  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.
