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Encoding a qubit in an oscillator

Gottesman, Daniel and Kitaev, Alexei and Preskill, John (2001) Encoding a qubit in an oscillator. Physical Review A, 64 (1). Art. No. 012310. ISSN 1050-2947. doi:10.1103/PhysRevA.64.012310.

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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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Additional Information:©2001 The American Physical Society Received 9 August 2000; published 11 June 2001 We gratefully acknowledge helpful discussions with Isaac Chuang, Sumit Daftuar, David DiVincenzo, Andrew Doherty, Steven van Enk, Jim Harrington, Jeff Kimble, Andrew Landahl, Hideo Mabuchi, Harsh Mathur, Gerard Milburn, Michael Nielsen, and Peter Shor. This work was supported in part by the Department of Energy under Grant No. DE-FG03-92-ER40701, and by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374. Some of this work was done at the Aspen Center for Physics.
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Deposited On:17 Jul 2006
Last Modified:08 Nov 2021 20:12

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