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I am wondering how to simulate spin-1 systems with qiskit or on the IBMQ platform? I want to initialize a qudit (a spin-1 system), and then define the usual operations (such as Sx, Sy, and Sz) on the system. If you have any experience with this, it would be much appreciated.

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What you can do is access higher energy levels on a real backend with Qiskit Pulse as described in their tutorial.

You can excite for example from the ground state $| 0 \rangle$ to the first excitation $|1 \rangle$ with an $\pi$-pulse and use another $\pi$-pulse with the frequency that matches the 1 -> 2 transition to reach $| 2 \rangle$. Then you can map:

$|0 \rangle \mapsto | s=1, m_s= -1 \rangle$

$|1 \rangle \mapsto | s=1, m_s = 0 \rangle$

$|2 \rangle \mapsto | s=1, m_s = +1 \rangle.$

Of course the downside is that in practice the measured signal for the excitations do overlap.These are the results that I obtained with that method using IBM Q Ehningen (not a public backend).

Another possibility for theoretical computations with Qiskit is to use the density matrices from Qiskit Quantum Info by mapping the 2-qubit states:

$|00 \rangle \mapsto |s = 1, m_s = -1 \rangle$

$|01 \rangle \mapsto |s = 1, m_s = 0 \rangle$

$|10 \rangle \mapsto |s = 1, m_s = +1 \rangle$

and drop $|11 \rangle$. The drop corresponds to removing the last row and column of the density matrix.

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