Here, we demonstrate the exceeding of the QEC break-even point by real-time feedback correction for a discrete-variable photonic qubit in a microwave cavity, whose code words remain mutually orthogonal and can be unambiguously discriminated.
The key stages of a QEC procedure are encoding the quantum information to the logical qubit from the auxiliary qubit, the error syndrome measurement, the real-time error correction of the system depending on the measurement output and the decoding process to read out the quantum information stored in the logical qubit. Our logical qubit is realized in a three-dimensional microwave cavity, and the dominant decoherence to combat is the excitation loss error.
where the number in each ket denotes the photon number in the cavity. The binomial code is a typical stabilizer QEC code: when the single-photon-loss error occurs, the quantum information is projected into the error space spanned by, with the photon number parity acting as the error syndrome to distinguish these two spaces. A general QEC protection of quantum information stored in the bosonic system is illustrated in Fig.
. After correctly measuring the photon number parity and applying the corresponding correction operations in real time, quantum information stored in the cavity can be recovered.The auxiliary qubit is first encoded to the logical qubit in an oscillator with. Once a single-photon-jump error occurs, the logical qubit state falls out of the code space to the error space with the basis states:.
\}\right\rangle=\left|{0}_{{\rm{L}}}\right\rangle ,\left|+{X}_{{\rm{L}}}\right\rangle=}\right\rangle +\left|{1}_{{\rm{L}}}\right\rangle )/\sqrt{2}\), respectively.
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