A simple comparative analysis of exact and approximate quantum error correction

TL;DR

This paper compares exact and approximate quantum error correction methods using simple models, analyzing their similarities, differences, and performance metrics like entanglement fidelity, with a focus on the role of self-complementarity.

Contribution

It provides a clear analytical comparison of exact and approximate quantum error correction using primitive codes and noise models, highlighting key differences and performance factors.

Findings

Exact and approximate error correction show distinct behaviors under different noise models.

Entanglement fidelity varies with recovery schemes in approximate correction.

Self-complementarity influences the effectiveness of approximate quantum error correction.

Abstract

We present a comparative analysis of exact and approximate quantum error correction by means of simple unabridged analytical computations. For the sake of clarity, using primitive quantum codes, we study the exact and approximate error correction of the two simplest unital (Pauli errors) and nonunital (non-Pauli errors) noise models, respectively. The similarities and differences between the two scenarios are stressed. In addition, the performances of quantum codes quantified by means of the entanglement fidelity for different recovery schemes are taken into consideration in the approximate case. Finally, the role of self-complementarity in approximate quantum error correction is briefly addressed.