Iterative Decoder for Quantum Turbo Codes: Performance Analysis and Enhancement.

Abstract

Quantum error correction is necessary in quantum communication. In that sense, quan- tum turbo codes present a remarkably low probability of error compared to other quantum error correcting codes. The document of this Final Degree Project analyses the performance of iterative SISO decoders in quantum turbo codes, especially when the decoder is under the influence of a channel mismatch. The obtained results suggest that the closer the es- timated depolarizing probability is to the actual depolarizing probability of the channel, the lower the WER of the SISO decoder will be. In this document, chapter 1 contemplates the relevance of quantum error correcting codes in current and future quantum technologies. Chapter 2 provides the basic background on linear algebra and quantum mechanics that are crucial in order to understand quantum error correction. Chapter 3 presents a few notions in quantum error correction and the sta- bilizer codes, which are the cornerstone in order to export classical error correcting codes into the quantum world. Chapter 4 presents the actual quantum turbo codes, their construc- tion, their decoding algorithm and their performance when the decoder suffers from channel mismatch. Chapter 5 summarizes the main conclusions of this Final Degree Project, and chapter 6 provides the budget of the whole project.