Letters to Nature

Nature 403, 869-871 (24 February 2000) | doi:10.1038/35002528; Received 22 July 1999; Accepted 14 December 1999

Geometric quantum computation using nuclear magnetic resonance

Jonathan A. Jones1,2, Vlatko Vedral1, Artur Ekert1 & Giuseppe Castagnoli3

  1. Centre for Quantum Computation, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
  2. Oxford Centre for Molecular Sciences, New Chemistry Laboratory, South Parks Road, Oxford OX1 3QT, UK
  3. Elsag, Via Puccini 2, 1615 Genova, Italy

Correspondence to: Jonathan A. Jones1,2 Correspondence and requests for materials should be addressed to J.A.J. (e-mail: Email: jonathan.jones@qubit.org).

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.