hiperwalk.ContinuousTime.uniform_state#
- ContinuousTime.uniform_state(vertices=None)#
Create a uniform state.
The uniform state is a unit vector with entries that have the same real amplitudes.
- Parameters:
- vertices: list of vertices, default=None
If
vertices is None, create the uniform superposition of all vertices. Otherwise, create the uniform superposition of the given vertices.
- Returns:
Notes
An example of the uniform state is
\[\ket{d} = \frac{1}{\sqrt{N}} \sum_{i = 0}^{N - 1} \ket{i}\]where \(N\) represents the dimension of the Hilbert space, and \(i\) is a label within the graph. In the continuous-time quantum walk model, \(i\) corresponds to the label of a vertex, while in the coined quantum walk model, \(i\) is the label of an arc.