Decompositions of general quantum gates
Decompositions of general quantum gates
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一般量子门的分解
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
J. Vartiainen
中科院分区：
文献类型：
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作者：
M. Möttönen;J. Vartiainen
量子算法可以通过被称为量子门的幺正变换的序列和应用于n个量子比特（qubit）的量子寄存器的测量来描述。量子门的集合被称为通用的，如果它可以用来构建任何n量子比特门。1995年，Barenco等人利用酉矩阵的QR分解证明了单量子比特门和受控非门集合的普适性。大约十年后，分解得到了改进，基本上包含了更少的基本门。此外，余弦-正弦矩阵分解被应用于有效地实现一般量子门的分解。在本章中，我们将回顾不同类型的一般门分解，并将受控非门的最佳已知门数略微改进为（23/48）4^n。在物理实现中，量子位之间的相互作用强度可以作为它们的距离的函数强烈地减小。因此，我们还讨论了限制在量子比特的线性链中的最近邻相互作用的分解。
Quantum algorithms may be described by sequences of unitary transformations called quantum gates and measurements applied to the quantum register of n quantum bits, qubits. A collection of quantum gates is called universal if it can be used to construct any n-qubit gate. In 1995, the universality of the set of one-qubit gates and controlled NOT gate was shown by Barenco et al. using QR decomposition of unitary matrices. Almost ten years later the decomposition was improved to include essentially fewer elementary gates. In addition, the cosine-sine matrix decomposition was applied to efficiently implement decompositions of general quantum gates. In this chapter, we review the different types of general gate decompositions and slightly improve the best known gate count for the controlled NOT gates to (23/48)4^n in the leading order. In physical realizations, the interaction strength between the qubits can decrease strongly as a function of their distance. Therefore, we also discuss decompositions with the restriction to nearest-neighbor interactions in a linear chain of qubits.