The effect of the Hadamard gate decomposition in the simulation of Grover's algorithm


Simulation of Grover’s algorithm in an Ising nuclear spin chain computer with first- and second-nearest neighbor interaction is considered. The most frequently used quantum gate in the algorithm is the Hadamard gate. We investigate the effect of its decomposition into several rotation matrices and numerically calculate the fidelity and probability of success of finding the target state. Using an appropriate decomposition, we obtain a high fidelity for different numbers of iterations. The probability of finding the target state also increased and is much closer to the ideal result.