Optimal control of entangling operations for trapped-ion quantum computing

Optimal control techniques are applied for the decomposition of unitary quantum operations into a sequence of single-qubit gates and entangling operations. To this end, we modify a gradient-ascent algorithm developed for systems of coupled nuclear spins in molecules to make it suitable for trapped-ion quantum computing. We decompose unitary operations into entangling gates that are based on a nonlinear collective spin operator and complemented by global spin flip and local light shift gates. Among others, we provide explicit decompositions of controlled-NOT and Toffoli gates, and a simple quantum error correction protocol.