Compact gate-based read-out of multiplexed quantum devices with a cryogenic CMOS active inductor

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.