拓扑量子位设计与泄漏
Topological Qubit Design and Leakage
摘要：
我们研究如何最好地设计用于拓扑量子计算的量子位。这些量子比特是与任意子的小群体相关联的拓扑希尔伯特空间。通过交换任意子来对这些进行操作。有人可能会说，为了尽可能多地进行简单的单量子比特操作，每组的任意子数量应该最大化。然而，我们证明了每个量子比特有一个最大的粒子数，即4，更一般地说，d维量子比特有一个最大的粒子数。我们还研究了具有拓扑量子位的可能性，对于拓扑量子位，人们可以执行两个量子位门，而不会泄漏到非计算状态。事实证明，所有双量子比特门都是无泄漏的要求是非常严格的，并且这种性质只能在与Ising类任意子模型相关的双量子比特系统中实现，这不允许通过编织进行通用量子计算。我们的结果直接来自于辫群的表示理论，这意味着它们对所有的任意子模型都有效。我们还对其他交换组的一般化做了一些评论。
英文摘要：
We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Op- erations are performed on these by exchanging the anyons. One might argue that, in order to have as many simple single qubit operations as possible, the number of anyons per group should be maximized. However, we show that there is a maximal number of particles per qubit, namely 4, and more generally a maximal number of particles for qudits of dimension d. We also look at the possibility of having topological qubits for which one can perform two-qubit gates without leakage into non-computational states. It turns out that the requirement that all two-qubit gates are leakage free is very restrictive and this property can only be realized for two-qubit systems related to Ising-like anyon models, which do not allow for universal quantum computation by braiding. Our results follow directly from the representation theory of braid groups which means they are valid for all anyon models. We also make some remarks on generalizations to other exchange groups.
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