A Naive Implementation of Logical Expression in Quantum Computing

In this paper, we present a straightforward implementation of a logical expression in quantum computing. We develop a quantum oracle for our logical expression and implement it using Grover's algorithm. The logical expression comprises two variables and two clauses involving the XOR and AND operators. For this expression, we require two qubits as variables, one qubit as the oracle, and one qubit as an ancilla. Additionally, we utilise CNOT and Toffoli gates to construct the quantum oracle. We then design its quantum circuit and execute it on a simulator. The implementation yields the quantum state of a two-qubit quantum system as the solution to our logical expression.