  We suggest using the method of quantum annealing for computing the ground
state of the Heisenberg spin chains. Our initial Hamiltonian describes a spin
system in a highly non-uniform magnetic field. The initial Hamiltonian
gradually transforms into the Heisenberg Hamiltonian, which describes the
exchange interaction and the Zeeman interaction with the uniform magnetic
field. We demonstrate quantum annealing for 2-, 3-, and 9-spin systems. In
particular, we consider the alternate (ferro- and antiferromagnetic) exchange
integral. By changing the sign of the exchange integrals we switch from the
frustrated to the corresponding non-frustrated spin system. We discuss the
similarity and difference between the frustrated and non-frustrated spin
systems.
