Observing the effect of amplitude amplification

We have already learned that, in a quantum system, we can have 2n states, where n is the number of qubits. One of the advantages of a quantum computer is that you can control those variables. For example, let’s say that we want to embed a number, such as 2, in a quantum computer so that when we measure the quantum system, the variable 2 (or 10 in binary) shows up with the highest probability possible. How could we selectively add these desired numbers to a quantum circuit?

Let’s work through this example, which is a slightly different way to approach amplitude amplification, though I hope it will make the whole process clearer.

Our goal is to measure the desired numbers in the output with high probability; the remaining numbers should have a low probability. One way to do this would be by creating a matrix that stores our numbers and then running an operator that will amplify the amplitude of those numbers.

We...