Throughout our everyday lives we are exposed to computation on a massive scale. Everyting from the phone in your pocket to the supercomputers of industry like Google. But there is one significant aspect that ties all of these together... and that is that every bit of information can and is represented by a sequence of 1's and 0's.
Although that may not seem problematic, it does have a big drawback. Consider conventional memory of 11 bits, this stores one binary number up to 2047. Now compare that to a register of 11 qubits, which stores all of the numbers from 0 to 2048. Now that is a huge improvement.
Now that we have our all-mighty qubits, we need a way to represent them, and also more specifically a way to visualise changes that occur on them. Low and a behold such a device exists! Utilising what is known as the Bloch Sphere to represent qubits as a 3-dimensional vector in Hilbert space... That was probably quite a mouthful, so rather than speaking mathematical gibberish lets take a look at this sphere.
The principle behind the Bloch Sphere is that we have the poles at the top and bottom represent a complete 1 state (up) and 0 state (down).
We write these in Bra-Ket notation |1> and |0>. But because we are talking quantum bits, we can represent more than just 1 and 0, rotating the position
on the sphere by 180 degrees we get a superpositon between the two, written as: |Ψ> = ½|0> + ½|1>. This shows that the state (when measured) has a
50/50 chance of being 1 or 0, as shown by the coefficients of |0> and |1>. Changing the positon of |Ψ>, represents different states.
Each of which is related to the values of theta (θ) and phi (φ).
