Geometric quantum computation

A Ekert, M Ericsson, P Hayden, H Inamori, J A Jones, D K L Oi, V Vedral

Research output: Contribution to journalArticle

199 Citations (Scopus)

Abstract

We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.

LanguageEnglish
Pages2501-2513
Number of pages13
JournalJournal of Modern Optics
Volume47
Issue number14-15
DOIs
Publication statusPublished - Nov 2000

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quantum computation
phase shift
geometry

Keywords

  • magnetic resonance
  • logic gates
  • quantum systems

Cite this

Ekert, A., Ericsson, M., Hayden, P., Inamori, H., Jones, J. A., Oi, D. K. L., & Vedral, V. (2000). Geometric quantum computation. Journal of Modern Optics, 47(14-15), 2501-2513. https://doi.org/10.1080/09500340008232177
Ekert, A ; Ericsson, M ; Hayden, P ; Inamori, H ; Jones, J A ; Oi, D K L ; Vedral, V . / Geometric quantum computation. In: Journal of Modern Optics. 2000 ; Vol. 47, No. 14-15. pp. 2501-2513.
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Ekert, A, Ericsson, M, Hayden, P, Inamori, H, Jones, JA, Oi, DKL & Vedral, V 2000, 'Geometric quantum computation' Journal of Modern Optics, vol. 47, no. 14-15, pp. 2501-2513. https://doi.org/10.1080/09500340008232177

Geometric quantum computation. / Ekert, A ; Ericsson, M ; Hayden, P ; Inamori, H ; Jones, J A ; Oi, D K L ; Vedral, V .

In: Journal of Modern Optics, Vol. 47, No. 14-15, 11.2000, p. 2501-2513.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Geometric quantum computation

AU - Ekert, A

AU - Ericsson, M

AU - Hayden, P

AU - Inamori, H

AU - Jones, J A

AU - Oi, D K L

AU - Vedral, V

PY - 2000/11

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N2 - We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.

AB - We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary transformation can be implemented with arbitrary precision using only single-spin operations and conditional phase shifts. Thus quantum geometrical phases can form the basis of any quantum computation. Moreover, as the induced conditional phase depends only on the geometry of the paths executed by the spins it is resilient to certain types of errors and offers the potential of a naturally fault-tolerant way of performing quantum computation.

KW - magnetic resonance

KW - logic gates

KW - quantum systems

UR - http://arxiv.org/PS_cache/quant-ph/pdf/0004/0004015v1.pdf

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Ekert A, Ericsson M, Hayden P, Inamori H, Jones JA, Oi DKL et al. Geometric quantum computation. Journal of Modern Optics. 2000 Nov;47(14-15):2501-2513. https://doi.org/10.1080/09500340008232177