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arXiv:1510.06944 · Physical Review Applied

Sensitive Radio-Frequency Measurements of a Quantum Dot by Tuning to Perfect Impedance Matching

N. Ares, F. J. Schupp, A. Mavalankar, G. Rogers, J. Griffiths, G. A. C. Jones, I. Farrer, D. A. Ritchie, C. G. Smith, A. Cottet, G. A. D. Briggs, Edward A. Laird

Published Mar 24, 2016• 63 citations
arXivHTMLPDF

Abstract

Electrical readout of spin qubits requires fast, sensitive measurements, which are hindered by poor impedance matching in a practical device. The authors demonstrate perfect impedance matching in an rf readout circuit, measure the absolute sensitivity to quantum capacitance changes, and establish a clear requirement for single-shot readout. This work will aid research not just in quantum computing, but also in nanomechanics and ac quantum transport.

DOI
10.1103/physrevapplied.5.034011

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Electrical readout of spin qubits requires fast, sensitive measurements, which are hindered by poor impedance matching in a practical device. The authors demonstrate perfect impedance matching in an rf readout circuit, measure the absolute sensitivity to quantum capacitance changes, and establish a clear requirement for single-shot readout. This work will aid research not just in quantum computing, but also in nanomechanics and ac quantum transport.
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.
Radio-frequency reflectometry allows for fast and sensitive electrical readout of charge and spin qubits hosted in quantum dot devices coupled to resonant circuits. Optimizing readout, however, requires frequency tuning of the resonators and impedance matching. This is difficult to achieve using conventional semiconductor or ferroelectric-based varactors in the detection circuit as their performance degrades significantly in the mK temperature range relevant for solid-state quantum devices. Here we explore a different type of material, strontium titanate, a quantum paraelectric with exceptionally large field-tunable permittivity at low temperatures. Using strontium titanate varactors we demonstrate perfect impedance matching and resonator frequency tuning at 6 mK and characterize the varactors at this temperature in terms of their capacitance tunability, dissipative losses and magnetic field sensitivity. We show that this allows us to optimize the radio-frequency readout signal-to-noise ratio of carbon nanotube quantum dot devices to achieve a charge sensitivity of 4.8 μμμe/Hz1/2^{1/2}1/2 and capacitance sensitivity of 0.04 aF/Hz1/2^{1/2}1/2.
Quantum computation requires a qubit-specific measurement capability to read out the final states of individual qubits. Promising semiconductor architectures use external readout electrometers, but these could be replaced by more scalable $g\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}e$ $s\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s$, based on the dispersive coupling between an electrical resonator and the qubit. The authors present an optimized gate sensor and show that significantly better sensitivity arises from changing circuit topology to enhance the resonator's QQQ factor. Here CMOS-based quantum devices achieve charge sensitivity on par with that of the best single-electron electrometers.
Abstract Radio-frequency measurements could satisfy DiVincenzo's readout criterion in future large-scale solid-state quantum processors, as they allow for high bandwidths and frequency multiplexing. However, the scalability potential of this readout technique can only be leveraged if quantum device tuning is performed using exclusively radio-frequency measurements, i.e. without resorting to current measurements. By exploiting their bandwidth and impedance matching, we demonstrate an algorithm that automatically tunes double quantum dots with only radio-frequency measurements. The tuning was completed within a few minutes without prior knowledge about the device architecture. Our results show that it is possible to eliminate the need for transport measurements for quantum dot tuning, paving the way for more scalable device architectures.
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.