Efficient quantum circuits for dense circulant and circulant like operators.
Efficient quantum circuits for dense circulant and circulant like operators.
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DOI：
10.1098/rsos.160906
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发表时间：
2017-05
影响因子：
3.5
通讯作者：
Wang JB
中科院分区：
文献类型：
--
作者：
Zhou SS;Wang JB
循环矩阵是一类重要的算子，在科学和工程相关领域有着广泛的应用。一般来说，它们是非稀疏和非酉的。在本文中，我们提出了有效的量子电路来实现循环算子，使用更少的资源和比现有方法更低的复杂性。此外，我们的量子电路可以很容易地扩展到Toeplitz， Hankel和块循环矩阵的实现。给出了实现循环算子的逆和积的有效量子算法，并讨论了在求解循环系统运动方程中的应用实例。
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources and with lower complexity than existing methods. Moreover, our quantum circuits can be readily extended to the implementation of Toeplitz, Hankel and block circulant matrices. Efficient quantum algorithms to implement the inverses and products of circulant operators are also provided, and an example application in solving the equation of motion for cyclic systems is discussed.