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We apply the adaptive variational quantum imaginary time evolution (AVQITE)method to prepare ground states of one-dimensional spin $S=1$ models. Wecompare different spin-to-qubit encodings (standard binary, Gray, unary, andmultiplet) with regard to the performance and quantum resource cost of thealgorithm. Using statevector simulations we study two well-known spin-1 models:the Blume-Capel model of transverse-field Ising spins with single-ionanisotropy, and the XXZ model with single-ion anisotropy. We consider systemsizes 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 AVQITEstate preparation circuit on the encoding, the initial state, and the choice ofoperator pool in the adaptive method. Independent on the choice of encoding, wefind that the CNOT gate count scales cubically with the number of spins for theBlume-Capel model and quartically for the anistropic XXZ model. However, themultiplet and Gray encodings present smaller prefactors in the scalingrelations. These results provide useful insights for the implementation ofAVQITE on quantum hardware.

Adaptive variational ground state preparation for spin-1 models on qubit-based architectures