In this paper we develop a classical algorithm of complexity (O(K \, 2^n)) to simulate parametrized quantum circuits (PQCs) of (n) qubits, where (K) is the total number of one-qubit and two-qubit control gates. The algorithm is developed by finding (2)-sparse unitary matrices of order (2^n) explicitly corresponding to any single-qubit and two-qubit control gates in an (n)-qubit system. Finally, we determine analytical expression of Hamiltonians for any such gate and consequently a local Hamiltonian decomposition of any PQC is obtained. All results are validated with numerical simulations.