Systems and methods directed to a quantum processing apparatus are provided. The apparatus comprises M solid-state qubits, where M>1, and control electronics, which are connected to the solid-state qubits. The control electronics comprise one or more qubit readout circuits, where each of the qubit readout circuits is connected to at least one of the solid-state qubits and comprises a downsampling analog-to-digital converter (hereafter DSADC). Each DSADC is configured to downsample analog signals obtained from the at least one of the solid-state qubits. Such a DSADC operates in the nth Nyquist zone of the spectrum of the analog signals obtained, so as to down-convert such analog signals from the nth Nyquist zone to the mth Nyquist zone of the spectrum, where n>m≥1, prior to sampling the analog signals to convert them into digital signals, in operation. One or more embodiments of the invention are further directed to a related method of operating such a quantum processing apparatus.