标题： 酉矩阵的构造性量子缩放 显示英文标题

标题： Constructive quantum scaling of unitary matrices

摘要： 在本工作中，我们提出了一种将任意酉矩阵$U\in\mathbf U(2^k)$分解为单量子比特反演门和受控$\sqrt{\mbox{NOT}}$门乘积的方法。 由于乘积结果得到反演矩阵，该矩阵可以被视为双随机矩阵的复数类比，因此我们的方法可以看作是 Sinkhorn-Knopp 算法的复数类比，其中对角矩阵被添加和移除一个单量子比特辅助比特所替代。 该分解可以构造性地找到，所得电路包含$O(4^k)$个纠缠门，已被证明是最佳的。 给出了此类变换的一个示例。 显示英文摘要

摘要： In this work we present a method of decomposition of arbitrary unitary matrix $U\in\mathbf U(2^k)$ into a product of single-qubit negator and controlled-$\sqrt{\mbox{NOT}}$ gates. Since the product results with negator matrix, which can be treated as complex analogue if bistochastic matrix, our method can be seen as complex analogue of Sinkhorn-Knopp algorithm, where diagonal matrices are replaced by adding and removing an one-qubit ancilla. The decomposition can be found constructively and resulting circuit consists of $O(4^k)$ entangling gates, which is proved to be optimal. An example of such transformation is presented.