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Realization of a new permutative gate library using controlled-kth-root-of-NOT quantum gates for exact minimization of quantum circuits

Zhiqiang Li

College of Information Engineering, Yangzhou University, Yangzhou 225127, P. R. China

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Xiaoyu Song

Department of ECE, Portland State University, Portland, Oregon 97201, USA

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Marek Perkowski

Department of ECE, Portland State University, Portland, Oregon 97201, USA

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Hanwu Chen

School of Computer Science and Engineering, Southeast University, Nanjing 211198, P. R. China

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, and

Xiaoxia Feng

College of Information Engineering, Yangzhou University, Yangzhou 225127, P. R. China

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https://doi.org/10.1142/S0219749914500348Cited by:1 (Source: Crossref)

Abstract

Since non-permutative quantum gates have more complex rules than permutative quantum gates, it is very hard to synthesize quantum logic circuits using non-permutative quantum gates, such as controlled-square-root-of-NOT gates (CV∕CV⁺ gates). In the efficient synthesis algorithm, direct use of quantum non-permutative gates should be avoided. Rather, the key method is to use quantum gates to create new permutative quantum gates that then replace non-permutative quantum gates. This method assumes the library of quantum gate primitives are constructed so as to have the lowest possible quantum cost. In this paper, we first propose some new CV∕CV⁺-like gates, i.e. controlled-kth-root-of-NOT gates where k = 2,4,8,…, and give all corresponding matrixes. Further, we also present a novel generic method to quickly and directly construct this new optimal quantum logic gate library using CNOT and these non-permutative quantum gates. Our method introduces new means to find permutative quantum gates with lower quantum cost.

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