Efficient feedback controllers for continuous quantum error correction

Bradley A. Chase, Andrew J. Landahl and JM Geremia
Department of Physics and Astronomy, The University of New Mexico, Albuquerque NM 87131 USA

Abstract. We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model.

Funded by: DOE-NINE/Sandia (60071-699182); NSF (PHY-0555573); AFOSR (FA9550-06-1-0178)

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Please follow these links to download the available items in tar-gzip format. All LaTeX source, including figure files and the history of drafts and revisions to the paper are included in the source archive. Matlab code and data files used to generate figures in the paper is included in various code archive files. Extensive use of Apple's XGrid distributed computing platform was utilized in the generation of data files. Although such infrastructure is not strictly required to reproduce the data presented in the figures, we found it to be essential to running the calculations in a practical length of time. All of the code written to dispatch jobs to grid hosts via the XGrid server is included below.

• [LaTeX Source and Figure Files] (tar.gz file with RevTeX source and pdf and eps figure files)
• [Simulation Code and Data Files] (tar.gz file with Matlab source and C++ integration code)

We have also made Mathematica derivations used in the research project available for download as well as some developmental notes:

• [Mathematica Source Files] (tar.gz file with Mathematica derivations)
• [Notes on Derivations] (tar.gz file with LaTeX source and pdf files)