  The quest of demonstrating beneficial quantum error correction in near-term
noisy quantum processors can benefit enormously from a low-resource
optimization of fault-tolerant schemes, which are specially designed for a
particular platform considering both state-of-the-art technological
capabilities and main sources of noise. In this work, we show that
flag-qubit-based fault-tolerant techniques for active error detection and
correction, as well as for encoding of logical qubits, can be leveraged in
current designs of trapped-ion quantum processors to achieve this break-even
point of beneficial quantum error correction. Our improved description of the
relevant sources of noise, together with detailed schedules for the
implementation of these flag-based protocols, provide one of the most complete
microscopic characterizations of a fault-tolerant quantum processor to date. By
extensive numerical simulations, we provide a comparative study of flag- and
cat-based approaches to quantum error correction, and show that the superior
performance of the former can become a landmark in the success of near-term
quantum computing with noisy trapped-ion devices.
