Error Correction for Continuous Quantum Variables

Error Correction for Continuous Quantum Variables

Quantum computers hold the promise for efficiently factoring large integers [1]. However, to do this beyond a most modest scale they will require quantum error correction [2]. The theory of quantum error correction is already well studied in two-level or spin2 systems (in terms of qubits or quantum bits) [2–7]. Some of these results have been generalized to higher-spin systems [8–11]. This work...

Continuous quantum error correction

We describe new implementations of quantum error correction that are continuous in time, and thus described by continuous dynamical maps. We evaluate the performance of such schemes using numerical simulations, and comment on the effectiveness and applicability of continuous error correction for quantum computing.

Operator quantum error correction for continuous dynamics

Ognyan Oreshkov, Daniel A. Lidar, and Todd A. Brun Grup de Física Teòrica, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA Department of Physics, University of Southern California, Los Angeles, California 90089, USA Department of Chemistry, Universi...

Quantum Error-Correction Codes on Abelian Groups

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.

Environment-assisted quantum-information correction for continuous variables