Understanding the basics of a qubit

A qubit is dramatically different from a classical bit because it stores more information than the single binary value that a classical bit can store. A quantum bit can be pictured as a sphere with a vector pointing at any point on that sphere. The top of the sphere is the zero-state, shown as |0⟩, while the bottom of the sphere is the one-state, shown as |1⟩. These two states can be represented in matrix form as follows:

However, we said that a qubit represents all the points on a sphere, called a Bloch sphere. So, these states can be represented as a combination of two state vectors:

Here, α0 and α1 are complex numbers.

Since α0 and α1 are complex numbers, they include both a real component and an imaginary phase component. We will represent this as a rotation about the vertical z-axis of the Bloch sphere:

Here, 𝜸 is...