Topological Quantum Computation with the universal R matrix for Ising anyons
Lachezar S. Georgiev
备注：
10 pages, 2 figures; Proc. of the VII Int. Workshop "Lie Theory and its Applications in Physics", June 2007, Varna, Bulgaria, H.-D. Doebner and V.K. Dobrev, Eds., Heron Press (2008), Sofia, pages 256--265
We show that the braid-group extension of the monodromy-based topological quantum computation scheme of Das Sarma et al. can be understood in terms of the universal R matrix for the Ising model giving similar results to those obtained by direct analytic continuation of multi-anyon Pfaffian wave functions. It is necessary, however, to take into account the projection on spinor states with definite total parity which is responsible for the topological entanglement in the Pfaffian topological quantum computer.
Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
拓扑量子计算可以提供一种鲁棒的方法，用于利用任意子准粒子激发的拓扑性质来编码和操纵信息。针对Chern-Simons-Witten SU（2）$_k$理论中的所有任意子模型，我们提出了一种有效的方法来映射量子信息（qubit）的密集和稀疏表示，并简单地构造了多量子比特门，该理论支持通过编织进行通用量子计算（$k\geq 3,\ k \neq 4$）.在这个过程中，我们展示了如何拓扑量子存储器和门的$k=2,4$连接自然那些$k\geq 3,\ k \neq 4$，统一这些概念在一个简单的框架。此外，我们说明了这些想法的潜在扩展到其他任何子模型以外的陈-西蒙斯-威滕场论。
