Quantum computers will eventually reach a size at which quantum error correction (QEC) becomes imperative. In order to make quantum information robust to errors introduced by qubit imperfections and flawed control operations, QEC protocols encode a logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent correction or detection of errors without destroying the logical state itself through direct measurement. While several experiments have shown a reduction of high intrinsic or artificially introduced errors in logical qubits, fault-tolerant encoding of a logical qubit has never been demonstrated. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. This advantage persists in the face of large added error rates and experimental calibration errors.

1 aLinke, N., M.1 aGutierrez, M.1 aLandsman, K., A.1 aFiggatt, C.1 aDebnath, S.1 aBrown, K., R.1 aMonroe, C. uhttps://arxiv.org/abs/1611.06946