and Topological Surfaces
• Authors: Matthew Buican and Rajath Radhakrishnan
• Abstract summary: We study maps from the space of rational CFTs with a fixed chiral algebra to the space of qudit stabilizer codes with a fixed generalized Pauli group. For CFTs admitting a stabilizer code description, we show that the full abelianized generalized Pauli group can be obtained from twisted sectors of certain 0-form symmetries of the CFT.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study general maps from the space of rational CFTs with a fixed chiral algebra and associated Chern-Simons (CS) theories to the space of qudit stabilizer codes with a fixed generalized Pauli group. We consider certain natural constraints on such a map and show that the map can be described as a graph homomorphism from an orbifold graph, which captures the orbifold structure of CFTs, to a code graph, which captures the structure of self-dual stabilizer codes. By studying explicit examples, we show that this graph homomorphism cannot always be a graph embedding. However, we construct a physically motivated map from universal orbifold subgraphs of CFTs to operators in a generalized Pauli group. We show that this map results in a self-dual stabilizer code if and only if the surface operators in the bulk CS theories corresponding to the CFTs in question are self-dual. For CFTs admitting a stabilizer code description, we show that the full abelianized generalized Pauli group can be obtained from twisted sectors of certain 0-form symmetries of the CFT. Finally, we connect our construction with SymTFTs, and we argue that many equivalences between codes that arise in our setup correspond to equivalence classes of bulk topological surfaces under fusion with invertible surfaces.

Related papers

• Topological stabilizer models on continuous variables [3.56772502352023]
  We construct a family of two-dimensional topological stabilizer codes on continuous variable (CV) degrees of freedom. We conjecture that these CV codes go beyond codes obtained from concatenating a topological qudit code with a local encoding into CVs.
  arXiv  Detail & Related papers  (2024-11-07T18:57:36Z)
• A holographic view of topological stabilizer codes [0.6290982779160698]
  We provide an explicit and general framework for understanding the bulk-boundary correspondence in Pauli topological stabilizer codes. We show that the boundary Hilbert space cannot be realized via local degrees of freedom. We show how linear and fractal subsystem symmetries naturally arise at the boundaries of fracton phases.
  arXiv  Detail & Related papers  (2023-12-07T19:00:00Z)
• Improving embedding of graphs with missing data by soft manifolds [51.425411400683565]
  The reliability of graph embeddings depends on how much the geometry of the continuous space matches the graph structure. We introduce a new class of manifold, named soft manifold, that can solve this situation. Using soft manifold for graph embedding, we can provide continuous spaces to pursue any task in data analysis over complex datasets.
  arXiv  Detail & Related papers  (2023-11-29T12:48:33Z)
• Holographic Codes from Hyperinvariant Tensor Networks [70.31754291849292]
  We show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states.
  arXiv  Detail & Related papers  (2023-04-05T20:28:04Z)
• Controlling the Complexity and Lipschitz Constant improves polynomial nets [55.121200972539114]
  We derive new complexity bounds for the set of Coupled CP-Decomposition (CCP) and Nested Coupled CP-decomposition (NCP) models of Polynomial Nets. We propose a principled regularization scheme that we evaluate experimentally in six datasets and show that it improves the accuracy as well as the robustness of the models to adversarial perturbations.
  arXiv  Detail & Related papers  (2022-02-10T14:54:29Z)
• Pauli stabilizer models of twisted quantum doubles [2.554567149842799]
  We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion phase of matter.
  arXiv  Detail & Related papers  (2021-12-21T17:53:48Z)
• Partial Counterfactual Identification from Observational and Experimental Data [83.798237968683]
  We develop effective Monte Carlo algorithms to approximate the optimal bounds from an arbitrary combination of observational and experimental data. Our algorithms are validated extensively on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-10-12T02:21:30Z)
• Finite-Function-Encoding Quantum States [52.77024349608834]
  We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions. We investigate some of their structural properties.
  arXiv  Detail & Related papers  (2020-12-01T13:53:23Z)
• 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)
• Tensor network models of AdS/qCFT [69.6561021616688]
  We introduce the notion of a quasiperiodic conformal field theory (qCFT) We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
  arXiv  Detail & Related papers  (2020-04-08T18:00:05Z)

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.