Encoding a qubit in an oscillator - art. no. 012310

Quantum error-correcting codes are constructed that embed a finite-dimensio nal code space in the infinite-dimensional Hilbert space of a system descri bed by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-t olerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, a nd photon counting; however, nonlinear mode coupling is required for the pr eparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes c an be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.