Adaptive variational ground state preparation of spin-1 models with multiple spin-qubit encodings

Recent advances in quantum computing hardware have stimulated the search for efficient quantum algorithms tailored for current noisy devices. One of the main targets of these algorithms are quantum spin models that cannot be solved efficiently on classical computers. Here, we focus on interacting spin-1 models, which are known to exhibit rich phase diagrams as they can contain local anisotropy terms, modeling crystal field effects of higher-S spin materials such as rare-earth magnets, including much sought-after quantum spin liquids. We investigate the optimal spin-to-qubit encoding scheme and apply it to use adaptive variational quantum imaginary time evolution to determine the ground state of a general XXZ spin-1 Hamiltonian in a transverse field. We compare the required CNOT gates of four different binary encodings: the standard binary, the triplet-singlet representation, the Gray code, and the unary. Our results show that the triplet-singlet and the Gray encoding are comparable and perform much better than the unary encoding.