Encoding a qubit in an oscillator

Details Encoding a qubit in an oscillator Encoding a qubit in an oscillator

2000-08-08

arxiv.org/abs/quant-ph/0008040v3

Phys.Rev.A64:012310,2001

Physics

Quantum Physics

22 pages, 8 figures, REVTeX, title change (qudit -> qubit) requested by Phys. Rev. A, minor corrections

Scientific paper

10.1103/PhysRevA.64.012310

Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described 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-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation 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 can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.

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