Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
A Blind Image Watermarking Algorithm in the Combine Domain Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Distributed Quantum Computation Assisted by Remote Toffoli Gate

verfasst von : Ming-Xing Luo, Hui-Ran Li

Erschienen in: Cloud Computing and Security

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Distributed quantum computation requires quantum operations to act on logical qubits over a distance. We will develop a formal model for the telegate-based distributive quantum computation. We show that a controlled-controlled-NOT (Toffoli) gate as an elementary gate of the universal quantum computation may be remotely implemented by exploring a high-level quantum system. These remote Toffoli gates cost at most two Einstein-Podolsky-Rosen (EPR) pairs, whereas four or six EPR pairs are required from the teleportation-based quantum computation or the remote CNOT gate, respectively. Thus, the previous Toffoli gate-based circuit synthesis may be used as an elementary subroutine of this distributed quantum computation.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

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

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

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

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

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




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

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




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel An Outsourcing Data Storage Scheme Supporting Privacy Preserving and Data Hiding Based on Digital Watermarking
Literatur
1.
2.
Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. A 400(1818), 97–117 (1985)MathSciNetCrossRefMATH
3.
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000). pp. 216–271MATH
4.
Barreiro, J.T., Langford, N.K., Peters, N.A., Kwiat, P.G.: Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005)CrossRef
5.
Wang, X.L., et al.: Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518(7540), 516–519 (2015)CrossRef
6.
Luo, M.X., Wang, X.: Parallel photonic quantum computation assisted by quantum dots in one-side optical microcavities. Sci. Rep. 4, 5732 (2014)
7.
8.
9.
Grover, L.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)CrossRef
10.
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)MathSciNetCrossRefMATH
11.
Murphy, B., Brent, R.P.: On quadratic polynomials for the number field sieve. Aust. Comput. Sci. Commun. 20, 199–213 (1998)MathSciNetMATH
12.
Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(6), 120–126 (1978)MathSciNetCrossRefMATH
13.
Farhi, E., et al.: A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292(5516), 472–475 (2001)MathSciNetCrossRefMATH
14.
Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10, 631–633 (2014)CrossRef
15.
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Berlin (2006). pp. 130–211MATH
16.
Gu, B., Sheng, V.S., Wang, Z., Ho, D., Osman, S., Li, S.: Incremental learning for v-support vector regression. Neural Netw. 67, 140–150 (2015)CrossRef
17.
Chen, B., Shu, H., Coatrieux, G., Chen, G., Sun, X., Coatrieux, J.-L.: Color image analysis by quaternion-type moments. J. Math. Imaging Vis. 51(1), 124–144 (2015)MathSciNetCrossRefMATH
18.
Xia, Z., Wang, X., Sun, X., Wang, B.: Steganalysis of least significant bit matching using multi-order differences. Sec. Commun. Netw. 7(8), 1283–1291 (2014)CrossRef
19.
20.
Kuperberg, G.: A subexponential-time quantum algorithm for the dihedral hidden subgroup problem. SIAM J. Comput. 35(1), 170–188 (2005)MathSciNetCrossRefMATH
21.
Barenco, A., et al.: Elementary gates for quantum computation. Phys. Rev. A 52, 34–57 (1995)CrossRef
22.
23.
Radhakrishnan, J., Rotteler, M., Sen, P.: Random measurement bases, quantum state distinction and applications to the hidden subgroup problem. Algorithmica 55, 490–516 (2006)MathSciNetCrossRefMATH
24.
Kawachi, A., Koshiba, T., Nishimura, H., Yamakami, T.: Computational indistinguishability between quantum states and its cryptographic application. J. Cryptol. 25, 528–555 (2009)MathSciNetCrossRefMATH
25.
Chuang, I.L., Vandersypen, L.M.K., Zhou, X., Leung, D.W., Lloyd, S.: Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998)CrossRef
26.
Jones, J.A., Mosca, M., Hansen, R.H.: Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344–346 (1998)CrossRef
27.
Vandersypen, L.M.K., et al.: Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)CrossRef
28.
Lucero, E., et al.: Computing prime factors with a Josephson phase qubit quantum processor. Nat. Phys. 8, 719–723 (2012)CrossRef
29.
Feng, G., Xu, G., Long, G.: Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110, 190501 (2013)CrossRef
30.
Tame, M.S., Bell, B.A., Di Franco, C., Wadsworth, W.J., Rarity, J.G.: Experimental realization of a one-way quantum computer algorithm solving Simon’s problem. Phys. Rev. Lett. 113, 200501 (2014)CrossRef
31.
Sun, C.P., Li, Y., Liu, X.F.: Quasi-spin-wave quantum memories with a dynamical symmetry. Phys. Rev. Lett. 91, 147903 (2003)CrossRef
32.
Simon, J., Haruka, T., Ghosh, S., Vuleti, V.: Single-photon bus connecting spin-wave quantum memories. Nat. Phys. 3, 765–769 (2007)CrossRef
33.
Reim, K.F., et al.: Towards high-speed optical quantum memories. Nat. Photon. 4, 218–221 (2010)CrossRef
34.
Diniz, I., et al.: Strongly coupling a cavity to inhomogeneous ensembles of emitters: potential for long-lived solid-state quantum memories. Phys. Rev. A 84, 063810 (2011)CrossRef
35.
George, C., Dollimore, J., Kindberg, T., Blair, G.: Distributed Systems: Concepts and Design. Addison-Wesley, Reading (2011). pp. 230–312MATH
36.
Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)CrossRef
37.
Cirac, J.I., Ekert, A., Huelga, S.F., Macchiavello, C.: Distributed quantum computation over noisy channels. Phys. Rev. A 59, 42–49 (1999)MathSciNetCrossRef
38.
Meter, R.V., Munro, W.J., Nemoto, K., Itoh, K.M.: Arithmetic on a distributed-memory quantum multicomputer. ACM J. Emerg. Tech. Comput. Syst. 3, 1–23 (2008)CrossRef
39.
Spiller, T.P., et al.: Quantum computation by communication. New J. Phys. 8, 30 (2006)CrossRef
40.
Danos, V., D’Hondt, E., Kashefi, E., Panangaden, P.: Distributed measurement-based quantum computation. Elect. Notes Theoret. Comput. Sci. 170, 73–94 (2007)CrossRefMATH
41.
Love, P.J., Boghosian, B.M.: Type II quantum algorithms. Phys. A 362(1), 210–214 (2006)CrossRef
42.
43.
Huang, Y.F., Ren, X.F., Zhang, Y.S., Duan, L.M., Guo, G.C.: Experimental teleportation of a quantum controlled-NOT gate. Phys. Rev. Lett. 93, 240501 (2004)CrossRef
44.
Meter, R.V., Nemoto, K., Munro, W.: Communication links for distributed quantum computation. IEEE Trans. Comput. 56(12), 1643–1653 (2007)MathSciNetCrossRef
45.
Ying, M., Feng, Y.: An algebraic language for distributed quantum computing. IEEE Trans. Comput. 58(6), 728–743 (2009)MathSciNetCrossRef
46.
Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Optically controlled phase gate and teleportation of a controlled-NOT gate for spin qubits in quantum dot-microcavity coupled system. Phys. Rev. A 87, 062337 (2013)CrossRef
47.
Luo, M.X., Li, H.R., Wang, X.: Teleportation of a controlled-Not gate for photon and electron-spin qubits assisted by the nitrogen-vacancy center. Quantum Inf. Comput. 15(15), 1397–1419 (2015)MathSciNet
48.
Luo, M.X., Wang, X.: Universal remote quantum computation assisted by the cavity input-output process. Proc. R. Soc. A 471(2184), 20150274 (2015)CrossRef
49.
Bennett, C.H., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)MathSciNetCrossRefMATH
50.
Toffoli, T.: Reversible computing. In: de Bakker, J., van Leeuwen, J. (eds.) Automata, Languages and Programming. LNCS, vol. 85, pp. 632–644. Springer, Berlin (2005)CrossRef
51.
Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493(R) (1995)CrossRef
52.
Calderbank, A., Rains, E., Shor, P.W., Sloane, N.: Quantum error correction via codes over GF(4). IEEE Trans. Inf. Theor. 44, 1369–1387 (1998)MathSciNetCrossRefMATH
53.
Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)CrossRef
54.
Knill, E., Laflamme, R., Martinez, R., Negrevergne, C.: Benchmarking quantum computers: the five-qubit error correcting code. Phys. Rev. Lett. 86, 5811–5814 (2001)CrossRef
55.
56.
Shi, Y.: Both Toffoli and controlled-NOT need little help to do universal quantum computation. Quantum Inf. Comput. 3(1), 84–92 (2003)MathSciNetMATH
57.
Yu, N., Duan, R., Ying, R.: Five two-qubit gates are necessary for implementing the Toffoli gate. Phys. Rev. A 88, 010304(R) (2013)CrossRef
58.
Lanyon, B.P., et al.: Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys. 5, 134–140 (2008)CrossRef
59.
Luo, M.X., Ma, S.Y., Chen, X.B., Wang, X.: Hybrid Toffoli gate on photons and quantum spins. Sci. Rep. 5, 16716 (2015)CrossRef
Metadaten
Titel
Distributed Quantum Computation Assisted by Remote Toffoli Gate
verfasst von
Ming-Xing Luo
Hui-Ran Li
Copyright-Jahr
2016
Buch
Cloud Computing and Security

Print ISBN: 978-3-319-48670-3

Electronic ISBN: 978-3-319-48671-0

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-48671-0_42