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Mapping from multiple-control Toffoli circuits to linear nearest neighbor quantum circuits

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Abstract

In recent years, quantum computing research has been attracting more and more attention, but few studies on the limited interaction distance between quantum bits (qubit) are deeply carried out. This paper presents a mapping method for transforming multiple-control Toffoli (MCT) circuits into linear nearest neighbor (LNN) quantum circuits instead of traditional decomposition-based methods. In order to reduce the number of inserted SWAP gates, a novel type of gate with the optimal LNN quantum realization was constructed, namely NNTS gate. The MCT gate with multiple control bits could be better cascaded by the NNTS gates, in which the arrangement of the input lines was LNN arrangement of the MCT gate. Then, the communication overhead measurement model on inserted SWAP gate count from the original arrangement to the new arrangement was put forward, and we selected one of the LNN arrangements with the minimum SWAP gate count. Moreover, the LNN arrangement-based mapping algorithm was given, and it dealt with the MCT gates in turn and mapped each MCT gate into its LNN form by inserting the minimum number of SWAP gates. Finally, some simplification rules were used, which can further reduce the final quantum cost of the LNN quantum circuit. Experiments on some benchmark MCT circuits indicate that the direct mapping algorithm results in fewer additional SWAP gates in about 50%, while the average improvement rate in quantum cost is 16.95% compared to the decomposition-based method. In addition, it has been verified that the proposed method has greater superiority for reversible circuits cascaded by MCT gates with more control bits.

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Acknowledgements

This work was supported by the Natural Science Foundation of Jiangsu Province under Grant BK20151274, General Project of Natural Science Research of Jiangsu Higher School under Grant 14KJB520033, and Postgraduate Research and Practice Innovation Program of Jiangsu Province under Grant KYCX17_1916.

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Authors and Affiliations

  1. College of Electronics and Information, Nantong University, Nantong, Jiangsu, China

    Xueyun Cheng

  2. College of Computer Science and Technology, Nantong University, Nantong, Jiangsu, China

    Xueyun Cheng, Zhijin Guan & Weiping Ding

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  1. Xueyun Cheng
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  2. Zhijin Guan
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Correspondence to Xueyun Cheng.

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Cheng, X., Guan, Z. & Ding, W. Mapping from multiple-control Toffoli circuits to linear nearest neighbor quantum circuits. Quantum Inf Process 17, 169 (2018). https://doi.org/10.1007/s11128-018-1908-8

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