Channel-Optimized Quantum Error Correction
arXiv:0810.2524 · doi:10.1109/TIT.2009.2039162
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.
12 pages, 9 figures
References in corpus (11)
- Vanishing quantum discord is necessary and sufficient for completely positive maps
- Direct Characterization of Quantum Dynamics
- Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
- Optimum Quantum Error Recovery using Semidefinite Programming
- Robust Quantum Error Correction via Convex Optimization
- Quantum Error Correction via Convex Optimization
- Environment-invariant measure of distance between evolutions of an open quantum system
- Suboptimal quantum-error-correcting procedure based on semidefinite programming
- Optimal Experiment Design for Quantum State and Process Tomography and Hamiltonian Parameter Estimation
- Channel-Adapted Quantum Error Correction
- Comment on "Optimum Quantum Error Recovery using Semidefinite Programming"
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