Comparison of encoding schemes for quantum computing of $S > 1/2$ spin chains

We compare four different encoding schemes for the quantum computing of spin chains with a spin quantum number $S>1/2$: a compact mapping, a direct (or one-hot) mapping, a Dicke mapping, and a qudit mapping. The three different qubit encoding schemes are assessed by conducting Hamiltonian simulation for $1/2 \le S \le 5/2$ using a trapped-ion quantum computer. The qudit mapping is tested by running simulations with a simple noise model. The Dicke mapping, in which the spin states are encoded as superpositions of multi-qubit states, is found to be the most efficient because of the small number of terms in the qubit Hamiltonian. We also investigate the $S$-dependence of the time step length $\Delta\tau$ in the Suzuki-Trotter approximation and find that, in order to obtain the same accuracy for all $S$, $\Delta\tau$ should be inversely proportional to $S$.