In this paper, we design and analyse the Circuit for Grover’s Quantum Search Algorithm on 2, 3 and 4-qubit systems, in terms of number of gates, representation of state vectors and measurement probability for the state vectors. We designed, examined and simulated the quantum circuit on IBM Q platform using Quantum Programming Studio. We present the theoretical implementation of the search algorithm on different qubit systems. We observe that our circuit design for 2 and 4-qubit systems are precise and do not introduce any error while experiencing a small error to our design of 3-qubit quantum system.