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I think it is extremely important after learning linear algebra exactly what context that quantum bits become useful. Otherwise if we focus too much on the math, it can start becoming a bit complicated. Here are some essential diagrams to understand.
The TL;DR version of this section is: given that qubits are connected to complex numbers, use imaginary complex sphere for their representation, and worry about angles and lattitudes.
Let’s see why is this the case. Consider the case of a quantum state:
|\psi\rangle = c_{0}\cdot|0\rangle + c_{1} \cdot |1\rangle
Reminder:
|c_{0}|^2 + |c_{1}|^2 = 1
where
c_{i} \in \mathbb{C}
Using the polar representation of a complex number, we have the following two equivalent representations:
c_{0} = r_{0} ^{ej\varphi_{0}} + r_{1}e^{j\varphi_{1}}
c0=r0ejφ0 and c1=r1ejφ1c0=r0ejφ0 and c1=r1ejφ1
where $riri$ are the amplitudes and φiφi are the angles. Thus, each individual number cici can be represented with a unit imaginary circle.
The unit circle (including imaginary complex numbers)
!
The bloch sphere representation also depicts the same information as above: