We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a cnot gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip.

中文翻译：

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在周期性钉扎结构上编织马约拉那费米子并创建带有涡旋的量子逻辑门

我们展示了如何通过使用探针尖端执行一系列特定移动，将支持马约拉纳费米子的涡旋置于周期性钉扎阵列上时如何用于涡旋交换和独立编织。使用这些编织操作，我们演示了Hadamard和cnot的实现门。我们专门考虑了第一个匹配场，在该场中每个钉扎点都有一个涡旋，并且我们展示了存在两个基本的动态操作（移动和交换），可以从中构造基本的编织操作以创建特定的逻辑门。周期性的钉扎阵列既可以控制旋涡的世界线，又可以使用探针的一组特定运动来自由控制旋涡，在此过程中，探针的尖端强度和高度保持不变。我们测量了针对热效应的不同动作的鲁棒性，并显示了三种不同的操作在活动尖端产生了不同的力特征。