Skip to main content
SpringerLink
Log in

Nondestructive discrimination of a new family of highly entangled states in IBM quantum computer

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Measurement-based quantum computation (MQC) is a leading paradigm for building a quantum computer. Cluster states being used in this context act as one-way quantum computers. Here, we consider Z-states as a type of highly entangled states like cluster states, which can be used for one-way or measurement-based quantum computation. We define Z-state basis as a set of orthonormal states which are as equally entangled as the cluster states. We design new quantum circuits to nondestructively discriminate these highly entangled Z-states. The proposed quantum circuits can be generalized for N-qubit quantum system. We confirm the preservation of Z-states after the performance of the circuit by quantum state tomography process.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. A 70, 1895 (1993)

    ADS  MathSciNet  MATH  Google Scholar 

  3. Ghosh, S., Kar, G., Roy, A., Sarkar, D., Sen, U.: Entanglement teleportation through GHZ-class states. New J. Phys. 4, 48 (2002)

    Article  ADS  Google Scholar 

  4. Muralidharan, S., Panigrahi, P.K.: Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state. Phys. Rev. A 77, 032321 (2008)

    Article  ADS  Google Scholar 

  5. Choudhury, S., Muralidharan, S., Panigrahi, P.K.: Quantum teleportation and state sharing using a genuinely entangled six-qubit state. J. Phys. A Math. Theor. 42, 115303 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Muralidharan, S., Karumanchi, S., Jain, S., Srikanth, R., Panigrahi, P.K.: 2N qubit “mirror states” for optimal quantum communication. Eur. Phys. J. D 61, 757–763 (2011)

    Article  ADS  Google Scholar 

  7. Paul, N., Menon, J.V., Karumanchi, S., Muralidharan, S., Panigrahi, P.K.: Quantum tasks using six qubit cluster states. Quantum Inf. Process. 10, 619–632 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jain, S., Muralidharan, S., Panigrahi, P.K.: Secure quantum conversation through non-destructive discrimination of highly entangled multipartite states. Europhys. Lett. 87, 60008 (2009)

    Article  ADS  Google Scholar 

  9. Prasath, E.S., Muralidharan, S., Mitra, C., Panigrahi, P.K.: Multipartite entangled magnon states as quantum communication channels. Quantum Inf. Process. 11, 397–410 (2012)

    Article  MathSciNet  Google Scholar 

  10. Panigrahi, P.K., Karumanchi, S., Muralidharan, S.: Minimal classical communication and measurement complexity for quantum information splitting of a two-qubit state. Pramana J. Phys. 73, 499–504 (2009)

    Article  ADS  Google Scholar 

  11. Muralidharan, S., Panigrahi, P.K.: Quantum-information splitting using multipartite cluster states. Phys. Rev. A 78, 062333 (2008)

    Article  ADS  Google Scholar 

  12. Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74, 062320 (2006)

    Article  ADS  Google Scholar 

  13. Moulick, S.R., Panigrahi, P.K.: Quantum cheques. Quantum Inf. Process. 15, 2475–2486 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Behera, B.K., Banerjee, A., Panigrahi, P.K.: Experimental realization of quantum cheque using a five-qubit quantum computer. Quantum Inf. Process. 16, 312 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Gupta, M., Pathak, A., Srikanth, R., Panigrahi, P.K.: General circuits for indirecting and distributing measurement in quantum computation. Int. J. Quantum Inf. 5, 627–640 (2007)

    Article  MATH  Google Scholar 

  16. Panigrahi, P.K., Gupta, M., Pathak, A., Srikanth, R.: Circuits for distributing quantum measurement. AIP Conf. Proc. 864, 197–207 (2006)

    Article  ADS  MATH  Google Scholar 

  17. Munro, W.J., et al.: Efficient optical quantum information processing. J. Opt. B Quantum Semiclass. Opt. 7, S135 (2005)

    Article  Google Scholar 

  18. Wang, X.-W., Zhang, D.-Y., Tang, S.-Q., Xie, L.-J.: Nondestructive Greenberger–Horne–Zeilinger-state analyzer. Quantum Inf. Process. 12, 1065–1075 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Zheng, C., Gu, Y., Li, W., Wang, Z., Zhang, J.: Complete distributed hyper-entangled-bell-state analysis and quantum super dense coding. Int. J. Theor. Phys. 55, 1019–1027 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Samal, J.R., Gupta, M., Panigrahi, P.K., Kuma, A.: Non-destructive discrimination of Bell states by NMR using a single ancilla qubit. J. Phys. B Atom. Mol. Opt. Phys. 43, 095508 (2010)

    Article  ADS  Google Scholar 

  21. Sisodia, M., Shukla, A., Pathak, A.: Experimental realization of nondestructive discrimination of Bell states using a five-qubit quantum computer. Phys. Lett. A 381, 3860–3874 (2017)

    Article  ADS  Google Scholar 

  22. Li, J., Shi, B.-S., Jiang, Y.-K., Fan, X.-F., Guo, G.-C.: A non-destructive discrimination scheme on 2n-partite GHz bases. J. Phys. B At. Mol. Opt. Phys. 33, 3215 (2000)

    Article  ADS  Google Scholar 

  23. Luo, Q.-B., Yang, G.-W., She, K., Niu, W-n, Wang, Y-q: Multi-party quantum private comparison protocol based on d-dimensional entangled states. Quantum Inf. Process. 13, 2343–2352 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Nielsen, M.A.: Quantum computation by measurement and quantum memory. Phys. Lett. A 308, 96–100 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Leung, D.W.: Quantum computation by measurements. Int. J. Quantum Inf. 2, 33–43 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  26. Raussendorf, R., Briegel, H.J.: Computational model underlying the one-way quantum computer. Quantum Inf. Comput. 2, 443–486 (2002)

    MathSciNet  MATH  Google Scholar 

  27. Raussendorf, R., Browne, D.E., Briegel, H.J.: Measurement-based quantum computation using cluster states. Phys. Rev. A 68, 022312 (2003)

    Article  ADS  Google Scholar 

  28. Aliferis, P., Leung, D.W.: Computation by measurements: A unifying picture. Phys. Rev. A 70, 062314 (2004)

    Article  ADS  Google Scholar 

  29. Danos, V., Kashefi, E., Panangaden, P.: The measurement calculus. J. Assoc. Comput. Mach. 54, 8 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Childs, A.M., Leung, D.W., Nielsen, M.A.: Unified derivations of measurement-based schemes for quantum computation. Phys. Rev. A 71, 032318 (2005)

    Article  ADS  Google Scholar 

  31. Browne, D .E., Kashefi, E., Mhalla, M., Perdrix, S.: Generalized flow and determinism in measurement-based quantum computation. New J. Phys. 9, 250 (2007)

    Article  ADS  Google Scholar 

  32. Verstraete, F., Cirac, J.I.: Valence-bond states for quantum computation. Phys. Rev. A 70, 060302 (2004)

    Article  ADS  Google Scholar 

  33. Gross, D., Eisert, J.: Novel schemes for measurement-based quantum computation. Phys. Rev. Lett. 98, 220503 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910 (2001)

    Article  ADS  Google Scholar 

  36. Nielsen, M.A., Chuang, I.L.: Programmable quantum gate arrays. Phys. Rev. Lett. 79, 321 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)

    Article  ADS  Google Scholar 

  38. Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)

    Article  ADS  Google Scholar 

  39. Rundle, R.P., Mills, P.W., Tilma, T., Samson, J.H., Everitt, M.J.: Simple procedure for phase-space measurement and entanglement validation. Phys. Rev. A 96, 022117 (2017)

    Article  ADS  Google Scholar 

  40. Alvarez-Rodriguez, U., Sanz, M., Lamata, L., Solano, E.: Quantum Artificial Life in an IBM Quantum Computer. arXiv:1711.09442 (2017)

  41. Grimaldi, D., Marinov, M.: Distributed measurement systems. Measurement 30, 279–287 (2001)

    Article  Google Scholar 

  42. Kalra, A.R., Prakash, S., Behera, B.K., Panigrahi, P.K.: Experimental Demonstration of the No Hiding Theorem Using a 5 Qubit Quantum Computer. arXiv:1707.09462 (2017)

  43. Ghosh, D., Agarwal, P., Pandey, P., Behera, B.K., Panigrahi, P.K.: Automated Error Correction in IBM Quantum Computer and Explicit Generalization. arXiv:1708.02297 (2017)

  44. Gangopadhyay, S., Manabputra, Behera, B.K., Panigrahi, P.K.: Generalization and Partial Demonstration of an Entanglement Based Deutsch–Jozsa Like Algorithm Using a 5-Qubit Quantum Computer. arXiv:1708.06375 (2017)

  45. Schuld, M., Fingerhuth, M., Petruccione, F.: Implementing a distance-based classifier with a quantum interference circuit. arXiv:1703.10793 (2017)

  46. Majumder, A., Mohapatra, S., Kumar, A.: Experimental Realization of Secure Multiparty Quantum Summation Using Five-Qubit IBM Quantum Computer on Cloud. arXiv:1707.07460 (2017)

  47. Li, R., Alvarez-Rodriguez, U., Lamata, L., Solano, E.: Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience arXiv:1611.07851 (2017)

  48. Sisodia, M., Shukla, A., Thapliyal, K., Pathak, A.: Design and Experimental Realization of an Optimal Scheme for Teleportation of an n-Qubit Quantum State. arXiv:1704.05294 (2017)

  49. Vishnu, P.K., Joy, D., Behera, B.K., Panigrahi, P.K.: Experimental Demonstration of Non-local Controlled-Unitary Quantum Gates Using a Five-qubit Quantum Computer. arXiv:1709.05697 (2017)

  50. Yalçnkaya, İ., Gedik, Z.: Optimization and Experimental Realization of Quantum Permutation Algorithm. arXiv:1708.07900 (2017)

  51. Dash, A., Rout, S., Behera, B.K., Panigrahi, P.K.: A Verification Algorithm and Its Application to Quantum Locker in IBM Quantum Computer. arXiv:1710.05196 (2017)

  52. Roy, S., Behera, B.K., Panigrahi, P.K.: Demonstration of Entropic Non-contextual Inequality Using IBM Quantum Computer. arXiv:1710.10717 (2017)

  53. Behera, B.K., Seth, S., Das, A., Panigrahi, P.K.: Experimental Demonstration of Quantum Repeater in IBM Quantum Computer. arXiv:1712.00854 (2017)

  54. Li, R., Alvarez-Rodriguez, U., Lamata, L., Solano, E.: Approximate quantum adders with genetic algorithms: an IBM quantum experience. Quantum Meas. Quantum Metrol. 4, 1–7 (2017)

    Article  ADS  Google Scholar 

  55. Huffman, E., Mizel, A.: Violation of noninvasive macrorealism by a superconducting qubit: Implementation of a Leggett–Garg test that addresses the clumsiness loophole. Phys. Rev. A 95, 032131 (2017)

    Article  ADS  Google Scholar 

  56. Alsina, D., Latorre, J.I.: Experimental test of Mermin inequalities on a five-qubit quantum computer. Phys. Rev. A 94, 012314 (2016)

    Article  ADS  Google Scholar 

  57. Wootton, J.R.: Demonstrating non-Abelian braiding of surface code defects in a five qubit experiment. Quantum Sci. Technol. 2, 015006 (2017)

    Article  ADS  Google Scholar 

  58. Berta, M., Wehner, S., Wilde, M.M.: Entropic uncertainty and measurement reversibility. New J. Phys. 18, 073004 (2016)

    Article  ADS  Google Scholar 

  59. Deffner, S.: Demonstration of entanglement assisted invariance on IBM’s quantum experience. Heliyon 3, e00444 (2016)

    Article  Google Scholar 

  60. Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017)

    Article  ADS  Google Scholar 

  61. Wootton, J.R., Loss, D.: A Repetition Code of 15 Qubits. arXiv:1709.00990 (2017)

  62. Enrquez, M., Wintrowicz, I., Yczkowski, K.: Maximally entangled multipartite states: a brief survey. J. Phys. Conf. Ser. 698, 012003 (2016)

    Article  Google Scholar 

  63. Tabia, G.N.M.: Quantum Computing with Cluster States (2011)

  64. Albash, T., Lidar, D.A.: Adiabatic quantum computation. Rev. Mod. Phys. 90, 015002 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  65. Bacon, D., Flammia, S.T.: Adiabatic cluster-state quantum computing. Phys. Rev. A 82, 030303(R) (2010)

    Article  ADS  Google Scholar 

  66. Tsai, C.W., Hsieh, C.R., Hwang, T.: Dense coding using cluster states and its application on deterministic secure quantum communication. Eur. Phys. J. D 61, 779–783 (2011)

    Article  ADS  Google Scholar 

  67. Chuang, L.D., Liang, C.Z.: Teleportation of two-particle entangled state via cluster state. Commun. Theor. Phys. 47, 464 (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

B.K.B. is financially supported by DST Inspire Fellowship. SS and KS acknowledge the support of HBCSE and TIFR for conducting National Initiative on Undergraduate Sciences (NIUS) Physics camp. We are extremely grateful to IBM team and IBM QE project. The discussions and opinions developed in this paper are only those of the authors and do not reflect the opinions of IBM or IBM QE team.

Author information

Authors and Affiliations

  1. Department of Physics, Indian Institute of Technology Bombay, Mumbai, 400076, India

    Saipriya Satyajit

  2. Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India

    Karthik Srinivasan

  3. Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, West Bengal, 741246, India

    Bikash K. Behera & Prasanta K. Panigrahi

Authors
  1. Saipriya Satyajit
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karthik Srinivasan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bikash K. Behera
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Prasanta K. Panigrahi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Prasanta K. Panigrahi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Satyajit, S., Srinivasan, K., Behera, B.K. et al. Nondestructive discrimination of a new family of highly entangled states in IBM quantum computer. Quantum Inf Process 17, 212 (2018). https://doi.org/10.1007/s11128-018-1976-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1976-9

Keywords

Search

Navigation