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Optimal control techniques are applied for the decomposition of unitaryquantum operations into a sequence of single-qubit gates and entanglingoperations. To this end, we modify a gradient-ascent algorithm developed forsystems of coupled nuclear spins in molecules to make it suitable for trappedion quantum computing. We decompose unitary operations into entangling gatesthat are based on a nonlinear collective spin operator and complemented byglobal spinflip and local light shift gates. Among others, we provide explicitdecompositions of controlled-NOT and Toffoli gates, and a simple quantum errorcorrection protocol.

Optimal control of entangling operations for trapped ion quantum computing