  We consider the feasibility of studying the anisotropic Heisenberg quantum
spin chain with the Variational Quantum Eigensolver (VQE) algorithm, by
treating Bethe states as variational states, and Bethe roots as variational
parameters. For short chains, we construct exact one-magnon trial states that
are functions of the variational parameter, and implement the VQE calculations
in Qiskit. However, exact multi-magnon trial states appear to be out out of
reach.
