Quantum Information Processing

, Volume 14, Issue 6, pp 1889–1906 | Cite as

Experimental implementation of quantum information processing by Zeeman-perturbed nuclear quadrupole resonance

  • João Teles
  • Christian Rivera-Ascona
  • Roberson S. Polli
  • Rodrigo Oliveira-Silva
  • Edson L. G. Vidoto
  • José P. Andreeta
  • Tito J. Bonagamba


Nuclear magnetic resonance (NMR) has been widely used in the context of quantum information processing (QIP). However, despite the great similarities between NMR and nuclear quadrupole resonance (NQR), no experimental implementation for QIP using NQR has been reported. We describe the implementation of basic quantum gates and their applications on the creation and manipulation of pseudopure states using linearly polarized radiofrequency pulses under static magnetic field perturbation. The NQR quantum operations were implemented using a single-crystal sample of \(\hbox {KClO}_{3}\) and observing \(^{35}\hbox {Cl}\) nuclei, which possess spin 3/2 and give rise to a two-qubit system. The results are very promising and indicate that NQR can be successfully used for performing fundamental experiments in QIP. One advantage of NQR in comparison with NMR is that the main interaction is internal to the sample, which makes the system more compact, lowering its cost and making it easier to be miniaturized to solid-state devices. Furthermore, as an example, the study of squeezed spin states could receive relevant contributions from NQR.


Quantum information processing Experimental realization NQR NMR 



This work was supported by Brazilian agencies FAPESP (2012/02208-5) and CNPq (483109/2011-8), and by the Brazilian National Institute of Science and Technology for Quantum Information (INCT-IQ). The authors also acknowledge Aparecido Donizeti Fernandes de Amorim and Elderson Cássio Domenicucci by the technical support.


  1. 1.
    Araujo-Ferreira, A.G., Auccaise, R., Sarthour, R.S., Oliveira, I.S., Bonagamba, T.J., Roditi, I.: Classical bifurcation in a quadrupolar nmr system. Phys. Rev. A 87(5), 053,605 (2013). doi: 10.1103/PhysRevA.87.053605 Google Scholar
  2. 2.
    Auccaise, R., Araujo-Ferreira, A.G., Sarthour, R.S., Oliveira, I.S., Bonagamba, T.J., Roditi, I.: Spin squeezing in a quadrupolar nuclei NMR system. Phys. Rev. Lett. 114(4), 043,604 (2015)Google Scholar
  3. 3.
    Auccaise, R., Maziero, J., Celeri, L.C., Soares-Pinto, D.O., deAzevedo, E.R., Bonagamba, T.J., Sarthour, R.S., Oliveira, I.S., Serra, R.M.: Experimentally witnessing the quantumness of correlations. Phys. Rev. Lett. 107(7), 070,501 (2011). doi: 10.1103/PhysRevLett.107.070501 Google Scholar
  4. 4.
    Auccaise, R., Teles, J., Sarthour, R.S., Bonagamba, T.J., Oliveira, I.S., de Azevedo, E.R.: A study of the relaxation dynamics in a quadrupolar nmr system using quantum state tomography. J. Magn. Reson. 192(1), 17–26 (2008). doi: 10.1016/j.jmr.2008.01.009 ADSGoogle Scholar
  5. 5.
    Bain, A., Khasawneh, M.: From NQR to NMR: the complete range of quadrupole interactions. Concepts Magn. Reson. Part A 22A(2), 69–78 (2004). doi: 10.1002/cmr.a.20013 Google Scholar
  6. 6.
    Baugh, J., Moussa, O., Ryan, C.A., Laflamme, R., Ramanathan, C., Havel, T.F., Cory, D.G.: Solid-state nmr three-qubit homonuclear system for quantum-information processing: control and characterization. Phys. Rev. A 73(2), 022,305 (2006). doi: 10.1103/PhysRevA.73.022305 Google Scholar
  7. 7.
    Bonk, F.A., Sarthour, R.S., deAzevedo, E.R., Bulnes, J.D., Mantovani, G.L., Freitas, J.C.C., Bonagamba, T.J., Guimaraes, A.P., Oliveira, I.S.: Quantum-state tomography for quadrupole nuclei and its application on a two-qubit system. Phys. Rev. A 69(4), 042322–042322 (2004)ADSGoogle Scholar
  8. 8.
    Cappellaro, P., Goldstein, G., Hodges, J.S., Jiang, L., Maze, J.R., Sorensen, A.S., Lukin, M.D.: Environment-assisted metrology with spin qubits. Phys. Rev. A 85(3), (2012). doi: 10.1103/PhysRevA.85.032336
  9. 9.
    Childress, L., Dutt, M.V.G., Taylor, J.M., Zibrov, A.S., Jelezko, F., Wrachtrup, J., Hemmer, P.R., Lukin, M.D.: Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science 314(5797), 281–285 (2006). doi: 10.1126/science.1131871 CrossRefADSGoogle Scholar
  10. 10.
    Chuang, I.L., Gershenfeld, N., Kubinec, M.G., Leung, D.W.: Bulk quantum computation with nuclear magnetic resonance: theory and experiment. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 454, 447–467 (1969)Google Scholar
  11. 11.
    Cory, D.G., Fahmy, A.F., Havel, T.F.: Ensemble quantum computing by nmr spectroscopy. Proc. Natl. Acad. Sci. USA 94(5), 1634–1639 (1997)ADSGoogle Scholar
  12. 12.
    Estrada, R.A., de Azevedo, E.R., Duzzioni, E.I., Bonagamba, T.J., Youssef Moussa, M.H.: Spin coherent states in nmr quadrupolar system: experimental and theoretical applications. Eur. Phys. J. D 67(6), 127 (2013). doi: 10.1140/epjd/e2013-30689-1 ADSGoogle Scholar
  13. 13.
    Fisher, A.: Quantum computing in the solid state: the challenge of decoherence. Philos Tr. R. Soc. S-A 361(1808), 1441–1450 (2003). doi: 10.1098/rsta.2003.1213 ADSGoogle Scholar
  14. 14.
    Fortunato, E.M., Pravia, M.A., Boulant, N., Teklemariam, G., Havel, T.F., Cory, D.G.: Design of strongly modulating pulses to implement precise effective hamiltonians for quantum information processing. J. Chem. Phys. 116(17), 7599–7606 (2002)ADSGoogle Scholar
  15. 15.
    Furman, G., Goren, S.: Pure nqr quantum computing. Zeitschrift Fur Naturforschung Sect. A-A J. Phys. Sci. 57(6–7), 315–319 (2002)ADSGoogle Scholar
  16. 16.
    Gershenfeld, N.A., Chuang, I.L.: Bulk spin-resonance quantum computation. Science 275(5298), 350–356 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Hanson, R., Awschalom, D.D.: Coherent manipulation of single spins in semiconductors. Nature 453(7198), 1043–1049 (2008). doi: 10.1038/nature07129 CrossRefADSGoogle Scholar
  18. 18.
    Itoh, K.: An all-silicon linear chain nmr quantum computer. Solid State Commun. 133(11), 747–752 (2005)ADSGoogle Scholar
  19. 19.
    Kampermann, H., Veeman, W.: Characterization of quantum algorithms by quantum process tomography using quadrupolar spins in solid-state nuclear magnetic resonance. J. Chem. Phys. 122(21), 214,108 (2005). doi: 10.1063/1.1904595 Google Scholar
  20. 20.
    Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbruggen, T., Glaser, S.: Optimal control of coupled spin dynamics: design of nmr pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172(2), 296–305 (2005). doi: 10.1016/j.jmr.2004.11.004 ADSGoogle Scholar
  21. 21.
    Khitrin, A.K., Fung, B.M.: Nmr simulation of an eight-state quantum system. Phys. Rev. A 64, 032,306 (2001). doi: 10.1103/PhysRevA.64.032306 Google Scholar
  22. 22.
    Kitagawa, M., Ueda, M.: Squeezed spin states. Phys. Rev. A 47(6), 5138–5143 (1993). doi: 10.1103/PhysRevA.47.5138 ADSGoogle Scholar
  23. 23.
    Knill, E., Chuang, I., Laflamme, R.: Effective pure states for bulk quantum computation. Phys. Rev. A 57, 3348–3363 (1998). doi: 10.1103/PhysRevA.57.3348 ADSMathSciNetGoogle Scholar
  24. 24.
    Law, C., Ng, H., Leung, P.: Coherent control of spin squeezing. Phys. Rev. A 63(5), 055,601 (2001). doi: 10.1103/PhysRevA.63.055601 Google Scholar
  25. 25.
    Leskowitz, G., Ghaderi, N., Olsen, R., Mueller, L.: Three-qubit nuclear magnetic resonance quantum information processing with a single-crystal solid. J. Chem. Phys. 119(3), 1643–1649 (2003). doi: 10.1063/1.1582171 ADSGoogle Scholar
  26. 26.
    Maziero, J., Auccaise, R., Celeri, L.C., Soares-Pinto, D.O., deAzevedo, E.R., Bonagamba, T.J., Sarthour, R.S., Oliveira, I.S., Serra, R.M.: Quantum discord in nuclear magnetic resonance systems at room temperature. Braz. J. Phys. 43(1–2), 86–104 (2013). doi: 10.1007/s13538-013-0118-1 ADSGoogle Scholar
  27. 27.
    Possa, D., Gaudio, A.C., Freitas, J.C.C.: Numerical simulation of nqr/nmr: applications in quantum computing. J. Magn. Reson. 209(2), 250–260 (2011). doi: 10.1016/j.jmr.2011.01.020 ADSGoogle Scholar
  28. 28.
    Ramanathan, C., Boulant, N., Chen, Z., Cory, D.G., Chuang, I., Steffen, M.: Nmr quantum information processing. Quantum Inf. Process. 3(1–5), 15–44 (2004). doi: 10.1007/s11128-004-3668-x zbMATHGoogle Scholar
  29. 29.
    Rochester, S.M., Ledbetter, M.P., Zigdon, T., Wilson-Gordon, A.D., Budker, D.: Orientation-to-alignment conversion and spin squeezing. Phys. Rev. A 85(2), (2012). doi: 10.1103/PhysRevA.85.022125
  30. 30.
    Sinha, N., Mahesh, T., Ramanathan, K., Kumar, A.: Toward quantum information processing by nuclear magnetic resonance: pseudopure states and logical operations using selective pulses on an oriented spin 3/2 nucleus. J. Chem. Phys. 114(10), 4415–4420 (2001). doi: 10.1063/1.1346645 ADSGoogle Scholar
  31. 31.
    Soares-Pinto, D.O., Moussa, M.H.Y., Maziero, J., deAzevedo, E.R., Bonagamba, T.J., Serra, R.M., Celeri, L.C.: Equivalence between redfield- and master-equation approaches for a time-dependent quantum system and coherence control. Phys. Rev. A 83(6), 062,336 (2011). doi: 10.1103/PhysRevA.83.062336 Google Scholar
  32. 32.
    Suter, D., Mahesh, T.S.: Spins as qubits: quantum information processing by nuclear magnetic resonance. J. Chem. Phys. 128(5), 052,206 (2008). doi: 10.1063/1.2838166 Google Scholar
  33. 33.
    Teles, J., deAzevedo, E.R., Auccaise, R., Sarthour, R.S., Oliveira, I.S., Bonagamba, T.J.: Quantum state tomography for quadrupolar nuclei using global rotations of the spin system. J. Chem. Phys. 126, 154506Google Scholar
  34. 34.
    Utton, D.: Temperature dependence of nuclear quadrupole resonance frequency of 35cl in kclo3 between 12 degrees and 90 degrees k. J. Chem. Phys. 47(2), 371 (1967). doi: 10.1063/1.1711901 ADSGoogle Scholar
  35. 35.
    Vandersypen, L., Chuang, I.: Nmr techniques for quantum control and computation. Rev. Mod. Phys. 76(4), 1037–1069 (2004)ADSGoogle Scholar
  36. 36.
    Wineland, D., Bollinger, J., Itano, W., Moore, F., Heinzen, D.: SPIN squeezing and reduced quantum noise in spectroscopy. Phys. Rev. A 46(11), R6797–R6800 (1992)ADSGoogle Scholar
  37. 37.
    Yusa, G., Muraki, K., Takashina, K., Hashimoto, K., Hirayama, Y.: Controlled multiple quantum coherences of nuclear spins in a nanometre-scale device. Nature 434(7036), 1001–1005 (2005). doi: 10.1038/nature03456 CrossRefADSGoogle Scholar
  38. 38.
    Zeldes, H., Livingston, R.: Zeeman effect on the quadrupole spectra of sodium, potassium, and barium chlorates. J. Chem. Phys. 26(5), 1102–1106 (1957). doi: 10.1063/1.1743479 ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • João Teles
    • 1
  • Christian Rivera-Ascona
    • 2
  • Roberson S. Polli
    • 2
  • Rodrigo Oliveira-Silva
    • 2
  • Edson L. G. Vidoto
    • 2
  • José P. Andreeta
    • 2
  • Tito J. Bonagamba
    • 2
  1. 1.Departamento de Ciências da Natureza, Matemática e EducaçãoUniversidade Federal de São CarlosArarasBrasil
  2. 2.Instituto de Física de São CarlosUniversidade de São PauloSão CarlosBrasil

Personalised recommendations