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 a 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 multiqubit 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 $\mathrm{\Delta }\tau$ in the Suzuki-Trotter approximation and find that $\mathrm{\Delta }\tau$ should be inversely proportional to $S$ in order to obtain the same accuracy for all $S$.

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• Quantum algorithms
• Quantum simulation
• Spin dynamics
• Spin chains