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A novel fault-tolerant quantum divider and its simulation

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Abstract

Efficient quantum circuits of algebraic operations are vital for quantum algorithms. In this paper, we propose a novel fault-tolerant quantum divider based on long division algorithm using Clifford+T gates. Firstly, two efficient quantum subtractors are designed which we call them equal-bit subtractor and unequal-bit subtractor. The advantage of these quantum subtractors is that the number of the constant inputs is 2, which will dramatically reduce the qubit cost. Then, based on the quantum comparator and the quantum subtractors, we propose a novel fault-tolerant quantum divider. Compared with existing work, the proposed quantum divider has better performances in quantum cost, T-depth, T-count, qubit cost, constant inputs and garbage outputs. Finally, we simulate these algorithms on IBM Quantum Experience (IBM Q Experience) platform, and the probability histograms show that these algorithms are feasible and efficient.

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Acknowledgements

The authors would like to acknowledge the financial support of the National Natural Science Foundation of China (61801061), The Natural Science Foundation of Chongqing(CSTC2016jcyjA0028), The Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJQN201800607, KJ1704090), and the valuable inputs of the reviewers.

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Authors and Affiliations

  1. The College of Opto Electronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Suzhen Yuan, Shengwei Gao, Chao Wen, Yuchan Wang & Yan Wang

  2. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611730, China

    Hong Qu

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  1. Suzhen Yuan
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Correspondence to Suzhen Yuan.

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Yuan, S., Gao, S., Wen, C. et al. A novel fault-tolerant quantum divider and its simulation. Quantum Inf Process 21, 182 (2022). https://doi.org/10.1007/s11128-022-03523-8

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