ELEMENTARY GATES FOR QUANTUM COMPUTATION
ELEMENTARY GATES FOR QUANTUM COMPUTATION
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DOI：
10.1103/physreva.52.3457
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发表时间：
1995-11-01
影响因子：
2.9
通讯作者：
WEINFURTER, H
中科院分区：
文献类型：
--
作者：
BARENCO, A;BENNETT, CH;WEINFURTER, H
我们证明了由所有一位量子门[U(2)]和两位异或门[将布尔值(x，y)映射到(x，x+y)]组成的门集合是普适的，因为任意多位n[U(2(N))]上的所有酉运算都可以表示为这些门的组合。我们研究了实现其他门所需的上述门的数量，例如广义Deutsch-Toffoli门，当且仅当满足所有剩余输入位的逻辑与时，这些门将特定的U(2)变换应用于一个输入位。这些门在许多拟议的量子计算网络的构建中发挥着核心作用。我们推导了建立各种两位和三位量子门所需的基本门的确切数目的上下界，以及n位Deutsch-Toffoli门所需的渐近数目，并对任意n位酉运算所需的数目进行了一些观察。
We show that a set of gates that consists of all one-bit quantum gates [U(2)] and the two-bit exclusive-OR gate [that maps Boolean values (x,y) to (x,x+y)] is universal in the sense that all unitary operations on arbitrarily many bits n [U(2(n))] can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.