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

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Abstract

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.

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Notes

  1. The sum of the horizontal and vertical distances between points on a grid.

  2. Quantum Design Automation Lab (QDA).

References

  1. Benenti, G.: Principles of Quantum Computation and Information: Basic Tools and Special Topics, vol. 2. World Scientific, Singapore (2007)

    Book  Google Scholar 

  2. Nakahara, M., Ohmi, T.: Quantum Computing: From Linear Algebra to Physical Realizations. CRC Press, Boca Raton (2010)

    MATH  Google Scholar 

  3. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  4. Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  5. Casati, G., Shepelyansky, D.L., Zoller, P.: Quantum computers, algorithms and chaos, vol. 162. IOS Press, Amsterdam (2006)

    MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

  9. Briegel, H.J., Browne, D.E., Dür, W., Raussendorf, R., Van den Nest, M.: Measurement-based quantum computation. Nat. Phys. 5, 19 (2009)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  12. Mohammadzadeh, N., Sedighi, M., Zamani, M.S.: Quantum physical synthesis: improving physical design by netlist modifications. Microelectron. J. 41, 219–230 (2010)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  14. Mohammadzadeh, N., Taqavi, E.: Quantum circuit physical design flow for the multiplexed trap architecture. Microprocess. Microsyst. 45, 23–31 (2016)

    Article  Google Scholar 

  15. Mohammadzadeh, N.: Physical design of quantum circuits in ion trap technology—a survey. Microelectron. J. 55, 116–133 (2016)

    Article  Google Scholar 

  16. Farghadan, A., Mohammadzadeh, N.: Quantum circuit physical design flow for 2D nearest-neighbor architectures. Int. J. Circuit Theory Appl. 45, 989–1000 (2017)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  18. Campbell, E.T., Fitzsimons, J.: An Introduction to One-Way Quantum Computing in Distributed Architectures, arXiv preprint arXiv:0906.2725

  19. Benjamin, S., Eisert, J., Stace, T.: Optical generation of matter qubit graph states. N. J. Phys. 7, 194 (2005)

    Article  MathSciNet  Google Scholar 

  20. Chen, J., Wang, L., Charbon, E., Wang, B.: Programmable architecture for quantum computing. Phys. Rev. A 88, 022311 (2013)

    Article  ADS  Google Scholar 

  21. Clark, S., Alves, C.M., Jaksch, D.: Efficient generation of graph states for quantum computation. N. J. Phys. 7, 124 (2005)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  23. Maslov, D., Falconer, S.M., Mosca, M.: Quantum circuit placement. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 27, 752–763 (2008)

    Article  Google Scholar 

  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. 495–500

  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)

    Article  Google Scholar 

  26. Geem, Z.W.: Music-Inspired Harmony Search Algorithm: Theory and Applications, vol. 191. Springer, Berlin (2009)

    Google Scholar 

  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. 95–100

  28. Zulehner, A., Paler, A., Wille, R.: Efficient Mapping of Quantum Circuits to the IBM QX Architectures, arXiv preprint arXiv:1712.04722

  29. Danos, V., Kashefi, E., Panangaden, P.: The measurement calculus. J. ACM (JACM) 54, 8 (2007)

    Article  MathSciNet  Google Scholar 

  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). https://doi.org/10.1017/CBO9781139193313.008

    Chapter  Google Scholar 

  31. Pius, E.: Automatic parallelisation of quantum circuits using the measurement based quantum computing model. In: High Performance Computing (2010)

  32. Newman, M.E.: The mathematics of networks. New Palgrave Encycl. Econ. 2, 1–12 (2008)

    Google Scholar 

  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. 64–69

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Authors and Affiliations

  1. Quantum Architectures and Computation Group (QACG), Department of Computer Engineering, Shahed University, Tehran, Iran

    Sajjad Sanaei & Naser Mohammadzadeh

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  1. Sajjad Sanaei
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  2. Naser Mohammadzadeh
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Correspondence to Naser Mohammadzadeh.

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Sanaei, S., Mohammadzadeh, N. Qubit mapping of one-way quantum computation patterns onto 2D nearest-neighbor architectures. Quantum Inf Process 18, 56 (2019). https://doi.org/10.1007/s11128-019-2177-x

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