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Pieceable fault tolerant conversion between 5-qubit code and 7-CSS code

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Abstract

We propose a non-transversal but pieceable fault tolerant conversion circuit that is used to convert encoded information between five-qubit code and seven-qubit CSS code. Since a syndrome extraction circuit requiring fewer ancillary qubit resources would facilitate the realization of large-scale quantum computations, we further adapt a flag-assisted fault tolerant syndrome measurement scheme to reduce the cost of ancillary preparation. Numerical simulations are also performed to further analyze the performance of our conversion method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 61572109.

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Authors and Affiliations

  1. Big Data Research Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Chen Lin & GuoWu Yang

  2. School of Information Engineering, Hubei Minzu University, Enshi, 44500, People’s Republic of China

    QingBin Luo

  3. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, People’s Republic of China

    XiaoYu Li

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  1. Chen Lin
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  2. GuoWu Yang
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Correspondence to GuoWu Yang.

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Appendix A The change of non-constant stabilizers

Appendix A The change of non-constant stabilizers

Here, we use Tables 7, 8 and 9 to list the transformations of the non-constant stabilizers in the 5-qubit code block A and 7-qubit code block B under the conjugate action of the Circuit \(\varGamma (Z,Z)\).

Table 7 Stabilizer generator generators \((Z_{0}X_{2}Z_{3}Y_{4})_{A}\otimes (I^{\otimes 7})_{B}\) under the conjugate action of \(\varGamma (Z,Z)\)
Full size table
Table 8 Stabilizer generator generators \((I^{\otimes 5})_{A}\otimes (X_{0}X_{2}X_{4}X_{6})_{B}\) under the conjugate action of \(\varGamma (Z,Z)\)
Full size table
Table 9 Stabilizer generator generators \((I^{\otimes 5})_{A}\otimes (X_{1}X_{2}X_{5}X_{6})_{B}\) under the conjugate action of \(\varGamma (Z,Z)\)
Full size table

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Lin, C., Yang, G., Luo, Q. et al. Pieceable fault tolerant conversion between 5-qubit code and 7-CSS code. Quantum Inf Process 19, 243 (2020). https://doi.org/10.1007/s11128-020-02740-3

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