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We study how to simulate, efficiently, pulse field gradients (PFG) used in nuclear magnetic resonance (NMR). An efficient simulation requires discretization in time and space. We study both discretizations and provide a guideline to choose best discretization values depending on the precision required experimentally. We provide a theoretical study and simulation showing the minimum number of divisions we need in space for simulating, with high precision, a sequence composed of several unitary evolution and PFG. We show that the fast simulation of PFG allow us to optimize sequences composed of PFG, radio-frequency pulses and free evolution, to implement non-unitary evolution (quantum channels). As an evidence of the success of our work, we performed two types of experiments. First, we implement two quantum channels and compare the results with their theoretical predictions. In the second experiment, we used the fast simulation of PFG to optimize and implement a sequence to prepare pseudo pure state with better signal to noise ratio than any known procedure till now.