论文标题
双方控制的对施密特等级的合成和上限
Synthesis and upper bound of Schmidt rank of the bipartite controlled-unitary gates
论文作者
论文摘要
量子电路模型是实施复杂量子计算的最流行范例。基于Cartan的分解，我们表明$ 2（N-1）$广义控制 - $ x $（GCX）大门，$ 6 $ $ y $ - $ y $ - 和$ z $ - 轴以及$ n+5 $ n+5 $ n+5 $ y $ y $ - 和$ z $ - $ - $ -Rotation-types，该论文适用于对立的对象。 $ \ MATHCAL {U} _ {Cu（2 \ otimes n）} $，$ a $ a $控制$ \ Mathbb {C}^2 \ otimes \ otimes \ Mathbb {c}^n $。在单一门的场景中$ 200万美元（N-1）+10 $单方面$ y $ - 和$ z $ - rotation-types进行模拟。出现了用于实现$ \ MATHCAL {U} _ {CU（2 \ otimes n）} $和$ \ Mathcal {U} _ {CD（M \ otimes n）} $的量子电路。此外，我们发现$ \ Mathcal {u} _ {Cu（2 \ otimes2）} $带有$ A $ CONTROTIONING具有Schmidt等级，并且在其他情况下，可以根据特定的简单产品统一运算符的特定类型的类型来扩展目标一级的对角度形式。
Quantum circuit model is the most popular paradigm for implementing complex quantum computation. Based on Cartan decomposition, we show that $2(N-1)$ generalized controlled-$X$ (GCX) gates, $6$ single-qubit rotations about the $y$- and $z$-axes, and $N+5$ single-partite $y$- and $z$-rotation-types which are defined in this paper are sufficient to simulate a controlled-unitary gate $\mathcal{U}_{cu(2\otimes N)}$ with $A$ controlling on $\mathbb{C}^2\otimes \mathbb{C}^N$. In the scenario of the unitary gate $\mathcal{U}_{cd(M\otimes N)}$ with $M\geq3$ that is locally equivalent to a diagonal unitary on $\mathbb{C}^M\otimes \mathbb{C}^N$, $2M(N-1)$ GCX gates and $2M(N-1)+10$ single-partite $y$- and $z$-rotation-types are required to simulate it. The quantum circuit for implementing $\mathcal{U}_{cu(2\otimes N)}$ and $\mathcal{U}_{cd(M\otimes N)}$ are presented. Furthermore, we find $\mathcal{U}_{cu(2\otimes2)}$ with $A$ controlling has Schmidt rank two, and in other cases the diagonalized form of the target unitaries can be expanded in terms of specific simple types of product unitary operators.
