Signal processing techniques for efficient compilation of controlled rotations in trapped ions

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 the Mølmer-Sørensen (MS) entangling operation, which effectively applies an Ising interaction to all pairs of 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 ≤. 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.