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We developed a high-speed and low-noise time-domain current measurementscheme using a homemade GaAs high-electron-mobility-transistor-based cryogenictransimpedance amplifier (TIA). The scheme is versatile for broad cryogeniccurrent measurements, including semiconductor spin-qubit readout, owing to theTIA's having low input impedance comparable to that of commercialroom-temperature TIAs. The TIA has a broad frequency bandwidth and a low noisefloor, with a trade-off between them governed by the feedback resistance$R_{FB}$. A lower $R_{FB}$ of 50 k$\Omega$ enables high-speed currentmeasurement with a -3dB cutoff frequency $f_{-3dB}$ = 28 MHz and noise-floor$NF = 8.5 \times 10^{-27}$ A$^{2}$/Hz, while a larger $R_{FB}$ of 400 k$\Omega$provides low-noise measurement with $NF = 1.0 \times 10^{-27}$ A$^{2}$/Hz and$f_{-3dB}$ = 4.5 MHz. Time-domain measurement of a 2-nA peak-to-peak squarewave, which mimics the output of the standard spin-qubit readout technique viacharge sensing, demonstrates a signal-to-noise ratio (SNR) of 12.7, with thetime resolution of 48 ns, for $R_{FB}$ = 200 k$\Omega$, which comparesfavorably with the best-reported values for the radio-frequency (RF)reflectometry technique. The time resolution can be further improved at thecost of the SNR (or vice versa) by using an even smaller (larger) $R_{FB}$,with a further reduction in the noise figure possible by limiting the frequencyband with a low-pass filter. Our scheme is best suited for readout electronicsfor cryogenic sensors that require a high time resolution and currentsensitivity and thus provides a solution for various fundamental research andindustrial applications.

Fast time-domain current measurement for quantum dot charge sensing using a homemade cryogenic transimpedance amplifier