Applying Grover’s algorithm to implement various numerical and comparison operations

Quantum search algorithm is used to perform fast data searching that finds data with high probability for any unstructured data. The quantum search algorithm searches data efficiently with fewer qubits and exploits the power of superposition. In this paper, using the quantum search algorithm, we have illustrated various arithmetic and comparison operations like addition, subtraction, multiplication, square, 1’s complement, 2’s complement, comparison operation, and palindrome. The generic structure of such operations is expressed in algorithms and quantum circuits for any size of binary numbers. All algorithms and analyses are parameterized with the size of the inputs, and some circuits are designed using the other’s circuit.