Type hierarchies · QuantumWalk

Type hierarchy

The package consists of two main type hierarchies: quantum walk model hierarchy, which is simply a description of the quantum walk model, and quantum walk dynamics, which are used for quantum walk analysis or simulation. The first one should in general be small, and should consist only of general parameters used in most of the models. Second one should possess all information needed for efficient simulation/analysis. For example CTQW model should consist of graph, on which the evolution is made and label which implies if adjacency or Laplacian matrix is used. Contrary QWEvolution{CTQW} should consist of Hamiltonian used for evolution.

Quantum walk models hierarchy

The main supertype is QWModel. As typically discrete and continuous evolution are simulated and analysed using different techniques, QWModelCont and QWModelDiscr are its direct subtypes. Furthermore every model have its direct abstract supertype, which is at least similar in the sense of implemented function to the supertype.

Any instance of quantum walk model consists of graph on which evolution is made. Such graph can be accessed via graph function. Hence an typical definition of quantum walk model type takes the from

struct Model <: AbstractModel
   graph::Graph
   ...
   function Model(graph::Graph, ...)
      ...
      new(graph, ...)
   end
end

At the moment CTQW and Szegedy walks are implemented. Note that arbitrary quantum walk model should consist of measure, evolve and check_qwdynamics for basic pure walk simulation implemented in QWEvolution.

Quantum dynamics hierarchy

The main supertype is QWDynamics. As the algorithms and analysis usually differs strongly, subtypes of QWDynamics should be mostly a composite types.

Any QWDynamics should consist of at least two parameters: model::QWModel, which is a quantum walk model, and parameters::Dict{Symbol,Any}, which is a dictionary consisting of values needed for model. Elements are accessible via function with the same name. In order to check correctness, check_qwdynamics should always be executed in the constructor. Typical quantum walk dynamics are defined as follows.

struct Dynamics{T} <: QWDynamics{T}
  model::T
  parameters::Dict{Symbol}
  ...

  function Dynamics(model::T, parameters::Dict{Symbol}, ...) where T<:QWModel
     ...
     check_qwdynamics(Dynamics, model, parameters, ...)
     ...
     new(model, parameters, ...)
  end
end

At the moment QWEvolution for pure walk evolution and QWSearch for quantum spatial search are implemented. All dynamics provides execute functionality, together with its variation.