nach oben

vorheriger Artikel Quantum information processing in collective-ro...

nächster Artikel Experimental implementation of quantum informat...

Tipp

Realization of quantum gates with multiple control qubits or multiple target qubits in a cavity

Zeitschrift:: Quantum Information Processing > Ausgabe 6/2015

Autoren:: Muhammad Waseem, Muhammad Irfan, Shahid Qamar

Abstract

We propose a scheme to realize a three-qubit controlled phase gate and a multi-qubit controlled NOT gate of one qubit simultaneously controlling n-target qubits with a four-level quantum system in a cavity. The implementation time for multi-qubit controlled NOT gate is independent of the number of qubit. Three-qubit phase gate is generalized to n-qubit phase gate with multiple control qubits. The number of steps reduces linearly as compared to conventional gate decomposition method. Our scheme can be applied to various types of physical systems such as superconducting qubits coupled to a resonator and trapped atoms in a cavity. Our scheme does not require adjustment of level spacing during the gate implementation. We also show the implementation of Deutsch–Joza algorithm. Finally, we discuss the imperfections due to cavity decay and the possibility of physical implementation of our scheme.

Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten

Jetzt einloggen Kostenlos registrieren

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 69.000 Bücher
über 500 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Umwelt
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 50.000 Bücher
über 380 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Umwelt
Maschinenbau + Werkstoffe

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 58.000 Bücher
über 300 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Jetzt informieren

Shor, W.P.: In proceedings of the 35th annual symposium on foundations of computer science (IEE Computer society press, Santa Fe, NM, 1994)

Grover, L.K.: Quantum mechanics helps in searching for a needle in a Haystack. Phys. Rev. Lett. 79(2), 325–328 (1997) CrossRefADS

Sleator, T., Weinfurter, H.: Realizable universal quantum logic gates. Phys. Rev. Lett. 74(20), 4087–4090 (1995) CrossRefADSMATHMathSciNet

DiCarlo, L., Chow, J.M., Gambetta, J.M., Bishop, L.S., Johnson, B.R., Schuster, D.I., Majer, J., Blais, A., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009) CrossRefADS

Bialczak, R.C., Ansmann, M., Hofheinz, M., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Wang, H., Wenner, J., Steffen, M., Cleland, A.N., Martinis, J.M.: Quantum process tomography of a universal entangling gate implemented with Josephson phase qubits. Nat. Phys. 6, 409413 (2010) CrossRef

Yamamoto, T., Neeley, M., Lucero, E., Bialczak, R.C., Kelly, J., Lenander, M., Mariantoni, M., O’Connell, A.D., Sank, D., Wang, H., Weides, M., Wenner, J., Yin, Y., Cleland, A.N., Martinis, J.M.: Quantum process tomography of two-qubit controlled-Z and controlled-NOT gates using superconducting phase qubits. Phys. Rev. B 82(18), 184515 (2010) CrossRefADS

Plantenberg, J.H., de Groot, P.C., Harmans, C.J.P.M., Mooij, J.E.: Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits. Nature (London) 447, 836–839 (2007) CrossRefADS

Leek, P.J., Filipp, S., Maurer, P., Baur, M., Bianchetti, R., Fink, J.M., Göppl, M., Steffen, L., Wallraff, A.: Using sideband transitions for two-qubit operations in superconducting circuits. Phys. Rev. B 79(18), 180511(R) (2009) CrossRefADS

Mottonen, M., Vartiainen, J.J., Bergholm, V., Salomaa, M.M.: Quantum circuits for general multiqubit gates. Phys. Rev. Lett. 93(13), 130502 (2004) CrossRefADS

10.

Monz, T., Kim, K., Hänsel, W., Riebe, M., Villar, A.S., Schindler, P., Chwalla, M., Hennrich, M., Blatt, R.: Realization of the quantum Toffoli gate with trapped ions. Phys. Rev. Lett. 102(4), 040501 (2009) CrossRefADS

11.

Fedorov, A., et al.: Implementation of a Toffoli gate with superconducting circuits. Nat. Phys. 481, 170172 (2011)

12.

Zubairy, M.S., Kim, M., Scully, M.O.: Cavity-QED-based quantum phase gate. Phys. Rev. A 68(3), 033820 (2003) CrossRefADS

13.

Chiaverini, J., Leibfried, D., Schaetz, T., Barrett, M.D., Blakestad, R.B., Britton, J., Itano, W.M., Jost, J.D., Knill, E., Langer, C., Ozeri, R., Wineland, D.J.: Realization of quantum error correction. Nature (London) 432, 602–605 (2004) CrossRefADS

14.

Zubairy, M.S., Matsko, A.B., Scully, M.O.: Resonant enhancement of high-order optical nonlinearities based on atomic coherence. Phys. Rev. A 65(4), 043804 (2002) CrossRefADS

15.

Waseem, M., Ahmed, R., Irfan, M., Qamar, S.: Three-qubit Grovers algorithm using superconducting quantum interference devices in cavity-QED. Quantum Inf. Process. 12, 3649 (2013) CrossRefADSMATHMathSciNet

16.

ŠaŠura, M., Buzek, V.: Multiparticle entanglement with quantum logic networks: application to cold trapped ions. Phys. Rev. A 64(1), 012305 (2001) CrossRefADS

17.

Gaitan, F.: Quantum Error Correction and Fault Tolerant Quantum Computing. CRC Press, Boca Raton (2008) CrossRefMATH

18.

Beth, T., Rötteler, M.: Quantum Information, vol. 173, Ch. 4, p. 96. Springer, Berlin (2001) CrossRef

19.

Braunstein, S.L., Buzek, V., Hillery, M.: Quantum-information distributors: quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit. Phys. Rev. A 63(5), 052313 (2001) CrossRefADS

20.

Chang, J.T., Zubairy, M.S.: Three-qubit phase gate based on cavity quantum electrodynamics. Phys. Rev. A 77(1), 012329 (2008) CrossRefADS

21.

Yang, C.P., Han, S.: n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator. Phys. Rev. A 72(3), 032311 (2005) CrossRefADS

22.

Yang, C.P., Han, S.: Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED. Phys. Rev. A 73(3), 032317 (2006) CrossRefADS

23.

Waseem, M., Irfan, M., Qamar, S.: Multiqubit quantum phase gate using four-level superconducting quantum interference devices coupled to superconducting resonator. Physica C 477, 24–31 (2012) CrossRefADS

24.

Yang, C.P., Zheng, S.B., Nori, F.: Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity. Phys. Rev. A 82(6), 062326 (2010) CrossRefADS

25.

Yang, C.P., Liu, Y.X., Nori, F.: Phase gate of one qubit simultaneously controlling n qubits in a cavity. Phys. Rev. A 81(6), 062323 (2010) CrossRefADS

26.

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

27.

Clarke, J., Wilhelm, F.K.: Superconducting quantum bits. Nature (London) 453, 1031–1042 (2008) CrossRefADS

28.

Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Katz, N., Lucero, E., O’Connell, A.D., Wang, H., Cleland, A.N., Martinis, J.M.: Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state. Nat. Phys. 4, 523–526 (2008) CrossRef

29.

Zagoskin, A.M., Ashhab, S., Johansson, J.R., Nori, F.: Quantum two-level systems in Josephson junctions as naturally formed qubits. Phys. Rev. Lett. 97(7), 077001 (2006) CrossRefADS

30.

Liu, Y.X., You, J.Q., Wei, L.F., Sun, C.P., Nori, F.: Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit. Phys. Rev. Lett. 95(8), 087001 (2005) CrossRefADS

31.

Yang, C.P., Chu, S.I., Han, S.: Simplified realization of two-qubit quantum phase gate with four-level systems in cavity QED. Phys. Rev. A 70(4), 044303 (2004) CrossRefADS

32.

Wang, L., Puri, R.R., Eberly, J.H.: Coupled-channel cavity QED model and exact solutions. Phys. Rev. A 46(11), 71927209 (1992)

33.

Zheng, S.B., Guo, G.C.: Generation of Schrdinger cat states via the Jaynes–Cummings model with large detuning. Phys. Lett. A 223(5), 332336 (1996) MathSciNet

34.

Scully, M.O., Zubairy, M.S.: Quantum Optics, 1st edn. Cambridge University Press, UK (1997) CrossRef

35.

Nielsen, M.A., Chuang, I.I.: Quantum Computing and Quantum Information. Cambridge University Press, Cambridge, England (2001)

36.

Diao, Z., Zubairy, M.S., Chen, G.: A quantum circuit design for Grover Algorithm. Z. Naturforsch. A: Phys. Sci. 57a, 701–708 (2002) ADS

37.

Deutsch, D., Josza, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992) CrossRefADSMATH

38.

DiCarlo, L., Reed, M.D., Sun, L., Johnson, B.R., Chow, J.M., Gambetta, J.M., Frunzio, L., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010) CrossRefADS

39.

Leek, P.J., Baur, M., Fink, J.M., Bianchetti, R., Steffen, L., Filipp, S., Wallraff, A.: Cavity quantum electrodynamics with separate photon storage and qubit readout modes. Phys. Rev. Lett. 104(10), 100504 (2010) CrossRefADS

Titel: Realization of quantum gates with multiple control qubits or multiple target qubits in a cavity
Autoren:: Muhammad Waseem
Muhammad Irfan
Shahid Qamar
Publikationsdatum: 01.06.2015
DOI: https://doi.org/10.1007/s11128-015-0947-7
Verlag: Springer US
Zeitschrift: Quantum Information Processing
Ausgabe 6/2015
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332

Springer Professional

Tipp

Weitere Artikel dieser Ausgabe durch Wischen aufrufen

Abstract

Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten

Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 6/2015

Maximal atom–photon entanglement in a double- quantum system

Unveiling -tangle and quantum phase transition in the one-dimensional anisotropic XY model

Efficient and faithful remote preparation of arbitrary three- and four-particle -class entangled states

Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and nine families of 4-qubit entangled states

Realizing an efficient fusion gate for W states with cross-Kerr nonlinearities and QD-cavity coupled system

Efficient protocols for unidirectional and bidirectional controlled deterministic secure quantum communication: different alternative approaches