  The prevalent approach to executing quantum algorithms on quantum computers
is to break-down the algorithms to a concatenation of universal gates,
typically single and two-qubit gates. However such a decomposition results in
long gate sequences which are exponential in the qubit register size.
Furthermore, gate fidelities tend to decrease when acting in larger qubit
registers. Thus high-fidelity implementations in large qubit registers is still
a prominent challenge. Here we propose and investigate multi-qubit entangling
gates for trapped-ions. Our gates couple many qubits at once, allowing to
decrease the total number of gates used while retaining a high gate fidelity.
Our method employs all of the normal-modes of motion of the ion chain, which
allows to operate outside of the adiabatic regime and at rates comparable to
the secular ion-trapping frequency. Furthermore we extend our method for
generating Hamiltonians which are suitable for quantum analog simulations, such
as a nearest-neighbour spin Hamiltonian or the Su-Schrieffer-Heeger
Hamiltonian.
