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The 1D Quantum Heisenberg model is

$$H_\textrm{Heisenberg} = -~J \sum_{\langle i\ j\rangle} \hat{S}_{i} \cdot \hat{S}_{j}$$

where each spin is an operator.

For simple cases, for example, a system with only 3 spins or 5 spins, how to get eigenvalues (energy levels) of Hamiltonian of this system using existing real Quantum Computers? (either IBM QC or QC on Amazon brakets, which supports: D-Wave, IonQ, or Rigetti QC.)

I searched online, and some articles talked about how to build quantum circuits for the Hamiltonian, but I did NOT know how to get eigenvalues of those Hamiltonian.

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