Apparatus and methods for removing leakage from a qubit. In one aspect, an apparatus includes one or more qubits, wherein each qubit facilitates occupation of at least one of a plurality of qubit levels, the qubit levels including two computational levels and one or more non-computational levels that are each higher than the computational levels, wherein the qubit facilitates transitions between qubit levels associated with a corresponding transition frequency; a cavity, wherein the cavity defines a cavity frequency; one or more couplers coupling each qubit to the cavity; one or more couplers coupling the cavity to an environment external to the one or more qubits and the cavity; a frequency controller that controls the frequency of each qubit such that, for each qubit, the frequency of the qubit is adjusted relative to the cavity frequency such that a population of a non-computational level is transferred to the cavity.