Fast quantum logic by selective displacement of hot trapped ions

The "pushing gate" proposed by Cirac and Zoller for quantum logic in ion traps is discussed, in which a force is used to give a controlled push to a pair of trapped ions and thus realize a phase gate. The original proposal had a weakness in that it involved a hidden extreme sensitivity to the size of the force. Also, the physical origin of this force was not fully addressed. Here, we discuss the sensitivity and present a way to avoid it by choosing the spatial form of the pushing force in an optimal way. We also analyze the effect of imperfections in a pair of pi pulses which are used to implement a "spin echo" to cancel correlated errors. We present a physical model for the force, namely, the dipole force, and discuss the impact of unwanted photon scattering, and of finite temperature of the ions. The main effect of the temperature is to blur the phase of the gate owing to the ions exploring a range of values of the force. When the distance scale of the force profile is smaller than the ion separation, this effect is more important than the high-order terms in the Coulomb repulsion which were originally discussed. Overall, we find that whereas the pushing gate is not as resistant to imperfection as was supposed, it remains a significant candidate for ion trap quantum computing since it does not require ground-state cooling, and in some cases it does not require the Lamb-Dicke limit, while the gate rate is fast, close to (rather than small compared to) the trap vibrational frequency.