Fast multi-qubit global-entangling gates without individual addressing of trapped ions

Abstract

We propose and study ways speeding up of the entangling operations in the trapped ions system with high fidelity. First, we find a scheme to increase the speed of a two-qubit gate without the limitation of trap frequency, which was considered as the fundamental limit. Second, we study the fast gate scheme for entangling more than two qubits simultaneously. We apply the method of applying multiple frequency components on laser beams for the gate operations. In particular, in order to avoid infinite terms from the coupling to carrier transition, we focus on the phase-insensitive gate scheme here. We carefully study the effect of large excitation of motional mode beyond the limit of Lamb-Dicke approximation by including up to second order terms of the Lamb-Dicke parameter. We study the speed limit of multi-qubit global entangling gates without individual addressing requirements. Furthermore, our gates can be made insensitive to the fluctuation of initial motional phases which are difficult to stabilise in the phase-insensitive gate scheme.

Entangling gates for trapped-ion quantum computation and quantum simulation

“…It is necessary to include the effects of both vibrational modes for the two-qubit gate operations. That is, the phase-space trajectories of both modes should be closed and the sum of the areas enclosed by the phase-space trajectories in both modes should be π 4 [38,51,[127][128][129][130]. These requirements can be achieved by using the modulation methods and experimentally realized [88,96].…”

“…To tackle this complicated situation, Refs. [45,48,51] proposed a multichromatic modulation scheme, which, compared to the prementioned monochromatic modulation scheme, introduces more controlling parameters to satisfy multiple constraints imposed by the requirements both to disentangle the motional modes and to apply effective spin-spin interactions.…”

“…We note that compared with amplitude modulation, it can change the orientation of the trajectory in phase space promptly, which is more proper to prevent the vibrational state of ions from being excited beyond the Lamb-Dicke regime and to implement a fast gate [51].…”

“…Furthermore, these schemes were extended to simultaneously or parallelly entangle more qubits [48][49][50][51].…”

Implementing quantum Fourier transform using three qubits

“…To give a physical implementation of our system, we generalize the process proposed by Ivanov and Vitanov [20] to the three qubit case with trilinear coupling. Indeed, to realize the circulant Hamiltonian, we proceed with trapped ions [29][30][31]. A crystal with 3 N ions with mass M is considered, the trap axis are z and x with the frequencies Ω z and Ω x , respectively.…”