  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.
