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.

Figure 1

Repetitive error correction of spin flips using three qubits for encoding the logical qubit and two ancilla qubits for error syndrome detection and coherent correction of errors. The optimal control algorithm looked for a decomposition of the unitary operation enclosed in the dashed box comprising syndrome detection and error correction.