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Wire-Crossings Optimization Based on Majority-of-Five and XOR-of-Three Primitives in QCA

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Abstract

The difficulty of manufacturing and noise sensitivity of quantum-dot cellular automata (QCA) make wire-crossings optimization increasingly important. Novel logic primitives such as majority-of-five (MAJ5) and XOR-of-three (XOR3) with efficient QCA realizations can alleviate the wire-crossings issue. In this paper, we aim at 13 standard three-input Boolean functions, the QCA layouts of which are designed by introducing MAJ5 (Method A) and its combinations with XOR3 (Method B). The proposed designs are verified by the QCADesigner tool. Experimental results show we can reduce the number of QCA cells and area. In terms of area, we can achieve 30.69% and 48.35% reduction by Method A and B, respectively, compared with the state-of-the-art approach. The proposed designs are further used as building blocks for large-scale circuit designs. In one implementation, the Peres reversible gate is implemented based on Method B to decrease the area by 33.3%.

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Funding

This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 61871242; in part by the State Key Laboratory of ASIC & System under Grant 2021KF008; and in part by the Scientific Research Project of the Department of Education of Zhejiang under Grant Y202045495.

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Authors and Affiliations

  1. EECS, Ningbo University, Fenghua Road, Ningbo, 315211, China

    Peng Liu, Jianguo Ni & Zhufei Chu

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  1. Peng Liu
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Contributions

P. Liu proposed the logic expressions for 13 standard three-input Boolean functions, and J. Ni simulated and verified the proposed designs using QCADesigner. P. Liu and Z. Chu contribute to the writing. The final manuscript was read and approved by all authors.

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Correspondence to Zhufei Chu.

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Appendices

Appendix A: QCA Layouts of of 13 Standard with Method A

Fig. 12
figure 12

The proposed QCA layouts of 13 functions based on Method A, (a) Function 1, (b) Function 2, (c) Function 3, (d) Function 4, (e) Function 5, (f) Function 6, (g) Function 7, (h) Function 8, (i) Function 9, (j) Function 10, (k) Function 11, (l) Function 12, (m) Function 13

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Appendix B: QCA Layouts of of 13 Standard with Method B

Fig. 13
figure 13

The proposed QCA layouts of 13 functions based on Method B, (a) Function 1, (b) Function 2, (c) Function 3, (d) Function 4, (e) Function 5, (f) Function 6, (g) Function 7, (h) Function 8, (i) Function 9, (j) Function 10, (k) Function 11, (l) Function 12, (m) Function 13

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Liu, P., Ni, J. & Chu, Z. Wire-Crossings Optimization Based on Majority-of-Five and XOR-of-Three Primitives in QCA. Int J Theor Phys 61, 86 (2022). https://doi.org/10.1007/s10773-022-05000-5

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