# Visualizing quantum walks on small graphs

This page has all the Julia code necessary for creating the images; as such, it must begin with a couple of trivialities, as loading the dependencies and defining the adjacency matrix of a graph.

31.4 μs
47.7 s
adjacency_matrix (generic function with 2 methods)
258 μs

# Quantum Walk representation

I am representing a quantum walk as the adjacency matrix of the graph.

25.5 μs
QuantumWalk
9.8 ms

I also created a custom heatmap function for displaying the matrices.

25.9 μs
heatmap (generic function with 1 method)
160 μs

Then it is easy to create an animation: Just iterate over a bunch of times and display the component-wise absolute value of $\mathrm{exp}\left(itA\right)$.

27.9 μs
animate (generic function with 1 method)
233 μs
14.4 ms

# Visualizations

I can now display some quantum walks. I will show for ${P}_{2}$ and for ${P}_{3}$ at their respective periods.

34.1 μs
31.5 s