Teleportation-Based Quantum Computation, Extended Temperley-Lieb Diagrammatical Approach and Yang--Baxter Equation

TL;DR

This paper reviews teleportation-based quantum computation, highlighting how topological features and diagrammatic approaches simplify fault-tolerant gate construction and entanglement, and explores the role of Yang--Baxter gates.

Contribution

It introduces an extended Temperley-Lieb diagrammatical approach and links it with Yang--Baxter gates, providing new insights into fault-tolerant quantum computation.

Findings

Topological features enable intuitive fault-tolerant gate construction

Extended Temperley-Lieb diagrams clarify quantum circuit models

Yang--Baxter gates relate to topological quantum computation

Abstract

This paper focuses on the study of topological features in teleportation-based quantum computation as well as aims at presenting a detailed review on teleportaiton-based quantum computation (Gottesman and Chuang, Nature 402, 390, 1999). In the extended Temperley-Lieb diagrammatical approach, we clearly show that such topological features bring about the fault-tolerant construction of both universal quantum gates and four-partite entangled states more intuitive and simpler. Furthermore, we describe the Yang--Baxter gate by its extended Temperley-Lieb configuration, and then study teleportation-based quantum circuit models using the Yang--Baxter gate. Moreover, we discuss the relationship between the extended Temperley-Lieb diagrammatical approach and the Yang-Baxter gate approach. With these research results, we propose a worthwhile subject, the extended Temperley-Lieb diagrammatical approach, for physicists in quantum information and quantum computation.