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Application of Quantum Gauss-Jordan Elimination Code to Quantum Secret Sharing Code

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Abstract

The QSS codes associated with a MSP code are based on finding an invertible matrix V, solving the system \(\mathbf {v}_{A}^{T}M_{B} \left (\begin {array}{c} \mathbf {s}\\ \mathbf {a} \end {array}\right )=\mathbf {s}\). We propose a quantum Gauss-Jordan Elimination Procedure to produce such a pivotal matrix V by using the Grover search code. The complexity of solving is of square-root order of the cardinal number of the unauthorized set \(\sqrt {2^{|B|}}\).

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References

  1. Diep, D.N., Giang, D.H., Minh, N.V.: Quantum Gauss-Jordan Elimination and simulation of accounting principles on quantum computers. Int. J. Theor. Phys. 56(6), 1948–1960 (2017)

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Authors and Affiliations

  1. TIMAS, Thang Long University, Nghiem Xuan Yem road, Hoang Mai district, Hanoi, Vietnam

    Do Ngoc Diep & Phan Huy Phu

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc viet Road, Cau Giay District, 10307, Hanoi, Vietnam

    Do Ngoc Diep

  3. K47A1T, Department of Mathematics, Mechanics and Informatics, College of Natural Sciences, Vietnam National University, 40 Nguyen Trai road, Thanh Xuan District, Hanoi, Vietnam

    Do Hoang Giang

Authors
  1. Do Ngoc Diep
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  2. Do Hoang Giang
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  3. Phan Huy Phu
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Correspondence to Do Ngoc Diep.

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Diep, D.N., Giang, D.H. & Phu, P.H. Application of Quantum Gauss-Jordan Elimination Code to Quantum Secret Sharing Code. Int J Theor Phys 57, 841–847 (2018). https://doi.org/10.1007/s10773-017-3617-y

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  • DOI: https://doi.org/10.1007/s10773-017-3617-y

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