Channel-adapted quantum error correction
Name
191822846-MIT.pdf
Description
Full printable version
Size
21.98 MB
Format
Adobe PDF
Checksum (MD5)
1519f3d4048c6ca2d970ef3374557fb8
Author(s)
Fletcher, Andrew Stephen
Advisor(s)
Peter W. Shor and Moe Z. Win.
Alternative Title
QEC error correction
Date Issued
2007
Publisher
Massachusetts Institute of Technology
Abstract
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and performance. We examine QEC methods that are adapted to the physical noise model. In physical systems, errors are not likely to be arbitrary; rather we will have reasonable models for the structure of quantum decoherence. We may choose quantum error correcting codes and recovery operations that specifically target the most likely errors. This can increase QEC performance and also reduce the required overhead. We present a convex optimization method to determine the optimal (in terms of average entanglement fidelity) recovery operation for a given channel, encoding, and information source. This is solvable via a semidefinite program (SDP). We derive an analytic solution to the optimal recovery for the case of stabilizer codes, the completely mixed input source, and channels characterized by Pauli group errors. We present computational algorithms to generate near-optimal recovery operations structured to begin with a projective syndrome measurement.
(cont.) These structured operations are more computationally scalable than the SDP required for computing the optimal; we can thus numerically analyze longer codes. Using Lagrange duality, we bound the performance of the structured recovery operations and show that they are nearly optimal in many relevant cases. We present two classes of channel-adapted quantum error correcting codes specifically designed for the amplitude damping channel. These have significantly higher rates with shorter block lengths than corresponding generic quantum error correcting codes. Both classes are stabilizer codes, and have good fidelity performance with stabilizer recovery operations. The encoding, syndrome measurement, and syndrome recovery operations can all be implemented with Clifford group operations.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.
Includes bibliographical references (p. 159-163).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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