  In the strive for scalable quantum processors, significant effort is being
devoted to the development of cryogenic classical hardware for the control and
readout of a growing number of qubits. Here we report on a cryogenic circuit
incorporating a CMOS-based active inductor enabling fast impedance measurements
with a sensitivity of 10 aF and an input-referred noise of 3.7 aF/sqrt(Hz).
This type of circuit is especially conceived for the readout of semiconductor
spin qubits. As opposed to commonly used schemes based on dispersive rf
reflectometry, which require mm-scale passive inductors, it allows for a
markedly reduced footprint (50$\mu$m $\times$ 60$\mu$m), facilitating its
integration in a scalable quantum-classical architecture. In addition, its
active inductor results in a resonant circuit with tunable frequency and
quality factor, enabling the optimization of readout sensitivity.
