p波超流涡旋的拓扑量子计算
Topological Quantum Computing with p-Wave Superfluid Vortices
摘要：
研究表明，在拓扑量子计算（TQC）中，囚禁在p波超流体中的三个涡旋中的Majorana费米子形成了一个量子比特。几个类似的想法已经被提出：伊万诺夫[物理学。{ \bf 86}，268（2001）]和Zhang { \it等人} [Phys. Rev. Lett. { \bf 99}，220502（2007）]提出了分别用两个和四个马约拉纳费米子实现量子位的方案，其中通过交换马约拉纳费米子的位置来执行量子位操作。这样得到的门的集合是相关酉群的离散子集。在本文中，我们提出了一个新的方案，其中三个马约拉纳费米子形成一个量子比特。我们表明，连续的1-量子比特门操作是可能的，通过交换的马约拉纳费米子的位置补充动态相变。2-量子比特门是通过使用不同量子比特的马约拉纳费米子之间的耦合来实现的。
英文摘要：
It is shown that Majorana fermions trapped in three vortices in a p-wave superfluid form a qubit in a topological quantum computing (TQC). Several similar ideas have already been proposed: Ivanov [Phys. Rev. Lett. {\bf 86}, 268 (2001)] and Zhang {\it et al.} [Phys. Rev. Lett. {\bf 99}, 220502 (2007)] have proposed schemes in which a qubit is implemented with two and four Majorana fermions, respectively, where a qubit operation is performed by exchanging the positions of Majorana fermions. The set of gates thus obtained is a discrete subset of the relevant unitary group. We propose, in this paper, a new scheme, where three Majorana fermions form a qubit. We show that continuous 1-qubit gate operations are possible by exchanging the positions of Majorana fermions complemented with dynamical phase change. 2-qubit gates are realized through the use of the coupling between Majorana fermions of different qubits.
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