IMPLEMENTING THREE-QUBIT GROVER’S ALGORITHM USING REAL QUANTUM PLATFORMS

Quantum computing is an innovative field that has opened up a whole new world of computational possibilities. At the forefront of this field is Grover's algorithm, a pioneering algorithm that has the remarkable ability to search an unsorted database quadratically faster than its classical counterparts. It harnesses the power of quantum mechanics, specifically quantum superposition and quantum parallelism, to explore a vast solution space simultaneously. In this work, we present an overview of Grover's algorithm, highlighting its key principles and proposing an implementation using fermionic quantum computing and a structured linear optics circuit in other cases. The approaches are technologically different, but both can implement Grover's algorithm. Our work aims to compare the two approaches, highlight their advantages and disadvantages, and try to conclude which one is the most promising for practical implementation. The former presented the advantage of having a simpler circuit schematisation and excellent scalability. Thanks to the use of the quantum properties of fermions, an essential feature of the algorithm, entanglement, can be easily achieved. The most evident disadvantage that was found is a lower probability of success than the theoretical one, due to a non-negligible decoherence of the quantum state due to the strong interaction with the environment by the fermions. The second has the advantage of being more flexible and easier to implement, as it is based on a more traditional and well-established approach: quantum linear optics, where bosons interact weakly with matter, and therefore, the phenomenon of decoherence is negligible. The disadvantage lies in the excessive difficulty of achieving entanglement without using non-linear optical subcircuits or ancillary quantum modes, and it has a low degree of scalability.