Demonstration of quantum error correction using linear optics

We describe a laboratory demonstration of a quantum error correction procedure that can correct intrinsic measurement errors in linear-optics quantum gates. The procedure involves a two-qubit encoding and fast feed-forward-controlled single-qubit operations. In our demonstration the qubits were represented by the polarization states of two single-photons from a parametric down-conversion source, and the real-time feed-forward control was implemented using an electro-optic device triggered by the output of single-photon detectors.

Figure 1

Quantum circuit diagram [1] illustrating protection and recovery from a $Z$-measurement error in LOQC [7]. An ancilla photon and encoding operation are used to convert a single-photon qubit $\mid \psi ⟩$ into the two-photon logical qubit $\mid {\psi }_L⟩$ according to Eq. (1). The dashed boxes $M_1$ and $M_2$ symbolize $Z$ measurements which may or may not occur. If one does occur, and returns the value 1, a bit flip $\left(X\right)$ is applied using feed-forward control. This procedure recovers the initial qubit $\mid \psi ⟩$. If needed, the logical qubit $\mid {\psi }_L⟩$ can then be regenerated by supplying a new ancilla photon and repeating the encoding operation.

Figure 2

Apparatus used to demonstrate LOQC QEC. The shaded areas relate key aspects of the apparatus to the quantum circuit diagram of Fig. 1. Details and symbols are described in the text.

Figure 3

Experimental results of the QEC procedure for several different values of input qubits $\mid \psi ⟩$. The data show the number of coincidence counts per 60 s as a function of the output qubit polarization analyzer $\theta$. The Key summarizes the experimental conditions for the three sets of data shown in each plot. In (a), (c), (d), and (e) the lines are sinusoidal fits to the data with an average visibility of 93.5%. The corrected qubit examples showed the ability to fully recover the qubit $\mid \psi ⟩$ from a $Z$ measurement error with an estimated average fidelity of about 98%.