Bloch Sphere conversion

[stewdio]

Qubit needs methods for converting between matrices and Bloch Spheres. From 𝒂 and 𝒃 to θ and ϕ and back again. And also from θ and ϕ to XYZ; coordinates for the point on the surface of the sphere.

[stewdio]

Created Q.Qubit.toBlochSphere with b9550dd

But still do not have a Q.Qubit.fromBlochSphere. (Is this possible or is some phase information lost and therefore perfect conversion back is not possible?)

[marwahaha]

The only thing that seems to be lost is the "symbol" and the "name" of the Q.Qubit .

The idea for the Bloch sphere is that it captures all the information of a single qubit.

Edit: specifying complex $a$ and $b$ has extra information (i.e. 4 real numbers); so converting back you can only know the phase difference between $a$ and $b$.