How to generate a Hadamard Gate in Spin 1 NMR?

I am studying about the gate controllability of Spin 1 systems and I would like make a Hadamard gate using only X,Y rotations and the offset. I want to do this without invoking techniques for making engineered pulses like GRAPE etc. I wrote a code which randomly generates the rotation angle about the X,Y,Z axes while trying to minimize the infidelity between the generated gate and the desired Hadamard Gate. This program gave the pulse rotations needed to prepare Hadamard Gate for spin 1/2 systems. But when I try something similar for Spin 1 systems I am not able to get Hadamard Gate. Thank you in advance for your answers

• As I don't totally understand what you are asking I'm not sure, but this might be better asked in quantumcomputing.stackexchange.com Oct 8, 2021 at 7:53