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Geometric quantum computation using nuclear magnetic resonance

Nature volume 403, pages 869–871 (2000)Cite this article

Abstract

A significant development in computing has been the discovery1 that the computational power of quantum computers exceeds that of Turing machines. Central to the experimental realization of quantum information processing is the construction of fault-tolerant quantum logic gates. Their operation requires conditional quantum dynamics, in which one sub-system undergoes a coherent evolution that depends on the quantum state of another sub-system2; in particular, the evolving sub-system may acquire a conditional phase shift. Although conventionally dynamic in origin, phase shifts can also be geometric3,4. Conditional geometric (or ‘Berry’) phases depend only on the geometry of the path executed, and are therefore resilient to certain types of errors; this suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations. Nuclear magnetic resonance techniques have already been used to demonstrate both simple quantum information processing5,6,7,8,9 and geometric phase shifts10,11,12. Here we combine these ideas by performing a nuclear magnetic resonance experiment in which a conditional Berry phase is implemented, demonstrating a controlled phase shift gate.

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Figure 1: Pulse sequence used to demonstrate controlled Berry phases.
Figure 2: Experimental values for the Berry phases γ0, γ1, and the controlled Berry phase difference, Δγ, as a function of the maximum radio-frequency field strength ν1.

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Acknowledgements

We thank N. Soffe for helpful discussions. J.A.J. and A.E. thank the Royal Society of London and Starlab (Riverland NV) for financial support.

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Authors and Affiliations

  1. Centre for Quantum Computation, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK

    Jonathan A. Jones, Vlatko Vedral & Artur Ekert

  2. Oxford Centre for Molecular Sciences, New Chemistry Laboratory, South Parks Road, Oxford, OX1 3QT, UK

    Jonathan A. Jones

  3. Elsag, Via Puccini 2, Genova, 1615, Italy

    Giuseppe Castagnoli

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  1. Jonathan A. Jones
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Correspondence to Jonathan A. Jones.

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Jones, J., Vedral, V., Ekert, A. et al. Geometric quantum computation using nuclear magnetic resonance. Nature 403, 869–871 (2000). https://doi.org/10.1038/35002528

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