  Leakage outside of the qubit computational subspace poses a threatening
challenge to quantum error correction (QEC). We propose a scheme using two
leakage-reduction units (LRUs) that mitigate these issues for a transmon-based
surface code, without requiring an overhead in terms of hardware or QEC-cycle
time as in previous proposals. For data qubits we consider a microwave drive to
transfer leakage to the readout resonator, where it quickly decays, ensuring
that this negligibly affects the coherence within the computational subspace
for realistic system parameters. For ancilla qubits we apply a
$|1\rangle\leftrightarrow|2\rangle$ $\pi$ pulse conditioned on the measurement
outcome. Using density-matrix simulations of the distance-3 surface code we
show that the average leakage lifetime is reduced to almost 1 QEC cycle, even
when the LRUs are implemented with limited fidelity. Furthermore, we show that
this leads to a significant reduction of the logical error rate. This LRU
scheme opens the prospect for near-term scalable QEC demonstrations.
