# Visualizing qubits in boxes

A qubit (quantum bit) can take values 0 or 1, and also any value between them.

The above statement looks like the notion of probability: the sum must be 100% and the values are less than one.

An important difference: the qubit domain is a complex number, not a real number. This gives rise to a further dimension to be explored.

Therefore, the correct way to visualize the status of a qubit is through the Bloch Sphere, because it captures the phase of a complex number.

However, visualization in the Bloch Sphere is difficult. And several of the quantum algorithms can be explained by a simpler notion.

A simplified visualization can be simply to represent the probability of 0 or 1 of the qubit (being aware that we are not capturing all its complexity).

Thus, |0> can be a white box, |1> can be a hatched box.

A state (| 0> + | 1>) / sqrt (2) gives an equal probability of 0 or 1, so it would be fifty-fifty.

Note that the state (|0> -|1>) / sqrt (2), with a 180 degree phase in the |1> component, also gives exactly the same probability (that is, this way of visualizing is simple, but we lose the phase information).

One last example. A state (sqrt (3) | 0> + | 1>) / 2 will give a 75% chance of 0 and a 25% chance of 1. The boxes will be proportional to this probability.

Post on Bloch Sphere: https://informacaoquantica.wordpress.com/2019/09/21/alguns-plots-na-esfera-de-bloch/

Technical ideas with a bit of philosophy: