Teleportation-based quantum computation, extended Temperley–Lieb diagrammatical approach and Yang–Baxter equation

• Published in: Quantum information processing Vol. 15; no. 1; pp. 405 - 464
• Main Authors: Zhang, Yong, Zhang, Kun, Pang, Jinglong
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2016
• Subjects: Data Structures and Information Theory; Mathematical Physics; Physics; Physics and Astronomy; Quantum Computing; Quantum Information Technology; Quantum Physics; Spintronics; Teleportation; Temperley–Lieb algebra; Quantum computation; Yang–Baxter equation
• ISSN: 1570-0755; 1573-1332
• DOI: 10.1007/s11128-015-1158-y

This paper focuses on the study of topological features in teleportation-based quantum computation and aims at presenting a detailed review on teleportation-based quantum computation (Gottesman and Chuang in 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.