  Physical qubits in experimental quantum information processors are inevitably
exposed to different sources of noise and imperfections, which lead to errors
that typically accumulate hindering our ability to perform long computations
reliably. Progress towards scalable and robust quantum computation relies on
exploiting quantum error correction (QEC) to actively battle these undesired
effects. In this work, we present a comprehensive study of crosstalk errors in
a quantum-computing architecture based on a single string of ions confined by a
radio-frequency trap, and manipulated by individually-addressed laser beams.
This type of errors affects spectator qubits that, ideally, should remain
unaltered during the application of single- and two-qubit quantum gates
addressed at a different set of active qubits. We microscopically model
crosstalk errors from first principles and present a detailed study showing the
importance of using a coherent vs incoherent error modelling and, moreover,
discuss strategies to actively suppress this crosstalk at the gate level.
Finally, we study the impact of residual crosstalk errors on the performance of
fault-tolerant QEC numerically, identifying the experimental target values that
need to be achieved in near-term trapped-ion experiments to reach the
break-even point for beneficial QEC with low-distance topological codes.
