1. Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
2. Physics Department, Campus Box 390, University of Colorado, Boulder, Colorado 80309, USA
3. Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
4. Institute of Physics, PO Box 57, 11001 Belgrade, Serbia-Montenegro

Correspondence to: D. J. Wineland¹ Correspondence and requests for materials should be addressed to D.J.W. (e-mail: Email: david.wineland@boulder.nist.gov).

Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum computation. Dynamical gates have been proposed^{1, 2} in the context of trapped ions; however, geometric phase gates (which change only the phase of the physical qubits) offer potential practical advantages because they have higher intrinsic resistance to certain small errors and might enable faster gate implementation. Here we demonstrate a universal geometric -phase gate between two beryllium ion-qubits, based on coherent displacements induced by an optical dipole force. The displacements depend on the internal atomic states; the motional state of the ions is unimportant provided that they remain in the regime in which the force can be considered constant over the extent of each ion's wave packet. By combining the gate with single-qubit rotations, we have prepared ions in an entangled Bell state with 97% fidelity—about six times better than in a previous experiment³ demonstrating a universal gate between two ion-qubits. The particular properties of the gate make it attractive for a multiplexed trap architecture^{4, 5} that would enable scaling to large numbers of ion-qubits.