  Excited states of spin-chains play an important role in condensed matter
physics. We present a method of calculating the single magnon excited states of
the Heisenberg spin-chain that can be efficiently implemented on a quantum
processor for small spin chains. Our method involves finding the stationary
points of the energy vs wavenumber curve. We implement our method for 4-site
and 8-site Heisenberg Hamiltonians using numerical techniques as well as using
an IBM quantum processor. Finally, we give an insight into the circuit
complexity and scaling of our proposed method.
