I am trying to simulate this Hamiltonian on IBM Qiskit, for varying values of $\theta$:

$H(\theta) = B(\sin\theta S_1^x +\cos\theta S_1^z +\sin\theta S_2^x +\cos\theta S_2^z)+aS_2^zI_z$

Where S is electron spin and I is nuclear spin which is treated as an effective magnetic field of $\pm \frac{1}{2}$, a is a hyperfine coupling constant.

I have attempted splitting this Hamiltonian into two non-commuting parts, and doing a Trotter Approximation.

I've tried using an Rx gate on both Qubit 1 and 2 with rotation angle of $Bt\sin\theta$ and Rz gate on Qubit 1 with rotation angle of $Bt\cos\theta$ and Rz gate on Qubit 2 with rotation angle of $Bt\cos\theta \pm \frac{a}{2}$ (repeating twice, once with + once with -). This is my first simulation and I am trying to replicate result in the graph of this paper - linked here https://link.springer.com/content/pdf/10.1007/s11433-016-0376-6.pdf, I am unable to produce similar results. Particularly, I'm struggling with knowing what to use for t. Any help would be appreciated (please try to use layman's terms, if possible)!



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