Optimal, robust, arbitrary, parallel single-qubit unitaries with limited individual control

The ability to robustly implement different single-qubit unitaries in parallel is crucial for scalable quantum information processing. However, local single-qubit manipulations are difficult to engineer in existing quantum platforms such as neutral atom arrays, where qubits are addressed by a global laser field. Here, we construct simple, optimal-length pulse sequences for the parallel realization of independent, arbitrary single-qubit unitaries under two restricted forms of individual control: (1) when each qubit can be individually detuned from resonance, and (2) when each qubit can be subject to a different laser phase. We further devise optimal-length modifications of these pulse sequences that feature robustness against amplitude error, a dominant source of imperfection arising from field inhomogeneity and laser fluctuations. These results provide a path towards achieving universal quantum computation on near-term technology.