The quantum oracle algorithm par excellence is the GROVER algorithm, so how to prove that the oracle needed for example for the GROVER algorithm is complete, and how to prove that it is realizable through quantum gates? In addition, let’s explore the nonlinear activation function which is difficult to realize in quantum machine learning. Is it possible to think of the softmax activation function as an oracle as well, except that it performs the operation: exp(A_i)/sum(exp(A_i)) on a matrix. Can it be converted to a quantum oracle? Is it possible to prove that it is quantum gate realizable? What I mean by completeness is to describe an oracle in a verbal format, and to include at least the necessary and sufficient conditions to ensure that the oracle can implement the desired functions without defects. That is, the minimum conditions that can fully describe an oracle. And how to prove that these conditions or requirements are complete, sufficient and necessary. It’s kind of like, well, the propositions we have in high school math class. The minimum number of conditions we need to prove an axiom that we think exists is mathematically necessary and sufficient to constitute a necessary and sufficient condition. Missing one, the result of that axiom will have no solution or multiple solutions. The other topic is once we have confirmed that the required conditions can be constructed completely and accurately for oracle. Prove whether these conditions can be constructed on a superconducting quantum computer, i.e., the quantum operatorization of the conditions. I would like to ask scholars majoring in mathematics or quantum theoretical physics to help answer this question.
Hi @RX1
Seems like a more theoretical question indeed. Let’s see if other people have more opinions. If not, you could also post it in more general physics forums.
Regarding the part about the implementation of Grover’s algorithm, I could suggest you to read the Codebook module about Grover’s search, in particular the topic on Searching with circuits that shows how to implement the oracle and the diffusion operator.
To build intuition about the oracle, you can check this Codebook topic as well.
I hope this was helpful.