Deep dive into Grover’s algorithm

First of all, given the complexity of the topic and the relevance of this algorithm to the foundations of quantum algorithms and computation, I want to provide some notes about the notation and terms used in this chapter, and the approach that will help to formalize our mathematical formulas.

If we have a function f that maps binary strings of some length N to the binary code alphabet expressed in the following table, we refer to a query model problem searching inside an unstructured dataset. We have to find a solution to the function f (the input of our problem) inside an unstructured dataset. You might think of a solution of complicated equations that is able to crack an asymmetric or symmetric algorithm, or generically you can think of a combination that opens a lock of a strongbox. That is the scope of this algorithm in cryptography.

It is also useful to note that the solution might not even exist. This could happen when the name...