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The flip-flop qubit, encoded in the states with antiparallel donor-boundelectron and donor nuclear spins in silicon, showcases long coherence times,good controllability, and, in contrast to other donor-spin-based schemes,long-distance coupling. Electron spin control near the interface, however, islikely to shorten the relaxation time by many orders of magnitude, reducing theoverall qubit quality factor. Here, we theoretically study the multilevelsystem that is formed by the interacting electron and nuclear spins and deriveanalytical effective two-level Hamiltonians with and without periodic driving.We then propose an optimal control scheme that produces fast and robustsingle-qubit gates in the presence of low-frequency noise without relying onparametrically restrictive sweet spots. This scheme increases considerably boththe relaxation time and the qubit quality factor.

Fast high-fidelity single-qubit gates for flip-flop qubits in silicon