Fast quantum logic by selective displacement of hot trapped ions

Abstract

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 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 to͒ the trap vibrational frequency.

Errors in trapped-ion quantum gates due to spontaneous photon scattering

“…The worst-case fidelity is clearly smaller than the average fidelity and therefore gives a conservative estimate to the gate error [62]. The worst-case fidelity for this kind of error was calculated in [63]. For ∆φ/φ < 1 it is…”

Quantum information processing using quasiclassical electromagnetic interactions between qubits and electrical resonators

“…The times τ at which this occurs are defined by the conditions 9 It is also possible to simply turn a force on for a fixed time, with no oscillatory component. Such a scheme was considered for trapped ions in [67], and related methods for superconducting qubits were proposed in [33][34][35]38]. Compared to our proposal, these techniques require much larger η to achieve the same gate speed (larger by a factor δ −1 m ), and they also provide no discrimination between the desired resonator mode and higher modes.…”

Fast and robust quantum computation with ionic Wigner crystals

“…Such terminology is typically used in quantum field theory [37]. Finally, it is worth to remind that the gate we aim to accomplish realizes the true table |ǫ 1 , ǫ 2 → e iθǫ1ǫ2 |ǫ 1 , ǫ 2 with ǫ 1,2 = 0, 1 and θ = θ 00 − θ 01 − θ 10 + θ 11 [33,34]. Specifically, we are interested in a phase gate with θ = π, which, up to additional single-qubit rotations, is tantamount to a two-qubit controlled NOT gate [24].…”

“…1). Depending on the configuration of lasers and polarizations the displacements of the ions away from their equilibrium positions can be either perpendicular to the plane of the crystal [29] or along the in-plane separation of the ions [30,[32][33][34]. The coupling between these displacements, mediated by phonons, yields entanglement of the internal states (qubits) of the ions, that is, the desired quantum gate between ions.…”