Qubit mapping of one-way quantum computation patterns onto 2D nearest-neighbor architectures

  • Sajjad Sanaei
  • Naser MohammadzadehEmail author


Distinct practical advantages of the one-way quantum computation (1WQC) have attracted the attention of many researchers. To physically realize a 1WQC pattern, its qubits should be mapped onto a quantum physical environment. The nearest-neighbor architectures are suitable for implementing 1WQC patterns because they provide nearest-neighbor sufficient interactions for full entanglement that are necessary for highly entangled configuration of 1WQC. To make a 1WQC nearest-neighbor compliant, swap gates are needed to bring the interacting qubits of a gate adjacent. More swap gates result in the higher latency and error probability. Therefore, an efficient mapping of qubits of a 1WQC pattern onto qubits provided by a nearest-neighbor architecture can dramatically reduce the number of swaps. This motivates us to propose an approach that maps qubits of a 1WQC pattern to qubits of a two-dimensional nearest-neighbor architecture. Our evaluations show that the proposed mapping approach reduces the number of swaps in the range of 0–96.2% in comparison with the best in the literature for the attempted benchmarks.


Quantum computing 1WQC Nearest-neighbor technologies Mapping Eigenvector centrality 



  1. 1.
    Benenti, G.: Principles of Quantum Computation and Information: Basic Tools and Special Topics, vol. 2. World Scientific, Singapore (2007)CrossRefGoogle Scholar
  2. 2.
    Nakahara, M., Ohmi, T.: Quantum Computing: From Linear Algebra to Physical Realizations. CRC Press, Boca Raton (2010)zbMATHGoogle Scholar
  3. 3.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  4. 4.
    Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    Casati, G., Shepelyansky, D.L., Zoller, P.: Quantum computers, algorithms and chaos, vol. 162. IOS Press, Amsterdam (2006)zbMATHGoogle Scholar
  6. 6.
    Saffman, M., Walker, T.: Analysis of a quantum logic device based on dipole–dipole interactions of optically trapped Rydberg atoms. Phys. Rev. A 72, 022347 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    Strauch, F.W., Johnson, P.R., Dragt, A.J., Lobb, C., Anderson, J., Wellstood, F.: Quantum logic gates for coupled superconducting phase qubits. Phys. Rev. Lett. 91, 167005 (2003)ADSCrossRefGoogle Scholar
  8. 8.
    Chan, T.M., Hoffmann, H.-F., Kiazyk, S., Lubiw, A.: Minimum length embedding of planar graphs at fixed vertex locations. In: International Symposium on Graph Drawing, pp. 376–387 (2013)Google Scholar
  9. 9.
    Briegel, H.J., Browne, D.E., Dür, W., Raussendorf, R., Van den Nest, M.: Measurement-based quantum computation. Nat. Phys. 5, 19 (2009)CrossRefGoogle Scholar
  10. 10.
    Devitt, S.J., Fowler, A.G., Stephens, A.M., Greentree, A.D., Hollenberg, L.C., Munro, W.J., et al.: Architectural design for a topological cluster state quantum computer. N. J. Phys. 11, 083032 (2009)CrossRefGoogle Scholar
  11. 11.
    Joo, J., Alba, E., García-Ripoll, J.J., Spiller, T.P.: Generating and verifying graph states for fault-tolerant topological measurement-based quantum computing in two-dimensional optical lattices. Phys. Rev. A 88, 012328 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    Mohammadzadeh, N., Sedighi, M., Zamani, M.S.: Quantum physical synthesis: improving physical design by netlist modifications. Microelectron. J. 41, 219–230 (2010)CrossRefGoogle Scholar
  13. 13.
    Mohammadzadeh, N., Zamani, M.S., Sedighi, M.: Quantum circuit physical design methodology with emphasis on physical synthesis. Quantum Inf. Process. 13, 445–465 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    Mohammadzadeh, N., Taqavi, E.: Quantum circuit physical design flow for the multiplexed trap architecture. Microprocess. Microsyst. 45, 23–31 (2016)CrossRefGoogle Scholar
  15. 15.
    Mohammadzadeh, N.: Physical design of quantum circuits in ion trap technology—a survey. Microelectron. J. 55, 116–133 (2016)CrossRefGoogle Scholar
  16. 16.
    Farghadan, A., Mohammadzadeh, N.: Quantum circuit physical design flow for 2D nearest-neighbor architectures. Int. J. Circuit Theory Appl. 45, 989–1000 (2017)CrossRefGoogle Scholar
  17. 17.
    Lin, C.-C., Sur-Kolay, S., Jha, N.K.: PAQCS: Physical design-aware fault-tolerant quantum circuit synthesis. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 23, 1221–1234 (2015)CrossRefGoogle Scholar
  18. 18.
    Campbell, E.T., Fitzsimons, J.: An Introduction to One-Way Quantum Computing in Distributed Architectures, arXiv preprint arXiv:0906.2725
  19. 19.
    Benjamin, S., Eisert, J., Stace, T.: Optical generation of matter qubit graph states. N. J. Phys. 7, 194 (2005)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Chen, J., Wang, L., Charbon, E., Wang, B.: Programmable architecture for quantum computing. Phys. Rev. A 88, 022311 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    Clark, S., Alves, C.M., Jaksch, D.: Efficient generation of graph states for quantum computation. N. J. Phys. 7, 124 (2005)CrossRefGoogle Scholar
  22. 22.
    Kay, A., Pachos, J.K., Adams, C.S.: Graph-state preparation and quantum computation with global addressing of optical lattices. Phys. Rev. A 73, 022310 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    Maslov, D., Falconer, S.M., Mosca, M.: Quantum circuit placement. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 27, 752–763 (2008)CrossRefGoogle Scholar
  24. 24.
    Shafaei, A., Saeedi, M., Pedram, M.: Qubit placement to minimize communication overhead in 2D quantum architectures. In: Design Automation Conference (ASP-DAC), 2014 19th Asia and South Pacific, 2014, pp. 495–500Google Scholar
  25. 25.
    Alfailakawi, M.G., Ahmad, I., Hamdan, S.: Harmony-search algorithm for 2D nearest neighbor quantum circuits realization. Exp. Syst. Appl. 61, 16–27 (2016)CrossRefGoogle Scholar
  26. 26.
    Geem, Z.W.: Music-Inspired Harmony Search Algorithm: Theory and Applications, vol. 191. Springer, Berlin (2009)Google Scholar
  27. 27.
    Shrivastwa, R.R., Datta, K., Sengupta, I.: Fast qubit placement in 2D architecture using nearest neighbor realization. In: 2015 IEEE International Symposium on Nanoelectronic and Information Systems (iNIS), 2015, pp. 95–100Google Scholar
  28. 28.
    Zulehner, A., Paler, A., Wille, R.: Efficient Mapping of Quantum Circuits to the IBM QX Architectures, arXiv preprint arXiv:1712.04722
  29. 29.
    Danos, V., Kashefi, E., Panangaden, P.: The measurement calculus. J. ACM (JACM) 54, 8 (2007)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Danos, V., Kashefi, E., Panangaden, P., Perdrix, S.: Extended measurement calculus. In: Gay, S., Mackie, I. (eds.) Semantic Techniques in Quantum Computation. Cambridge University Press, Cambridge, pp. 235–310. (2009). CrossRefGoogle Scholar
  31. 31.
    Pius, E.: Automatic parallelisation of quantum circuits using the measurement based quantum computing model. In: High Performance Computing (2010)Google Scholar
  32. 32.
    Newman, M.E.: The mathematics of networks. New Palgrave Encycl. Econ. 2, 1–12 (2008)Google Scholar
  33. 33.
    Houshmand, M., Samavatian, M.H., Zamani, M.S., Sedighi, M.: Extracting one-way quantum computation patterns from quantum circuits. In: 2012 16th CSI International Symposium on Computer Architecture and Digital Systems (CADS), 2012, pp. 64–69Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Quantum Architectures and Computation Group (QACG), Department of Computer EngineeringShahed UniversityTehranIran

Personalised recommendations