Bloch sphere implementation

[niccololaurora]

I added a visualization method which implements a Bloch Sphere. This tool could be useful to plot the final states of a classification task.
Example:

state = np.array([1, 0], dtype="complex")
b_sphere = Bloch()
b_sphere.add_vector(state, mode="vector", color="black")
b_sphere.save_plot("b_sphere.pdf")
b_sphere.plot()

[MatteoRobbiati]

Thanks a lot for this @niccololaurora!
Some suggestions follow.

[MatteoRobbiati]

I think it would be more natural to use it as follows:

state = circuit.execute().state()
bs = Bloch(state=state)
bs.plot(save=True) 

Then one can just update the cached state as bs.set_state(state=new_state).
I think this would be lighter and intuitive.

[niccololaurora]

Thank you Matteo for the suggestions.

I may be mistaken, but I don't think the concept of a "cached state" would be useful in this context. Based on my experience, I often find myself needing to plot multiple states. Therefore, a natural approach is to create a Bloch object and then add states to it.

state = np.array([1, 0])
bs = Bloch()
bs.add_state(state)

I will implement the option to pass both a single state (already possible) and a list of states to the add_state function.
Additionally, I have introduced the options of "color" and "mode":

• Color: In classification tasks, it may be necessary to plot final states associated with different classes, with each class represented by a different color.
• Mode: "vector" or "point". When plotting many states, a point on the sphere is often clearer and cleaner than a cluster of arrows.

Here I have an example:
sfera_a_q1_l1.pdf]

As evident from the uploaded image, it is challenging to distinguish points at the front and back of the sphere. Hence, I plan to implement a method to blur the color of points on the sphere based on their distance from the observer's perspective. Additionally, another approach could involve saving the image as an .html file, enabling users to interact with the sphere by rotating it to view it from different angles.
Implementing both options is also feasible.

[MatteoRobbiati]

This function should be very problem dependent, right?
If your idea is to encode a 3d polygon inside the sphere, then I would suggest to just define a method bs.distribute_labels_on_surface or bs.inscribed_solid(n_vertexes=10). This will be very useful to show the inscribed solid and also, if needed, to return the label states corresponding to the vertexes.

[niccololaurora]

The function label_states (maybe it could be renamed to something more intuitive) plots the fidelity label states on the Sphere.
I added a flag which if is True, it plots also the 3d polygon, which is supported when there are at least 4 classes

nclasses = 4
bs = Bloch()
label_states = bs.label_states(nclasses, solid=False)

bloch_sphere_4.pdf
bloch_sphere_N4.pdf