Physics – Quantum Physics
Scientific paper
2007-06-22
Physics
Quantum Physics
Ph.D. dissertation, 163 pages, 38 figures
Scientific paper
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. 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. 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 present computational algorithms to generate near-optimal recovery operations structured to begin with a projective syndrome measurement. 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.
No associations
LandOfFree
Channel-Adapted Quantum Error Correction does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Channel-Adapted Quantum Error Correction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Channel-Adapted Quantum Error Correction will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-188429