Optical quantum bit string comparator

  • C. P. de Sousa
  • J. B. R. Silva
  • R. V. RamosEmail author


Quantum computation has attracted much attention and several quantum algorithms have been proposed in the literature. However, the hardware able to implement such algorithms is still a challenge. In this work, we provide an optical setup for implementation of a quantum bit string comparator, QBSC, for polarization-based qubit, using the non-linear Kerr effect. The QBSC is an important structure for implementation of conditional statements in quantum algorithms.


Quantum computation Non-linear Kerr effect Quantum bit string comparator 



This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001, and CNPq via Grant No. 307062/2014-7. Also, this work was performed as part of the Brazilian National Institute of Science and Technology for Quantum Information.


  1. Botsinis, P., Alanis, D., Babar, Z., Nguyen, H.V., Chandra, D., Ng, S.X., Hanzo, L.: Quantum-aided multi-user transmission in non-orthogonal multiple access systems. IEEE Access 4, 7402–7424 (2016). CrossRefGoogle Scholar
  2. Braginsky, V.B., Khalili, F.Y.: Quantum nondemolition measurements: the route from toys to tools. Rev. Mod. Phys. 68, 1–11 (1996)MathSciNetCrossRefADSGoogle Scholar
  3. Caraiman, S., Manta, V.I.: Histogram-based segmentation of quantum images. Theor. Comput. Sci. 529, 46–60 (2014)MathSciNetCrossRefGoogle Scholar
  4. Cheng, S.-T., Wang, C.-Y.: Quantum switching and quantum merge sorting. IEEE Trans. Circuit Syst. 53(2), 315–325 (2006)MathSciNetzbMATHGoogle Scholar
  5. de Sousa, P.B.M., Ramos, R.V.: Multiplayer quantum games and its application as access controller in architecture of quantum computers. Quantum Inf. Process. 7(2–3), 125–135 (2008)MathSciNetCrossRefGoogle Scholar
  6. Fleischhauer, M., Imamoglu, A., Marangos, J.P.: Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005)CrossRefADSGoogle Scholar
  7. Geremia, J.M., Stockton, J.K., Mabuchi, H.: Real-time quantum feedback control of atomic spin-squeezing. Science 304, 270–273 (2004)CrossRefADSGoogle Scholar
  8. Grangier, P., Levenson, J.A., Poizat, J.P.: Quantum non-demolition measurements in optics. Nature 396, 537–542 (1998)CrossRefADSGoogle Scholar
  9. Imoto, N., Haus, H.A., Yamamoto, Y.: Quantum nondemolition measurement of the photon number via the optical Kerr effect. Phys. Rev. A 32, 2287–2292 (1985)CrossRefADSGoogle Scholar
  10. Kok, P., Lee, H., Dowling, J.P.: Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements. Phys. Rev. A 66, 1–9 (2002)CrossRefGoogle Scholar
  11. Kok, P., Munro, W.J., Nemoto, K., Ralph, T.C., Dowling, J.P., Milburn, G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–175 (2007)CrossRefADSGoogle Scholar
  12. Li, S.-J., Yang, X.-D., Cao, X.-M., Zhang, C.-H., Xie, C.-D., Wang, H.: Enhanced cross-phase modulation based on a double electromagnetically induced transparency in a four-level tripod atomic system. Phys. Rev. Lett. 101, 073602 (2008)CrossRefADSGoogle Scholar
  13. Lupaşcu, A., Saito, S., Picot, T., de Groot, P.C., Harmans, C.J.P.M., Mooij, J.E.: Quantum non-demolition measurement of a superconducting two-level system. Nat. Phys. 3, 119–125 (2007). CrossRefGoogle Scholar
  14. Nogues, G., et al.: Seeing a single photon without destroying it. Nature 400, 239–242 (1999)CrossRefADSGoogle Scholar
  15. Oliveira, D.S., de Sousa, P.B.M., Ramos, R.V.: Quantum search algorithm using quantum bit string comparator. In: International Telecommunications Symposium, Fortaleza (2006).
  16. Oliveira, D.S., Ramos, R.V.: Quantum bit string comparator: circuits and applications. Quantum Comput. Comput. 7, 17–26 (2007)Google Scholar
  17. Ono, T., Okamoto, R., Tanida, M., Hofmann, H.F., Takeuchi, S.: Implementation of a quantum controlled-SWAP gate with photonic circuits. Sci. Rep. 7(45353), 1–9 (2017). CrossRefGoogle Scholar
  18. Peil, S., Gabrielse, G.: Observing the quantum limit of an electron cyclotron: QND measurements of quantum jumps between Fock states. Phys. Rev. Lett. 83, 1287–1290 (1999)CrossRefADSGoogle Scholar
  19. Ramos, R.V., de Sousa, P.B., Oliveira, D.S.: Solving mathematical problems with quantum search algorithm. arXiv:quant-ph/0605003v1 (2006)
  20. Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001)CrossRefADSGoogle Scholar
  21. Ruskov, R., Korotkov, A.N.: Entanglement of solid-state qubits by measurement. Phys. Rev. B 67, 241305 (2003)Google Scholar
  22. Schmidt, H., Imamoglu, A.: Giant Kerr nonlinearities obtained by electromagnetically induced transparency. Opt. Lett. 21, 1936–1938 (1996)CrossRefADSGoogle Scholar
  23. Shi, J., Shi, R., Guo, Y., Peng, X., Tang, Y.: Batch proxy quantum blind signature scheme. Sci. China Inf. Sci. 56(5), 1–9 (2013)MathSciNetCrossRefGoogle Scholar
  24. Shiau, B.-W., Wu, M.-C., Lin, C.-C., Chen, Y.-C.: Low-light-level cross-phase modulation with double slow light pulses. Phys. Rev. Lett. 106, 193006 (2011)CrossRefADSGoogle Scholar
  25. Silva, J.B.R., Ramos, R.V.: Implementations of quantum and classical gates with linear optical devices and photon number quantum non-demolition measurement for polarization encoded qubits. Phys. Lett. A 359(6), 592–597 (2006)CrossRefADSGoogle Scholar
  26. Steane, A.M.: Simple quantum error-correcting codes. Phys. Rev. A 54, 4741–4751 (1996)MathSciNetCrossRefADSGoogle Scholar
  27. Sun, X., Guo, Y., Shi, J., Zhang, W., Xiao, Q., Lee, M.: Quantum group signature scheme based on Chinese remainder theorem. J. Softw. Eng. Appl. 6(5B), 16–20 (2013). CrossRefGoogle Scholar
  28. Yan, F., Iliyasu, A.M., Venegas-Andraca, S.E.: A survey of quantum image representations. Quantum Inf. Process. 15(1), 1–35 (2016). MathSciNetCrossRefzbMATHADSGoogle Scholar
  29. Yuan, S., Mao, X., Li, T., Xue, Y., Chen, L.: Quantum morphology operations based on quantum representation mode. Quantum Inf. Process. 14(5), 1625–1645 (2015)MathSciNetCrossRefADSGoogle Scholar
  30. Yurke, B.: Optical back-action-evading amplifiers. J. Opt. Soc. Am. B 2, 732–738 (1985)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory of Quantum Information Technology, Department of Teleinformatic EngineeringFederal University of Ceara - DETI/UFCFortalezaBrazil

Personalised recommendations