Classification of transversal gates in qubit stabilizer codes
Classification of transversal gates in qubit stabilizer codes
复制标题
量子位稳定器代码中横向门的分类
DOI：
10.26421/qic16.9-10-3
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Tomas Jochym
中科院分区：
文献类型：
--
作者：
Jonas T. Anderson;Tomas Jochym
这项工作对能够为量子比特稳定子码实现单量子比特或双量子比特横向逻辑门的对角门集合进行了分类。我们表明，构成该码的底层量子比特上的单个物理门在其对角线上被限制为具有$e^{i\pi c/2^k}$形式的元素，从而导致以这种方式可实现的逻辑门类别也受到类似的限制。此外，我们表明所有能够由单个物理对角门横向实现的对角逻辑门都必须属于克利福德层级。而且，我们可以利用这一结果来证明曾等人在2007年提出的关于横向门的一个猜想。
This work classifies the set of diagonal gates that can implement a single or two-qubit transversal logical gate for qubit stabilizer codes. We show that individual physical gates on the underlying qubits that compose the code are restricted to have entries of the form $e^{i \pi c/2^k}$ along their diagonal, resulting in a similarly restricted class of logical gates that can be implemented in this manner. Moreover, we show that all diagonal logical gates that can be implemented transversally by individual physical diagonal gates must belong to the Clifford hierarchy. Furthermore, we can use this result to prove a conjecture about transversal gates made by Zeng et al. in 2007.