Possible Implementations of Oracles in Quantum Algorithms

Quantum computing is an inspiring technic on solving complicate problems, which shows the superiority over the classical computing. Contemporarily, the quantum-based algorithms were invented in many purposes on solving those problems. The thing is some of the algorithms were composed with oracles, which can be treated as a black box. It can be worked out/analyzed in theoretical mathematical expressions, but it can never fall in the ground without those actual implementations. Therefore, this paper will illustrate the idea and possible implementations on some quantum algorithm. Among various algorithms, this research will choose those relatively famous quantum algorithms, i.e., Deutsch-Jozsa Algorithm, Shor’s Algorithm, and Grover’s Algorithm. Different algorithms have the different intrinsic logics, which means there is no general description for all solution in this problem, but all of those can achieve the goal according to the same framework. Since those oracles are black boxes that can only be analyzed by its behavior with different cases, and then based on the behaviors and cases, and in IBM quantum platform, one can fill out the oracle by manipulate with different quantum operators. Lastly, the figures of some the possible implementation of those oracles with the three quantum algorithms will be shown in the IBM quantum platform, as well as the histograms of probability distributions that can justify the correctness of the implementations. These results shed light on guiding further exploration of the design and analysis on quantum algorithms.