Frequency-multiplexed radio-frequency (RF) reflectometry is a promising technique for large-scale quantum dot-based qubit systems because it enables simultaneous readout of multiple qubits and helps to reduce the wiring density in peripheral circuits. However, in the conventional L-C-type matching circuits, resonator frequency tunability is limited by poor design flexibility of the shunt capacitance and hence the circuit. Recently, L-L-type matching circuits comprising a series and a shunt inductor have been proposed to address this issue. Here, we report RF reflectometry readout of silicon quantum dot-based charge sensors embedded in L-L-type circuits. We determine the inductance values for target resonance frequencies based on our equivalent circuit model that incorporates the parasitic elements of the inductors and demonstrate resonator frequency tunability of up to 1 GHz with 3-dB resonator bandwidths on the order of MHz. The measured conductance sensitivities, on the order of 10−5(e2/h)/Hz at 4 K, are only moderately dependent on the resonance frequency up to 630 MHz. These results highlight the prospects of L-L-type matching circuits for rapid and multiplex reflectometry readout of semiconductor spin qubits.
Frequency-multiplexed radio-frequency (RF) reflectometry is a promising technique for large-scale quantum dot-based qubit systems because it enables simultaneous readout of multiple qubits and helps to reduce the wiring density in peripheral circuits. However, in the conventional L-C-type matching circuits, resonator frequency tunability is limited by poor design flexibility of the shunt capacitance and hence the circuit. Recently, L-L-type matching circuits comprising a series and a shunt inductor have been proposed to address this issue. Here, we report RF reflectometry readout of silicon quantum dot-based charge sensors embedded in L-L-type circuits. We determine the inductance values for target resonance frequencies based on our equivalent circuit model that incorporates the parasitic elements of the inductors and demonstrate resonator frequency tunability of up to 1 GHz with 3-dB resonator bandwidths on the order of MHz. The measured conductance sensitivities, on the order of 10−5(e2/h)/Hz at 4 K, are only moderately dependent on the resonance frequency up to 630 MHz. These results highlight the prospects of L-L-type matching circuits for rapid and multiplex reflectometry readout of semiconductor spin qubits.
This paper reports on the extraction of the equivalent circuit model parameters of a physically defined silicon quantum dot at a cryogenic temperature and design of the impedance matching circuits to improve the performance of a charge sensor for radio-frequency (RF) reflectometry. The I-V characteristics and the S-parameters of the quantum dot device are measured around a Coulomb peak at 4.2 K. The measured results are modeled by an RC parallel circuit, and the model parameters for the quantum dot device were obtained. We consider three impedance matching circuits for RF reflectometry of a quantum dot: shunt capacitor-series inductor type, shunt inductor-series capacitor type, and shunt inductor-series inductor-type. We formulate and compare the sensitivity and bandwidth of RF reflectometry for the three types of circuits. The analysis should be useful for selecting the optimal matching circuit and the circuit parameters for given equivalent circuit parameters and working frequency. This procedure is demonstrated for a quantum dot with the characterized model circuit along with simulated performance. This design technique of matching circuit for RF reflectometry can be applied to any device that can be represented by an RC parallel circuit. These results will facilitate to realize fast semiconductor qubit readout in various quantum dot platforms.
We introduce a multimode superconducting inductor architecture that enables radio-frequency reflectometry at multiple discrete frequencies up to 2 GHz, addressing limitations of conventional single-mode designs. The spiral inductor's distributed inter-turn capacitance yields distinct resonant modes with varied impedance-matching conditions. By probing a quantum dot across several modes, we extract tunneling rates over a broad frequency range and identify signatures of nearby charge defects. Using one of the higher-order modes, we demonstrate single-shot spin readout via a radio-frequency single-electron transistor (RF-SET), achieving singlet-triplet readout with an integration time of 8 us and a readout fidelity of 98%. These results establish multimode inductance as a scalable and flexible component for fast spin-qubit readout and device-quality characterization.
We introduce a multimode superconducting inductor architecture that enables radio frequency reflectometry at multiple discrete frequencies up to 2 GHz, addressing limitations of conventional single-mode designs. The spiral inductor's distributed capacitance yields distinct resonant modes with varied impedance-matching conditions. By probing a quantum dot across several modes, we extract tunneling rates over a broad frequency range and identify signatures of nearby charge defects. Using a higher-order mode of the distributed inductor, rather than the fundamental mode, we demonstrate single-shot spin readout via a radio frequency single-electron transistor (RF-SET), achieving singlet-triplet readout with an integration time of 8 μs and a readout fidelity of 98%. These results establish multimode inductance as a scalable and flexible component for fast spin qubit readout and device-quality characterization.
Electrical readout of spin qubits requires fast and sensitive measurements, which are hindered by poor impedance matching to the device. We demonstrate perfect impedance matching in a radio-frequency readout circuit, using voltage-tunable varactors to cancel out parasitic capacitances. An optimized capacitance sensitivity of 1.6 aF/√Hz is achieved at a maximum source-drain bias of 170−μV root-mean-square and with a bandwidth of 18 MHz. Coulomb blockade in a quantum-dot is measured in both conductance and capacitance, and the two contributions are found to be proportional as expected from a quasistatic tunneling model. We benchmark our results against the requirements for single-shot qubit readout using quantum capacitance, a goal that has so far been elusive.
This thesis focuses on implementing radio frequency (rf) reflectometry techniques for dispersive detection of charge and spin dynamics in nanoscale devices. I have investigated three aspects of rf reflectometry using state-of-the-art silicon (Si) complementary metal-oxide-semiconductor (CMOS) nanowire field effect transistors (NWFETs). First, a high-sensitivity capacitive gate-based charge sensor is developed by optimising the external matching circuit to detect capacitive changes in the high frequency resonator. A new circuit topology is used where superconducting niobium nitride (NbN) inductor is connected in parallel with a single-gate Si NWFET resulting in resonators with loaded Q-factors in the 400-800 range. For a resonator operating at 330 MHz, I have achieved a charge sensitivity of 7.7 μe/Hz and, when operating at 616 MHz, I get 1.3 μe/Hz. This gate-based sensor can be used for fast, accurate and scalable techniques for quantum state readout in Si CMOS based quantum computing. Second, this new circuit topology for the resonator is used with a dual-gate Si NWFET. This dual-gate device geometry provides access to a double quantum dot (DQD) system in few electron regime. The spin-state of the two-electron DQD system is detected dispersively using Pauli spin blockade between joint singlet S(2,0) and triplet T−(1,1) states in a finite magnetic field B. The singlet-triplet relaxation time T1 at B=4.5~T is measured to be $\sim$1 ms using standard homodyne detection technique. Third, I expand the range of applications of gate-based sensing to accurate temperature measurements. I have experimentally demonstrated a primary thermometer by embedding a single-gate Si NWFET with the rf capacitive gate-based sensor. The thermometer, termed as gate-based electron thermometer (GET), relies on cyclic electron tunneling between discrete energy levels of a quantum dot and a single electron reservoir in the NWFET. I have found that the full-width-half-maximum (FWHM) of the resonator phase response depends linearly with temperature via well known physical law by using the ratio kB/e between the Boltzmann constant and the electron charge. The GET is also found to be magnetic field independent like other primary thermometers such as Coulomb blockade and shot noise thermometers.
Rapid single shot spin readout is a key ingredient for fault tolerant quantum computing with spin qubits. An RF-SET (radio-frequency single electron transistor) is predominantly used as its the readout timescale is far shorter than the spin decoherence time. In this work, we experimentally demonstrate a transmission-based RF-SET using a multi-module semiconductor-superconductor assembly. A monolithically integrated SET placed next to a double quantum dot in a Si/SiGe heterostructure is wire-bonded to a superconducting niobium inductor forming the impedance-transforming network. Compared to RF reflectometry, the proposed set-up is experimentally simpler without the need for directional couplers. Read-out performance is benchmarked by the signal-to-noise (SNR) of a dot-reservoir transition (DRT) and an interdot charge transition (ICT) in the double quantum dot near the SET as a function of RF power and integration time. The minimum integration time for unitary SNR is found to be 100 ns for ICT and 300 ns for DRT. The obtained minimum integration times are comparable to the state of the art in conventional RF reflectometry set-ups. Furthermore, we study the turn-on properties of the RF-SET to investigate capacitive shifts and RF losses. Understanding these effects are crucial for further optimisations of the impedance transforming network as well as the device design to assist RF read-out. This new RF read-out scheme also shows promise for multiplexing spin-qubit readout and further studies on rapid charge dynamics in quantum dots.