Encoding a qubit in an oscillator

作者：Daniel Gottesman, Alexei Kitaev, John P. Preskill · 发表于：Physical Review A · 年份：2001 · DOI：10.1103/physreva.64.012310 · 被引用次数：1569 · 研究领域：Quantum Computing Algorithms and Architecture、Quantum Information and Cryptography、Quantum Mechanics and Applications

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.