  Quantum logic gates with many control qubits are essential in many quantum
algorithms, but remain challenging to perform in current experiments. Trapped
ion quantum computers natively feature a different type of entangling
operation, namely the Molmer-Sorensen (MS) gate which effectively applies an
Ising interaction to all qubits at the same time. We consider a sequence of
equal all-to-all MS operations, interleaved with single qubit gates that act
only on one special qubit. Using a connection with quantum signal processing
techniques, we find that it is possible to perform an arbitray SU(2) rotation
on the special qubit if and only if all other qubits are in the state |1>. Such
controlled rotation gates with N-1 control qubits require 2N applications of
the MS gate, and can be mapped to a conventional Toffoli gate by demoting a
single qubit to ancilla.
