Channel-optimized quantum error correction

Authors:
Soraya Taghavi;Robert L. Kosut;Daniel A. Lidar
Affiliations:
Department of Electrical Engineering and the Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA;SC Solutions, Systems and Control Division, Sunnyvale, CA;Departments of Electrical Engineering, Chemistry, Physics and the Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 8
Cited 1

Topics in matrix analysis

Topics in matrix analysis
Semidefinite programming

SIAM Review
Quantum computation and quantum information

Quantum computation and quantum information
Convex Optimization

Convex Optimization
Quantum Error Correction and Fault Tolerant Quantum Computing

Quantum Error Correction and Fault Tolerant Quantum Computing
Channel-adapted quantum error correction

Channel-adapted quantum error correction
Quantum error correction via convex optimization

Quantum Information Processing
Quantum computer with dipole-dipole interacting two-level systems

Quantum Information & Computation

Fidelity as a figure of merit in quantum error correction

Quantum Information & Computation

Quantified Score

Hi-index	754.84

Visualization

Abstract

We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate, via numerical examples, that our optimized QEC procedures always achieve a higher channel fidelity than the standard error correction method, which is agnostic about the specifics of the channel. This demonstrates the importance of channel characterization before QEC procedures are applied. Our main novel finding is that in the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction. We show this using a general rank minimization heuristic and supporting numerical calculations. Therefore, one can further improve the fidelity by utilizing all the available ancillas in the encoding block.