Numerical Simulation of the Performance of Single Qubit Gates for Trapped Ions

Finite gate errors limit performance of modern quantum computers. In this work, we study single qubit gate fidelities for trapped ions. For this we have numerically solved Schrödinger equation using full Hamiltonian of the system for one, two, three and four ions. This approach allows us to analyze gate errors beyond the LambDicke approximation and to take into account not only a finite occupation of the phonon modes, but also the effects related to the ion–phonon 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.