# How to simulate spin-1 systems with qiskit or on the IBMQ platform?

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.

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.

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.