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Radix-independent, efficient arrays for multi-level n-qudit quantum and reversible computation

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Abstract

Multiple-valued quantum logic allows the designers to reduce the number of cells while obtaining more functionality in the quantum circuits. Large r-valued reversible or quantum gates (r stands for radix and is more than 2) cannot be directly realized in the current quantum technology. Therefore, we are interested in designing the large reversible and quantum controlled gates using the arrays of one-quantum digit (qudit) or two-qudit gates. In our previous work, we proposed quantum arrays to implement the r-valued quantum circuits. In this paper, we propose novel efficient structures and arrays, for r-valued quantum logic gates. The quantum costs of the developed quantum arrays are independent of the radix of calculations in the quantum circuit.

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References

  1. Mohammadi, M., Niknafs, A., Eshghi, M.: Controlled gates for multi-level quantum computation. Quantum Inf. Process. 10, 175–192 (2011)

    Article  MathSciNet  Google Scholar 

  2. Lukac, M., Pivtoraiko, M., Mishchenko, A., Perkowski, M.: Automated synthesis of generalized reversible cascades using genetic algorithms. In: Proceedings of the Fifth International Workshop on Boolean Problems, Freiberg, Sachsen, Germany, 19–20 Sept, pp. 33–45 (2006)

  3. Kahn, M.H.A., Perkowski, M.: Evolutionary algorithm based synthesis of multi-output ternary functions using quantum cascade of generalized ternary gates. Int. J. Mult. Valued Log. Soft Comput. (2005)

  4. Mohammadi, M., Eshghi, M.: Heuristic methods to use don’t cares in automated design of reversible and quantum logic circuits. Quantum Inf. Process. J. 7(4), 175–192 (2008)

    Article  MathSciNet  Google Scholar 

  5. Mohammadi, M., Eshghi, M.: On figures of merit in reversible and quantum logic designs. Quantum Inf. Process. J. 8(4), 297–318 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mohammadi, M., Eshghi, M., Dueck, G.W.: Design and optimization of single and multiple-loop reversible and quantum feedback circuits. World Sci. J. Circuits Syst. Comput. 21(2), 301–315 (2012)

    Google Scholar 

  7. Mohammadi M.: Efficient genetic based methods for optimizing the reversible and quantum logic circuits. J. Adv. Comput. Res. 3(3), 85–96 (2012)

  8. Mohammadi, M., Niknafs, A.: Synthesis and optimization of multiple-valued combinational and sequential reversible circuits with don’t cares. Integr. VLSI J. 46(2), 189–196 (2013)

  9. Miller, D.M., Maslov, D., Dueck, G.W.: Synthesis of quantum multiple-valued circuits. J. Mult. Valued Log. Soft. Comput. 12(5/6), 431 (2006)

  10. Khan, M.H.A.: Design of reversible/quantum ternary multiplexer and demultiplexer. Eng. Lett. 13(2), 65–69 (2006)

    Google Scholar 

  11. Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52(5), 3457–3467 (1995)

    Article  ADS  Google Scholar 

  12. Brennen, G.K., Bullock, S.S., O’Leary, D.P.: Efficient circuits for exact-universal computation with qudits. Quantum Inf. Comput. 6, 436–454 (2006)

    MathSciNet  MATH  Google Scholar 

  13. Rosenbaum, D., Perkowski, M.: Efficient implementation of controlled operations for multivalued quantum logic. In: ISMVL, 2009 39th International Symposium on Multiple-Valued Logic, pp. 86–91 (2009)

  14. Khan, M.H.A., Perkowski, M.A., Kerntopf, P.: Multi-output Galois field sum of products (GFSOP) synthesis with new quantum cascades. In: Proceedings of the International Symposium on Multiple-Valued Logic, May, pp. 146–153 (2003)

  15. Al-Rabadi, A.: New multiple-valued Galois field sum-of-product cascades and lattices for multiple-valued quantum logic synthesis. In: 6th International Symposium on Representations and Methodology of Future Computing Technologies, March, pp. 171–182 (2003)

  16. Muthukrishnan, A., Stroud Jr, C.R.: Multivalued logic gates for quantum computation. Phys. Rev. A 62(5), 052309/1–052309/8 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  17. Picton, P.: A universal architecture for multiple-valued reversible logic. MVL J. 5, 27–37 (2000)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Majid Mohammadi

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  1. Majid Mohammadi
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Correspondence to Majid Mohammadi.

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Mohammadi, M. Radix-independent, efficient arrays for multi-level n-qudit quantum and reversible computation. Quantum Inf Process 14, 2819–2832 (2015). https://doi.org/10.1007/s11128-015-1011-3

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  • DOI: https://doi.org/10.1007/s11128-015-1011-3

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