Error budget investigation of an ion-trap based quantumcomputer

Trapped ions are a promising platform for reaching quantum-computation at or beyond fault tolerance level. The long qubit coherence time and low gate error-rates demonstrate important steps towards this goal~[1]. Our group has recently demonstrated low error rate entanglement operations based on near-field oscillating magnetic field gradients~[2][3]. We give a detailed road-map towards pushing the error in the two-qubit gate operations towards or below the $10^{-4}$ per gate level by means of a detailed numerical study of the computation register and associated physical processes.