  Quantum error correction requires the detection of errors by reliable
measurements of suitable multi-qubit correlation operators. Here, we
experimentally demonstrate a fault-tolerant weight-4 parity check measurement
scheme. An additional 'flag' qubit serves to detect errors occurring throughout
the parity measurement, which would otherwise proliferate into uncorrectable
weight-2 errors on the qubit register. We achieve a flag-conditioned parity
measurement single-shot fidelity of 93.2(2)\%. Deliberately injecting bit and
phase-flip errors, we show that the fault-tolerant protocol is capable of
reliably intercepting such faults. For holistic benchmarking of the parity
measurement scheme, we use entanglement witnessing to show that the implemented
circuit generates genuine six-qubit multi-partite entanglement. The
fault-tolerant parity measurement scheme is an essential building block in a
broad class of stabilizer quantum error correction protocols, including
topological color codes. Our hardware platform is based on atomic ions stored
in a segmented microchip ion trap. The qubit register is dynamically
reconfigured via shuttling operations, enabling effective full connectivity
without operational cross-talk, which provides key capabilities for scalable
fault-tolerant quantum computing.
