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The prevalent approach to executing quantum algorithms on quantum computersis to break-down the algorithms to a concatenation of universal gates,typically single and two-qubit gates. However such a decomposition results inlong gate sequences which are exponential in the qubit register size.Furthermore, gate fidelities tend to decrease when acting in larger qubitregisters. Thus high-fidelity implementations in large qubit registers is stilla prominent challenge. Here we propose and investigate multi-qubit entanglinggates for trapped-ions. Our gates couple many qubits at once, allowing todecrease 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, whichallows to operate outside of the adiabatic regime and at rates comparable tothe secular ion-trapping frequency. Furthermore we extend our method forgenerating Hamiltonians which are suitable for quantum analog simulations, suchas a nearest-neighbour spin Hamiltonian or the Su-Schrieffer-HeegerHamiltonian.

Theory of robust multi-qubit non-adiabatic gates for trapped-ions