A method for removing the occupation of higher qubit levels in one or more qubits of a quantum system, the quantum system comprising: one or more qubits, wherein each qubit has states corresponding to a plurality of qubit levels, the qubit levels including two computational qubit levels and one or more non-computational qubit levels that are each higher than the computational qubit levels, and wherein said each qubit is configured to transition between qubit levels with corresponding transition frequencies; a cavity, wherein the cavity defines a cavity frequency; one or more couplers configured to couple each qubit to the cavity; and one or more couplers (no) configured to couple the cavity to an environment external to the one or more qubits and the cavity such that the cavity is damped; a frequency controller; the method being characterized in that it comprises: controlling the transition frequencies of each qubit using the frequency controller such that, for each qubit, the transition frequencies of the qubit are adjusted relative to the cavity frequency such that a population of a non- computational qubit level is transferred to the cavity, wherein the adjusting comprises: for each of the non-computational qubit level, tuning the transition frequency corresponding to the non-computational qubit level by aligning said tuned transition frequency with or by sweeping said tuned transition frequency past the cavity frequency. the quantum system comprising: one or more qubits, wherein each qubit has states corresponding to a plurality of qubit levels, the qubit levels including two computational qubit levels and one or more non-computational qubit levels that are each higher than the computational qubit levels, and wherein said each qubit is configured to transition between qubit levels with corresponding transition frequencies; a cavity, wherein the cavity defines a cavity frequency; one or more couplers configured to couple each qubit to the cavity; and one or more couplers (no) configured to couple the cavity to an environment external to the one or more qubits and the cavity such that the cavity is damped; a frequency controller; one or more qubits, wherein each qubit has states corresponding to a plurality of qubit levels, the qubit levels including two computational qubit levels and one or more non-computational qubit levels that are each higher than the computational qubit levels, and wherein said each qubit is configured to transition between qubit levels with corresponding transition frequencies; a cavity, wherein the cavity defines a cavity frequency; one or more couplers configured to couple each qubit to the cavity; and one or more couplers (no) configured to couple the cavity to an environment external to the one or more qubits and the cavity such that the cavity is damped; a frequency controller; the method being characterized in that it comprises: controlling the transition frequencies of each qubit using the frequency controller such that, for each qubit, the transition frequencies of the qubit are adjusted relative to the cavity frequency such that a population of a non- computational qubit level is transferred to the cavity, wherein the adjusting comprises: for each of the non-computational qubit level, tuning the transition frequency corresponding to the non-computational qubit level by aligning said tuned transition frequency with or by sweeping said tuned transition frequency past the cavity frequency.