ua nt - p h / 04 04 08 3 v 1 1 4 A pr 2 00 4 Quantum phase gate between ions in a solid

Due to their potential for long coherence times, dopant ions have long been considered promising candidates for scalable solid state quantum computing. However, the demonstration of a universal set of quantum logic operations using dopant ions has proven to be problematic, largely due to the difficulty of addressing closely spaced ions. Here we use optically active ions and frequency addressing to demonstrate a conditional phase shift between two qubits. This, along with the single qubit unitary operations that have been demonstrated previously,[1] constitutes a universal set of quantum gates. In this work we demonstrate a conditional quantum phase shift in a two-qubit system, based on local interactions between optically active centers in a solid. The qubits were based on optical transitions of the dopant ions. The gate operations are performed with sequences of precise optical pulses in a manner analogous to techniques used in nuclear magnetic resonance. This logic gate has the potential to be used in scalable quantum computer architectures, along the lines proposed by Lloyd.[2] The material chosen for the demonstration was Eu doped yttrium orthosilicate (YSO). This material was selected because of the narrow homogeneous linewidth of the F0 ↔ D0 transition of the Eu3+ ions at 579 nm, which can be as narrow as 100 Hz[3]. The long coherence time associated with this narrow line width simplifies the implementation of the optical pulse sequences as it allows the use of microsecond time scale pulses to control the gate operations. These pulses can be generated by simple modulation of the output of a narrowband continuous wave laser. The dominant interaction between the Eu ions is a non-resonant electric dipole-dipole interaction. The Eu3+ dopant ion possesses a permanent electric dipole moment that