A simple comparative analysis of exact and approximate quantum error correction (Q2925883)

This article is interesting and relevant for anyone interested in quantum computation and quantum technologies, providing for an important contribution to the quantum error correction literature.NEWLINENEWLINEOne of the major problems with quantum technologies and, in particular, with developing quantum computation on a viable and widespread way, lies in difficulty to protect the quantum computer from the loss of coherence (decoherence).NEWLINENEWLINEThe protection of quantum information from error, and the development of quantum error correcting codes (QECCs) is, therefore, an important area of research for the advancement of quantum computation and possible future quantum computer-based technologies.NEWLINENEWLINEWhile, as the authors stress, the classical information theory-based techniques of taking advantage of redundancy do not work for quantum computation due to the no-cloning theorem. The quantum approaches to error correction, however, take advantage of quantum entanglement to build QECCs.NEWLINENEWLINEThe authors begin, in Section 1., by providing for a review of the research field on QECCs reviewing some major references in the field and providing a basis for the rest of the article's work.NEWLINENEWLINEIn Section 2., the authors address the exact and approximate error correction conditions. This section stands on its own, in the sense that it provides for a ground work for different noise models, addressing the formalism and conditions to deal with different problems of application of QEC theory.NEWLINENEWLINEIn Section 3., the authors apply the theory to two channels:NEWLINENEWLINE-- The unital channel with Pauli errors (Subsection 3.1);NEWLINENEWLINE-- The nonunital noise channel with non-Pauli errors (Subsection 3.2).NEWLINENEWLINEThe authors implement QECCs for these two noise channels, and test their performance by means of entanglement fidelity.NEWLINENEWLINEThe authors' work on each example extends between the body of the article and the appendices, resulting from the combination of the general analytical results and the examples worked upon, where the authors contribute methodologically for the implementation QECCs and evaluation of different recovery schemes for their performance, in particular, for the case of amplitude damping quantum noisy channel (worked upon in Section 3.2), the performance comparison showed that the Fletcher-type recovery scheme works better than both the standard QEC and the code-projected recovery schemes, the standard QEC performing the worst, with regards to entanglement fidelity.NEWLINENEWLINEStill regarding the amplitude damping, the authors also show that there are only three possible self-complementary quantum codes, characterized by a two-dimensional subspace of the sixteen dimensional Hilbert space capable of error-correcting single amplitude damping errors, these three codes are addressed in the article's appendix B. (B.6, B.7 and B.8).NEWLINENEWLINEWhile basic noise models were addressed with elementary QECCs, the results constitute a relevant analytical and methodological contribution that can support further research on QEC, by providing for: a synthesis of major contributions and references, general analytical results and an implementation allowing the illustration of a comparison methodology that may be used for other noise models and QECCs.