We apply the adaptive variational quantum imaginary time evolution (AVQITE)
method to prepare ground states of one-dimensional spin S=1 models. We
compare different spin-to-qubit encodings (standard binary, Gray, unary, and
multiplet) with regard to the performance and quantum resource cost of the
algorithm. Using statevector simulations we study two well-known spin-1 models:
the Blume-Capel model of transverse-field Ising spins with single-ion
anisotropy, and the XXZ model with single-ion anisotropy. We consider system
sizes of up to 20 qubits, which corresponds to spin-1 chains up to length
10. We determine the dependence of the number of CNOT gates in the AVQITE
state preparation circuit on the encoding, the initial state, and the choice of
operator pool in the adaptive method. Independent on the choice of encoding, we
find that the CNOT gate count scales cubically with the number of spins for the
Blume-Capel model and quartically for the anistropic XXZ model. However, the
multiplet and Gray encodings present smaller prefactors in the scaling
relations. These results provide useful insights for the implementation of
AVQITE on quantum hardware.Comment: 11 pages, 6 figure