9.6 Amplitude amplification and interference

Suppose we have three qubits, and one of their quantum state standard basis kets {|000⟩, …, |111⟩} corresponds to a solution to some problem. We want to devise an algorithm to pick the correct ket and find the answer. I’m purposely not telling you the problem or how the kets map to the data and solution. Just assume we want to identify one of them that the algorithm can determine as best. algorithm$amplitude amplification amplitude$amplification

The first question is how to see that this best ket stands out from the others. The general form for a 3-qubit quantum register state is

with

If we initialize each qubit to |0⟩ and then apply H^⊗3, we get a balanced superposition: balanced superposition superposition$balanced

All the coefficients are equal, and the square of each absolute value is 1/8. If we measure the qubits now, we have an...