Skip to main content
Log in

Cavity control as a new quantum algorithms implementation treatment

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Based on recent experiments [Nature 449, 438 (2007) and Nature Physics 6, 777 (2010)], a new approach for realizing quantum gates for the design of quantum algorithms was developed. Accordingly, the operation times of such gates while functioning in algorithm applications depend on the number of photons present in their resonant cavities. Multi-qubit algorithms can be realized in systems in which the photon number is increased slightly over the qubit number. In addition, the time required for operation is considerably less than the dephasing and relaxation times of the systems. The contextual use of the photon number as a main control in the realization of any algorithm was demonstrated. The results indicate the possibility of a full integration into the realization of multi-qubit multiphoton states and its application in algorithm designs. Furthermore, this approach will lead to a successful implementation of these designs in future experiments.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proc. Lond. Math. Soc. s2–42(1), 230 (1937)

    Article  MathSciNet  MATH  Google Scholar 

  2. R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21(6–7), 467 (1982)

    Article  MathSciNet  Google Scholar 

  3. P. Benioff, Quantum mechanical models of Turing machines that dissipate no energy, Phys. Rev. Lett. 48(23), 1581 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  4. D. Deutsch, Quantum theory, the Church-Turing Principle and the universal quantum computer, Proc. R. Soc. Lond. A 400(1818), 97 (1985)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. D. Deutsch, Quantum computational networks, Proc. R. Soc. Lond. A 425(1868), 73 (1989)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. D. P. DiVincenzo, Quantum computation, Science 270(5234), 255 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. D. P. DiVincenzo, The physical implementation of quantum computation, Fortschr. Phys. 48(9–11), 771 (2000)

    Article  MATH  Google Scholar 

  8. M. Nakahara, S. Kanemitsu, M. M. Salomaa, and S. Takagi (Eds.), Physical Realization of Quantum Computing: Are the DiVincenzo Criteria Fulfilled in 2004? Singapore: World Scientific, 2006

    Google Scholar 

  9. L. M. K. Vandersypen and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76(4), 1037 (2005)

    Article  ADS  Google Scholar 

  10. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Trapping of neutral sodium atoms with radiation pressure, Phys. Rev. Lett. 59(23), 2631 (1987)

    Article  ADS  Google Scholar 

  11. G. Wendin and V. S. Shumeiko, Superconducting quantum circuits, qubits and computing, arXiv: condmat/0508729 (2005)

    Google Scholar 

  12. B. D. Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1(7), 251 (1962)

    Article  ADS  MATH  Google Scholar 

  13. B. D. Josephson, The discovery of tunnelling supercurrents, Rev. Mod. Phys. 46(2), 251 (1974)

    Article  ADS  Google Scholar 

  14. U. Meirav, M. A. Kastner, and S. J. Wind, Singleelectron charging and periodic conductance resonances in GaAs nanostructures, Phys. Rev. Lett. 65(6), 771 (1990)

    Article  ADS  Google Scholar 

  15. O. Gamel, H. Chan, G. Fleming, and K. B. Whaley, Fully quantum analysis of photosynthetic coherent energy absorption and transfer, Bull. Am. Phys. Soc. 62, 4 (2017)

    Google Scholar 

  16. B. Schumacher, Quantum coding, Phys. Rev. A 51(4), 2738 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  17. J. M. Martinis, Superconducting phase qubits, Quant. Inf. Proc. 8(2–3), 81 (2009)

    Article  Google Scholar 

  18. H. Eleuch, Entanglement and autocorrelation function in semiconductor microcavities, Int. J. Mod. Phys. B 24(29), 5653 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. H. Eleuch, Autocorrelation function of microcavityemitting field in the linear regime, EPJD 48(1), 139 (2008)

    Article  ADS  Google Scholar 

  20. E. A. Sete, A. A. Svidzinsky, H. Eleuch, Z. Yang, R. D. Nevels, and M. O. Scully, Correlated spontaneous emission on the Danube, J. Mod. Opt. 57(14–15), 1311 (2010)

    Article  ADS  MATH  Google Scholar 

  21. E. A. Sete, A. A. Svidzinsky, Y. V. Rostovtsev, H. Eleuch, P. K. Jha, S. Suckewer, and M. O. Scully, Using quantum coherence to generate gain in the XUV and X-ray: Gain-Swept superradiance and lasing without inversion, IEEE J. Sel. Top. Quantum Electron. 18(1), 541 (2012)

    Article  Google Scholar 

  22. H. Eleuch and R. Bennaceur, An optical soliton pair among absorbingthree-level atoms, J. Opt. A 5(5), 528 (2003)

    Article  ADS  Google Scholar 

  23. M. Tinkham, Introduction to Superconductivity, 2nd Ed., New York: McGraw Hill, 1996

    Google Scholar 

  24. R. W. Simmonds, K. Lang, D. Hite, S. Nam, D. Pappas, and J. Martinis, Decoherence in Josephson Phase Qubits from Junction Resonators, Phys. Rev. Lett. 93(7), 077003 (2004)

    Article  ADS  Google Scholar 

  25. M. A. Sillanpää, J. I. Park, and R. W. Simmonds, Coherent quantum state storage and transfer between two phase qubits via a resonant cavity, Nature 449, 438 (2007)

    Article  ADS  Google Scholar 

  26. F. Altomare, J. I. Park, K. Cicak, M. A. Sillanpää, M. S. Allman, D. Li, A. Sirois, J. A. Strong, J. D. Whittaker, and R. W. Simmonds, Tripartite interactions between two phase qubits and a resonant cavity, Nat. Phys. 6(10), 777 (2010)

    Article  Google Scholar 

  27. O. Gamel and D. F. V. James, Time-averaged quantum dynamics and the validity of the effective Hamiltonian model, Phys. Rev. A 82, 052106 (2010)

    Article  ADS  Google Scholar 

  28. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge: Cambridge University Press, Ch. 4 and 6 (2000)

    MATH  Google Scholar 

  29. H. F. Wang, X.Q. Shao, Y.F. Zhao, S. Zhang, and K.H. Yeon, Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED, J. Phys. At. Mol. Opt. Phys. 43(6), 065503 (2010)

    Article  ADS  Google Scholar 

  30. H. F. Wang, J. J. Wen, A. D. Zhu, S. Zhang, and K. H. Yeon, Deterministic CNOT gate and entanglement swapping for photonic qubits using a quantum-dot spin in a double-sided optical microcavity, New J. Phys. 13, 013021 (2011)

    Article  ADS  MATH  Google Scholar 

  31. H. F. Wang, X. X. Jiang, S. Zhang, and K. H. Yeon, Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits, J. Phys. At. Mol. Opt. Phys. 44(11), 115502 (2011)

    Article  ADS  Google Scholar 

  32. A. S. F. Obada, H. A. Hessian, A. B. A. Mohamed, and A. H. Homid, Efficient protocol of NN-bit discrete quantum Fourier transform via transmon qubits coupled to a resonator, Quant. Inf. Proc. 13(2), 475 (2014)

    Article  MATH  Google Scholar 

  33. A. H. Homid, A. Abdel-Aty, M. Abdel-Aty, A. Badawi, and A. S. F. Obada, Efficient realization of quantum search algorithm using quantum annealing processor with dissipation, J. Opt. Soc. Am. B 32(9), 2025 (2015)

    Article  ADS  Google Scholar 

  34. D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation, Proc. R. Soc. Lond. A 439(1907), 553 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. D. R. Simon, On the power of quantum computation, Proc. 35th IEEE Symp. Found. Comp. Sci., Santa Fe, NM 116–123 (1994)

  36. D. R. Simon, On the power of quantum computation, SIAM J. Comput. 26(5), 1474 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  37. B. C. Sanders and G. J. Milburn, Optimal quantum measurements for phase estimation, Phys. Rev. Lett. 75(16), 2944 (1995)

    Article  ADS  Google Scholar 

  38. P. Shor, Discrete logarithms and factoring, Proc. 35th Ann. Symp. Found.Comp. Sci. 124 (1994)

  39. P. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput. 26(5), 1484 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  40. O. Manasreh, Semiconductor Heterojunctions and Nanostructures, New York: McGraw-Hill Profes-sional, 2005

    Google Scholar 

  41. R. D. Levine, Quantum Mechanics of Molecular Rate Processes, New York: Dover Publications, 1999

    MATH  Google Scholar 

  42. N. Froman and P. O. Froman, JWKB Approximation, Amsterdam: North-Holland, Amsterdam, 1965

    MATH  Google Scholar 

  43. H. Eleuch, Y. V. Rostovtsev, and M. O. Scully, New analytic solution of Schrödinger’s equation, EPL (Europhys. Lett.) 89(5), 50004 (2010)

    Article  ADS  Google Scholar 

  44. J. Q. You and F. Nori, Superconducting circuits and quantum information, Phys. Today 58(11), 42 (2005)

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to thank Prof. Arthur R. McGurn from Western Michigan University for comments that redressed some of our presentation for this manuscript, we gratefully acknowledge the help provided during the editorial process.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. AbuGhanem.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

AbuGhanem, M., Homid, A.H. & Abdel-Aty, M. Cavity control as a new quantum algorithms implementation treatment. Front. Phys. 13, 130303 (2018). https://doi.org/10.1007/s11467-017-0709-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-017-0709-3

Keywords

Navigation