Subfactors from regular graphs induced by association schemes

• URL: http://arxiv.org/abs/2201.07310v4
• Date: Mon, 27 Nov 2023 14:25:55 GMT
• Title: Subfactors from regular graphs induced by association schemes
• Authors: Radhakrishnan Balu
• Abstract summary: We set up quantum walks on growing distance-regular graphs induced by association schemes via interacting Fock spaces. We discuss in detail a large family of graphs that may be treated within this approach.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We clarify the relations between the mathematical structures that enable fashioning quantum walks on regular graphs and their realizations in anyonic systems. Our protagonist is association schemes that may be synthesized from type-II matrices which have a canonical construction of subfactors. This way we set up quantum walks on growing distance-regular graphs induced by association schemes via interacting Fock spaces and relate them to anyon systems described by subfactors. We discuss in detail a large family of graphs that may be treated within this approach. Classification of association schemes and realizable anyon systems are complex combinatorial problems and we tackle a part of it with a quantum walk application based approach.

Related papers

• Graphical Symplectic Algebra [0.0]
  We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical systems, as well as odd-prime-dimensional stabiliser quantum circuits.
  arXiv  Detail & Related papers  (2024-01-15T19:07:33Z)
• Integrating Subsystem Embedding Subalgebras and Coupled Cluster Green's Function: A Theoretical Foundation for Quantum Embedding in Excitation Manifold [5.735524739317933]
  We introduce a novel approach to coupled-cluster Green's function (CCGF) embedding by seamlessly integrating CCGF theory and SES-CC formalism. Our work paves the way for the quantum mechanical description of multiple embedded domains. This expansion holds significant promise for the exploration and application of non-equilibrium quantum systems.
  arXiv  Detail & Related papers  (2023-10-26T05:52:36Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• Quantum walks on regular graphs with realizations in a system of anyons [0.0]
  We build interacting Fock spaces from association schemes and set up quantum walks on regular graphs. In the dual perspective interacting Fock spaces gather a new meaning in terms of anyon systems.
  arXiv  Detail & Related papers  (2021-09-22T18:01:20Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• Structural Landmarking and Interaction Modelling: on Resolution Dilemmas in Graph Classification [50.83222170524406]
  We study the intrinsic difficulty in graph classification under the unified concept of resolution dilemmas'' We propose SLIM'', an inductive neural network model for Structural Landmarking and Interaction Modelling.
  arXiv  Detail & Related papers  (2020-06-29T01:01:42Z)
• Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case [0.0]
  We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit. We incidentally point out a possible interpretation of the Q-SSEP correlation functions via a surprising conneatorics and the associahedron polytopes.
  arXiv  Detail & Related papers  (2020-06-22T13:20:40Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.