Quantifying the Performance of Quantum Codes

Abstract

We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and characterize the performance of both a repetition code and an error avoiding code in terms of the entanglement fidelity. We also consider the concatenation of such codes and show that it is especially advantageous in the regime of partial correlations. Finally, we characterize the effectiveness of the codes and their concatenation by means of the code entropy and find, in particular, that the effort required for recovering such codes decreases when the error probability decreases and the memory parameter increases. Second, we consider both symmetric and asymmetric depolarizing noisy quantum memory channels and perform quantum error correction via the five qubit stabilizer code. We characterize this code by means of the entanglement fidelity and the code entropy as function of the asymmetric error probabilities and the degree of memory. Specifically, we uncover that while the asymmetry in the depolarizing errors does not affect the entanglement fidelity of the five qubit code, it becomes a relevant feature when the code entropy is used as a performance quantifier.

arXiv comment21 pages, 10 figures

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Cited by in corpus (8)

• Quantum channels and memory effects
• Errors and pseudo-thresholds for incoherent and coherent noise
• Approximate quantum error correction for generalized amplitude damping errors
• Quantum Stabilizer Codes Embedding Qubits Into Qudits
• Surface Code Design for Asymmetric Error Channels
• Concatenating quantum error-correcting codes with decoherence-free subspaces and vice versa
• Stabilizer codes for Open Quantum Systems
• Facets of correlated non-Markovian channels