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)!



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.