Finite gate errors limit performance of modern quantum computers. In this paper we study single qubit gate fidelities for trapped ions. For this we numerically solved Schrodinger equation using full Hamiltonian of the system for one, two, three and four ions. This approach allows us to analyse gate errors beyond Lamb-Dicke approximation and accounts not only for finite occupation of the phonon modes, but also for the effects related to the ions-to-mode entanglement. As a result, we show, how infidelity of the global single qubit gates depend on the initial phonon mode occupations, the Lamb-Dicke parameter, Rabi frequency and the number of ions.
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