Elementary gates for quantum computation

Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. Divincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, Harald Weinfurter

    Research output: Contribution to journalArticle

    Abstract

    We show that a set of gates that consists of all one-bit quantum gates [U(2)] and the two-bit exclusive-OR gate [that maps Boolean values (x,y) to (x,xy)] is universal in the sense that all unitary operations on arbitrarily many bits n [U(2n)] can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical and of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.

    Original languageEnglish (US)
    Pages (from-to)3457-3467
    Number of pages11
    JournalPhysical Review A
    Volume52
    Issue number5
    DOIs
    StatePublished - 1995

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    ASJC Scopus subject areas

    • Physics and Astronomy(all)
    • Atomic and Molecular Physics, and Optics

    Cite this

    Barenco, A., Bennett, C. H., Cleve, R., Divincenzo, D. P., Margolus, N., Shor, P., ... Weinfurter, H. (1995). Elementary gates for quantum computation. Physical Review A, 52(5), 3457-3467. https://doi.org/10.1103/PhysRevA.52.3457

    Elementary gates for quantum computation. / Barenco, Adriano; Bennett, Charles H.; Cleve, Richard; Divincenzo, David P.; Margolus, Norman; Shor, Peter; Sleator, Tycho; Smolin, John A.; Weinfurter, Harald.

    In: Physical Review A, Vol. 52, No. 5, 1995, p. 3457-3467.

    Research output: Contribution to journalArticle

    Barenco, A, Bennett, CH, Cleve, R, Divincenzo, DP, Margolus, N, Shor, P, Sleator, T, Smolin, JA & Weinfurter, H 1995, 'Elementary gates for quantum computation', Physical Review A, vol. 52, no. 5, pp. 3457-3467. https://doi.org/10.1103/PhysRevA.52.3457
    Barenco A, Bennett CH, Cleve R, Divincenzo DP, Margolus N, Shor P et al. Elementary gates for quantum computation. Physical Review A. 1995;52(5):3457-3467. https://doi.org/10.1103/PhysRevA.52.3457
    Barenco, Adriano ; Bennett, Charles H. ; Cleve, Richard ; Divincenzo, David P. ; Margolus, Norman ; Shor, Peter ; Sleator, Tycho ; Smolin, John A. ; Weinfurter, Harald. / Elementary gates for quantum computation. In: Physical Review A. 1995 ; Vol. 52, No. 5. pp. 3457-3467.
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