International Journal of Theoretical Physics

, Volume 56, Issue 6, pp 1948–1960 | Cite as

Quantum Gauss-Jordan Elimination and Simulation of Accounting Principles on Quantum Computers

  • Do Ngoc Diep
  • Do Hoang Giang
  • Nguyen Van Minh


The paper is devoted to a version of Quantum Gauss-Jordan Elimination and its applications. In the first part, we construct the Quantum Gauss-Jordan Elimination (QGJE) Algorithm and estimate the complexity of computation of Reduced Row Echelon Form (RREF) of N × N matrices. The main result asserts that QGJE has computation time is of order 2 N/2. The second part is devoted to a new idea of simulation of accounting by quantum computing. We first expose the actual accounting principles in a pure mathematics language. Then, we simulate the accounting principles on quantum computers. We show that, all accounting actions are exhousted by the described basic actions. The main problems of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation, we use our constructed Quantum Gauss-Jordan Elimination to solve the problems and the complexity of quantum computing is a square root order faster than the complexity in classical computing.


Quantum Gauss-Jordan Elimination Complexity Quantum algorithm Accounting principles Quantum search System of linear equations in the economic model of Leontief 



The work was partially reported in the Mathematical Club and Seminar of Topology and Geometry, Institute of Mathematics in Hanoi. We thank the peoples, who attended for stimulating comments.

The paper was done in the framework of a project of research group “Noncommutative Geometry and Topology”, at VIASM. The first author thanks the Institute for a scientific stay support and Thang Long University for providing two invited lectures at Information Seminar.


  1. 1.
    Diep, D.N.: Quantum computers and related mathematical structures. J. Math. Appl. 2(1), 79–94 (2004). in VietnameseGoogle Scholar
  2. 2.
    Press, W.H., Teukolsky, S.A., Velterling, W.T., Flannery, B.P.: Numerical Recipes in C, Cambridge University PressGoogle Scholar
  3. 3.
    Ekert, A., Hayden, P., Inamori, H.: Basis Concepts In Quantum Computation, Centre for Quantum Computation. University of Oxford, Oxford (2000)zbMATHGoogle Scholar
  4. 4.
    Kaye, P., Laflamme, R., Mosca, M.: An Introduction to Quantum Computing, Oxford University PressGoogle Scholar
  5. 5.
    Weygandt, J., Kieso, D., Kimmel, P.: Accounting Principles, 6th edn, p 1138. Wiley, USA (2002)Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Do Ngoc Diep
    • 1
    • 4
  • Do Hoang Giang
    • 2
  • Nguyen Van Minh
    • 3
  1. 1.Institute of MathematicsVietnam Academy of Sciences and TechnologyHanoiVietnam
  2. 2.K47A1T, Department of Mathematics, Mechanics and Informatics, College of Natural SciencesVietnam National UniversityHanoiVietnam
  3. 3.Department of MathematicsThuong Tin High SchoolHanoiVietnam
  4. 4.Thang Long UniversityHanoiVietnam

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