Optimizing Qubit Mapping with Quasi-Orthogonal Space-Time Block Codes and Quaternion Orthogonal Designs

TL;DR

This paper investigates the use of Quasi-Orthogonal Space-Time Block Codes combined with Quaternion Orthogonal Designs to improve qubit error correction, demonstrating enhanced error resilience and correction rates in quantum systems.

Contribution

It introduces a novel integration of QOSTBCs with QODs for qubit mapping, showing improved error correction performance over traditional stabilizer group methods.

Findings

QOSTBCs outperform stabilizer groups in correction percentage for most cases.

QOSTBCs achieve over 100% correction rates in high-error environments.

Stabilizer groups perform better in certain cases, like Z3.

Abstract

This study explores the qubit mapping through the integration of Quasi-Orthogonal Space-Time Block Codes (QOSTBCs) with Quaternion Orthogonal Designs (QODs) in quantum error correction (QEC) frameworks. QOSTBCs have gained prominence for enhancing performance and reliability in quantum computing and communication systems. These codes draw on stabilizer group formalism and QODs to boost error correction, with QOSTBCs mapping logical qubits to physical ones, refines error handling in complex channels environments. Simulations results demonstrate the effectiveness of this approach by comparing the percentage improvement under various detected and corrected error conditions for four different cases, \textbf{$Z_1$} up to \textbf{$Z_4$}. The obtained simulations and implemental results show that QOSTBCs consistently achieve a higher correction improvement percentage than stabilizer Group for \textbf{$Z_1$}, \textbf{$Z_2$}, and \textbf{$Z_4$}; QOSTBCs can correct more errors than those detected, achieving over 100\% correction rates for first two cases, which indicates their enhanced resilience and redundancy in high-error environments. While for \textbf{$Z_3$}, stabilizer consistently remains above that of QOSTBCs, reflecting its slightly better performance. These outcomes indicate that QOSTBCs are reliable in making better logarithmic efficiency and error resilience, making them a valuable asset for quantum information processing and advanced wireless communication.