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Preparation of pseudo-pure states for NMR quantum computing with one ancillary qubit

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Abstract

Quantum state preparation plays an equally important role as quantum operations and measurements in quantum information processing. The previous methods for initialization require either an exponential number of experiments, or cause signal reduction or place restrictions on molecular structures. In this study, we propose three types of quantum circuits for preparing the pseudo-pure states of (n − 1) qubits in the n-coupled Hilbert space, which simply needs the assistance of one ancilla spin and two different experiments independent of n. Most importantly, our methods work well on homo-nuclear and hetero-nuclear molecules without the reduction of signals in the gradient field. As a proof-of-principle demonstration, we experimentally prepared the pseudo-pure states of heteronuclear 2-qubit and homonuclear 4-qubit molecules using a nuclear magnetic resonance quantum information processor.

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References

  1. D. R. Simon, SIAM J. Comput. 26, 1474 (1997).

    Article  MathSciNet  Google Scholar 

  2. P. W. Shor, SIAM J. Comput. 26, 1484 (1997).

    Article  MathSciNet  Google Scholar 

  3. L. K. Grover, Phys. Rev. Lett. 79, 4709 (1997).

    Article  ADS  Google Scholar 

  4. A. Ekert, and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).

    Article  ADS  Google Scholar 

  5. I. L. Chuang, N. Gershenfeld, and M. Kubinec, Phys. Rev. Lett. 80, 3408 (1998).

    Article  ADS  Google Scholar 

  6. D. P. DiVincenzo, Science 270, 255 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  7. C. H. Bennett, and D. P. DiVincenzo, Nature 404, 247 (2000).

    Article  ADS  Google Scholar 

  8. M. A. Nielsen, and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

    MATH  Google Scholar 

  9. R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, and C. F. Roos, Nature 463, 68 (2010), arXiv: 0909.0674.

    Article  ADS  Google Scholar 

  10. L. Lamata, J. León, T. Schätz, and E. Solano, Phys. Rev. Lett. 98, 253005 (2007).

    Article  ADS  Google Scholar 

  11. Y. S. Weinstein, S. Lloyd, J. Emerson, and D. G. Cory, Phys. Rev. Lett. 89, 157902 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  12. D. Lu, N. Xu, R. Xu, H. Chen, J. Gong, X. Peng, and J. Du, Phys. Rev. Lett. 107, 020501 (2011), arXiv: 1105.4228.

    Article  ADS  Google Scholar 

  13. A. Aspuru-Guzik, Science 309, 1704 (2005).

    Article  ADS  Google Scholar 

  14. J. Du, N. Xu, X. Peng, P. Wang, S. Wu, and D. Lu, Phys. Rev. Lett. 104, 030502 (2010).

    Article  ADS  Google Scholar 

  15. S. J. Wei, T. Xin, and G. L. Long, Sci. China-Phys. Mech. Astron. 61, 070311 (2018), arXiv: 1706.08080.

    Article  ADS  Google Scholar 

  16. D. S. Abrams, and S. Lloyd, Phys. Rev. Lett. 83, 5162 (1999).

    Article  ADS  Google Scholar 

  17. A. W. Harrow, A. Hassidim, and S. Lloyd, Phys. Rev. Lett. 103, 150502 (2009), arXiv: 0811.3171.

    Article  ADS  MathSciNet  Google Scholar 

  18. J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).

    Article  ADS  Google Scholar 

  19. D. Loss, and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).

    Article  ADS  Google Scholar 

  20. A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, Phys. Rev. Lett. 74 4083 (1995).

    Article  ADS  Google Scholar 

  21. B. E. Kane, Nature 393 133 (1998).

    Article  ADS  Google Scholar 

  22. A. Shnirman, G. Schön, and Z. Hermon, Phys. Rev. Lett. 79, 2371 (1997).

    Article  ADS  Google Scholar 

  23. D. G. Cory, A. F. Fahmy, and T. F. Havel, Proc. Natl. Acad. Sci. USA 94, 1634 (1997).

    Article  ADS  Google Scholar 

  24. N. A. Gershenfeld, and I. L. Chuang, Science 275, 350 (1997).

    Article  MathSciNet  Google Scholar 

  25. X. Y. Pan, Sci. China-Phys. Mech. Astron. 60, 020333 (2017).

    Article  ADS  Google Scholar 

  26. S. Gulde, M. Riebe, G. P. T. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. L. Chuang, and R. Blatt, Nature 421, 48 (2003).

    Article  ADS  Google Scholar 

  27. F. Mintert, and C. Wunderlich, Phys. Rev. Lett. 87, 257904 (2001).

    Article  ADS  Google Scholar 

  28. H. Li, Y. Liu, and G. L. Long, Sci. China-Phys. Mech. Astron. 60, 080311 (2017), arXiv: 1703.10348.

    Article  ADS  Google Scholar 

  29. X. Peng, X. Zhu, X. Fang, M. Feng, M. Liu, and K. Gao, J. Chem. Phys. 120, 3579 (2004).

    Article  ADS  Google Scholar 

  30. D. G. Cory, M. D. Price, and T. F. Havel, Phys. D-Nonlinear Phenom. 120, 82 (1998).

    Article  ADS  Google Scholar 

  31. E. Knill, I. Chuang, and R. Laflamme, Phys. Rev. A 57, 3348 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  32. L. M. K. Vandersypen, C. S. Yannoni, M. H. Sherwood, and I. L. Chuang, Phys. Rev. Lett. 83, 3085 (1999).

    Article  ADS  Google Scholar 

  33. E. Knill, R. Laflamme, R. Martinez, and C. H. Tseng, Nature 404, 368 (2000).

    Article  ADS  Google Scholar 

  34. M. Kawamura, R. Sawae, T. Kumaya, K. Takarabe, Y. Manmoto, and T. Sakata, Int. J. Quantum Chem. 100, 1033 (2004).

    Article  Google Scholar 

  35. S. L. Huang, J. X. Chen, Y. N. Li, and B. Zeng, Sci. China-Phys. Mech. Astron. 61, 110311 (2018), arXiv: 1711.10878.

    Article  ADS  Google Scholar 

  36. S. M. Fei, Sci. China-Phys. Mech. Astron. 60, 020331 (2017).

    Article  ADS  Google Scholar 

  37. N. A. Gershenfeld, and I. L. Chuang, Science 275, 350 (1997).

    Article  MathSciNet  Google Scholar 

  38. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1990).

    Google Scholar 

  39. T. Xin, J. S. Pedernales, L. Lamata, E. Solano, and G. L. Long, Sci. Rep. 7, 12797 (2017), arXiv: 1606.00686.

    Article  ADS  Google Scholar 

  40. G. M. Leskowitz, and L. J. Mueller, Phys. Rev. A 69, 052302 (2004).

    Article  ADS  Google Scholar 

  41. J. S. Lee, Phys. Lett. A 305, 349 (2002).

    Article  ADS  Google Scholar 

  42. T. Xin, D. Lu, J. Klassen, N. Yu, Z. Ji, J. Chen, X. Ma, G. Long, B. Zeng, and R. Laflamme, Phys. Rev. Lett. 118, 020401 (2017), arXiv: 1604.02046.

    Article  ADS  MathSciNet  Google Scholar 

  43. N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, J. Magn. Reson. 172, 296 (2005).

    Article  ADS  Google Scholar 

  44. C. A. Ryan, C. Negrevergne, M. Laforest, E. Knill, and R. Laflamme, Phys. Rev. A 78, 012328 (2008), arXiv: 0803.1982.

    Article  ADS  Google Scholar 

  45. D. Lu, K. Li, J. Li, H. Katiyar, A. J. Park, G. Feng, T. Xin, H. Li, G. Long, A. Brodutch, J. Baugh, B. Zeng, and R. Laflamme, npj Quantum Inf. 3, 45 (2017), arXiv: 1701.01198.

    Article  ADS  Google Scholar 

  46. J. Li, X. Yang, X. Peng, and C. P. Sun, Phys. Rev. Lett. 118, 150503 (2017), arXiv: 1608.00677.

    Article  ADS  Google Scholar 

  47. Y. G. Chen, and J. B. Wang, Comput. Phys. Commun. 184, 853 (2013), arXiv: 1208.0194.

    Article  ADS  MathSciNet  Google Scholar 

  48. M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, Phys. Rev. Lett. 93, 130502 (2004).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, China

    Tao Xin & Gui-Lu Long

  2. Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Tao Xin

  3. Peng Cheng Laboratory, Center for Quantum Computing, Shenzhen, 518055, China

    Tao Xin

  4. Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Tao Xin

  5. Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China

    Liang Hao

  6. Center for Computational Sciences, Sichuan Normal University, Chengdu, 610068, China

    Shi-Yao Hou

  7. College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu, 610068, China

    Shi-Yao Hou

  8. Institute for Quantum Computing, Waterloo, N2L 3G1, Canada

    Guan-Ru Feng

  9. Tsinghua National Laboratory of Information Science and Technology, Beijing, 100084, China

    Gui-Lu Long

  10. The Innovative Center of Quantum Matter, Beijing, 100084, China

    Gui-Lu Long

Authors
  1. Tao Xin
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  2. Liang Hao
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  3. Shi-Yao Hou
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  4. Guan-Ru Feng
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  5. Gui-Lu Long
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Corresponding author

Correspondence to Gui-Lu Long.

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Xin, T., Hao, L., Hou, SY. et al. Preparation of pseudo-pure states for NMR quantum computing with one ancillary qubit. Sci. China Phys. Mech. Astron. 62, 960312 (2019). https://doi.org/10.1007/s11433-019-9366-7

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  • DOI: https://doi.org/10.1007/s11433-019-9366-7

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