  Many realizations of solid-state qubits involve couplings to leakage states
lying outside the computational subspace, posing a threat to high-fidelity
quantum gate operations. Mitigating leakage errors is especially challenging
when the coupling strength is unknown, e.g., when it is caused by noise. Here
we show that simple pulse sequences can be used to strongly suppress leakage
errors for a qubit embedded in a three-level system. As an example, we apply
our scheme to the recently proposed charge quadrupole (CQ) qubit for quantum
dots. These results provide a solution to a key challenge for fault-tolerant
quantum computing with solid-state elements.
