  A major challenge in practical quantum computation is the ineludible errors
caused by the interaction of quantum systems with their environment.
Fault-tolerant schemes, in which logical qubits are encoded by several physical
qubits, enable correct output of logical qubits under the presence of errors.
However, strict requirements to encode qubits and operators render the
implementation of a full fault-tolerant computation challenging even for the
achievable noisy intermediate-scale quantum technology. Here, we experimentally
demonstrate the existence of the threshold in a special fault-tolerant
protocol. Four physical qubits are implemented using 16 optical spatial modes,
in which 8 modes are used to encode two logical qubits. The experimental
results clearly show that the probability of correct output in the circuit,
formed with fault-tolerant gates, is higher than that in the corresponding
non-encoded circuit when the error rate is below the threshold. In contrast,
when the error rate is above the threshold, no advantage is observed in the
fault-tolerant implementation. The developed high-accuracy optical system may
provide a reliable platform to investigate error propagation in more complex
circuits with fault-tolerant gates.
