High-fidelity Z -measurement error encoding of optical qubits
Jeremy L. O’Brien, Geoff J. Pryde, Andrew G. White, Timothy C. Ralph · Physical Review A · 2005
We demonstrate a quantum error correction scheme that protects against accidental measurement, using a parity encoding where the logical state of a single qubit is encoded into two physical qubits using a nondeterministic photonic controlled-NOT gate. For the single qubit input states $\ensuremath{\mid}0⟩$, $\ensuremath{\mid}1⟩$, $\ensuremath{\mid}0⟩\ifmmode\pm\else\textpm\fi{}\ensuremath{\mid}1⟩$, and $\ensuremath{\mid}0⟩\ifmmode\pm\else\textpm\fi{}i\ensuremath{\mid}1⟩$ our encoder produces the appropriate two-qubit encoded state with an average fidelity of $0.88\ifmmode\pm\else\textpm\fi{}0.03$ and the single qubit decoded states have an average fidelity of $0.93\ifmmode\pm\else\textpm\fi{}0.05$ with the original state. We are able to decode the two-qubit state (up to a bit flip) by performing a measurement on one of the qubits in the logical basis; we find that the 64 one-qubit decoded states arising from 16 real and imaginary single-qubit superposition inputs have an average fidelity of $0.96\ifmmode\pm\else\textpm\fi{}0.03$.