Impact of various IBM Quantum architectures with different properties on Grover's algorithm

Quantum computing and quantum algorithms have been said to be able to provide significant speed-up over classical computation with classical algorithms by exploiting the nature of quantum mechanical systems. In this work, we will study the qubit architecture of quantum systems available at IBM Quantum (IBM-Q) such as the properties of the qubit system, the qubit layout and connectivity as well as the transpilation process of circuits and its effects to the circuits. We investigate the correspondence between limited and sparse connectivity and connected physical qubits to Grover's algorithm implementation of 2 and 3 qubits. We will also test Grover's algorithm on the different connectivity available on four IBM-Q systems for 2, 3, 4 and 5 qubits using optimization level of 0, 1, 2 and 3 to compare the circuit depth of the transpiled circuits as well as their execution times. This work will provide guidance for researchers on the important factors to consider before implementing a quantum algorithm on a real quantum system.