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arXiv:2512.05087

Multimode RF Reflectometry for Spin Qubit Readout and Device Characterization

Joffrey Rivard, Alexis Morel, Olivier Romain, El Bachir Ndiaye, Idris Aboubakari, Christian Lupien, Clément Godfrin, Julien Jussot, Stefan Kubicek, Kristiaan De Greve, Danny Wan, Claude Rohrbacher, Eva Dupont-Ferrier

cond-mat.mes-hallquant-phSubmitted Dec 4, 2025• Announced Dec 5, 2025• 0 citations
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Abstract

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.

Comments
5 pages, 5 figures

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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.
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.
Superconducting spiral inductors are emerging as key components for radio-frequency (RF) reflectometry, a widely used readout technique for semiconductor spin qubits. Future scalable quantum-computing architectures are expected to operate at elevated temperatures and magnetic fields, placing new demands on the performance and stability of superconducting circuit elements. Here, we present a systematic study of NbTiN spiral inductors under temperatures of several kelvin and magnetic fields approaching 1 T. By combining weakly coupled resonator measurements with independent two-port inductance extraction, we separate inductive and capacitive contributions to device behaviour and directly identify the origin of resonance shifts and quality factor degradation. Furthermore, we establish practical design metrics linking geometry, temperature sensitivity, and magnetic-field robustness. These results provide a general framework for benchmarking superconducting inductors and guiding the design of future RF-reflectometry circuits for practical quantum technologies.
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.
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.
A scalable spin-qubit quantum processor requires fast, high-fidelity readout circuits operating at cryogenic temperatures (CTs). This work analyzes the radio frequency (RF) reflectometry readout mechanism to establish the link between conductance modulation, single-electron transistor (SET) matching network design, reflected signal power, and receiver (RX) noise temperature. Based on this analysis, a cryogenic RX architecture employing a passive switched-capacitor front-end is proposed. The front-end performs RF amplification and downconversion using transistors as switches, avoiding active RF amplification and mitigating shot-noise limitations. The RX is implemented in 40-nm CMOS and operates from 100 MHz to 2.2 GHz. Measurements demonstrate a minimum noise temperature of approximately 15 K at 4.2 K. When integrated with a quantum device, the RX achieves a signal-to-noise ratio (SNR) of 9.8 dB for a 10-µs integration time and enables 99.9% charge-state readout fidelity without external cryogenic amplifiers. This work represents the first demonstration of such fidelity using a cryo-CMOS RX and constitutes an important step toward scalable integration of qubit readout electronics.