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arXiv:1801.09759 · Physical Review Applied

Radio-Frequency Capacitive Gate-Based Sensing

Imtiaz Ahmed, J. A. Haigh, Simon Schaal, Sylvain Barraud, Yi Zhu, Chang-Min Lee, Mario Amado, Jason W. A. Robinson, Alessandro Rossi, John J. L. Morton, M. Fernando González-Zalba

Published Jul 19, 2018• 75 citations
arXivHTMLPDF

Abstract

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 $Q$ factor. Here CMOS-based quantum devices achieve charge sensitivity on par with that of the best single-electron electrometers.

DOI
10.1103/physrevapplied.10.014018

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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.
Quantum computation requires a qubit-specific measurement capability to readout the final state of individual qubits. Promising solid-state architectures use external readout electrometers but these can be replaced by a more compact readout element, an in situ gate sensor. Gate-sensing couples the qubit to a resonant circuit via a gate and probes the qubit’s radiofrequency polarizability. Here we investigate the ultimate performance of such a resonant readout scheme and the noise sources that limit its operation. We find a charge sensitivity of 37 μe Hz−1/2, the best value reported for this technique, using the example of a gate sensor strongly coupled to a double quantum dot at the corner states of a silicon nanowire transistor. We discuss the experimental factors limiting gate detection and highlight ways to optimize its sensitivity. In total, resonant gate-based readout has advantages over external electrometers both in terms of reduction of circuit elements as well as absolute charge sensitivity. Reading out the state of quantum bits is an essential requirement that any quantum computer implementation must satisfy. Gonzalez-Zalba et al. now show that in situresonant gate-based detection can be a more sensitive approach than external electrometers while reducing the qubit architecture’s complexity.
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\mu e/\sqrt{\text{Hz}}μe/Hz​ and, when operating at 616 MHz, I get 1.3 μe/Hz\mu e/\sqrt{\text{Hz}}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 BBB. The singlet-triplet relaxation time T1T_1T1​ at B=4.5B=4.5B=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/ek_\text{B}/ekB​/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.
For scalable semiconductor-based quantum computer, integration of qubit, electrometer and readout circuit on CMOS platform needs to be explored. Here, for qubit readout, the use of charge-based capacitance measurement (CBCM) is proposed to detect the atto-farad change in the gate input capacitance of single-electron transistor (SET) electrometer. Mixed SET-CMOS circuit simulation revealed that a few hundred microvolts signal appeared at the integration capacitance at 1MHz data rate and the gate capacitance profile with respect to the gate voltage was successfully reproduced.
Sensitive charge detection has enabled qubit readout in solid-state systems. Recently, an alternative to the well-established charge detection via on-chip electrometers has emerged, based on in situ gate detectors and radio-frequency dispersive readout techniques. This approach promises to facilitate scalability by removing the need for additional device components devoted to sensing. Here, we perform gate-based dispersive readout of an accumulation-mode silicon quantum dot. We observe that the response of an accumulation-mode gate detector is significantly affected by its bias voltage, particularly if this exceeds the threshold for electron accumulation. We discuss and explain these results in light of the competing capacitive contributions to the dispersive response.
Sensitive charge detection has enabled qubit readout in solid-state systems. Recently, an alternative to the well-established charge detection via on-chip electrometers has emerged, based on in situ\textit{in situ}in situ gate detectors and radio-frequency dispersive readout techniques. This approach promises to facilitate scalability by removing the need for additional device components devoted to sensing. Here, we perform gate-based dispersive readout of an accumulation-mode silicon quantum dot. We observe that the response of an accumulation-mode gate detector is significantly affected by its bias voltage, particularly if this exceeds the threshold for electron accumulation. We discuss and explain these results in light of the competing capacitive contributions to the dispersive response.
Spin qubits in gate-defined semiconductor quantum dots are a promising platform for realising a scalable quantum computer. This platform encodes quantum information into the intrinsic angular momentum (spin) of individual electrons or holes. In particular, hole spins in quantum dots enable the possibility of all-electrical spin control due to their intrinsic spin-orbit coupling. One important criterion of a quantum computer is the ability to reliably read out the state of the qubit. This is done by mapping spin information to the charge degree of freedom, combined with a method for charge detection. Charge detection can be facilitated by coupling a resonator directly to the quantum dot gate or to a charge sensor and measuring the resonator's phase or amplitude response. In this thesis, we describe a set of experiments relating to the implementation of hole spin qubit readout with superconducting resonators. First, we study gate-based charge sensing in a Si fin field-effect transistor (finFET) device using a superconducting NbN nanowire resonator. We find that the resonator amplifies capacitive crosstalk when electrical control pulses are applied to gate electrodes in this device. This occurs whenever a spectral component of qubit control pulses overlaps with the resonance frequency, which we show may occur for both baseband and radio-frequency (RF) drive signals. We quantify this crosstalk in a transport-based method, and attribute its source to the capacitance between the bondpads of neighbouring gate electrodes. In a second experiment, we use an RF charge sensor with the same nanowire technology to read out hole spin qubits formed in the quantum well of a Ge/SiGe heterostructure. A screening layer approach is used to facilitate RF matching due to large RF dissipation found in the heterostructure. We implement a double-latched readout scheme in this system to reduce errors arising from both spin and charge decay during readout. The spin-to-charge conversion process and its dependence on magnetic field orientation is studied. Spin and charge decay processes arising after spin-to-charge conversion are mitigated by choosing an optimal working point for the field orientation, field amplitude and readout pulse times. By doing so, we achieve an average single-shot state-preparation-and-measurement fidelity of 97%, primarily bounded by imperfect state preparation and limited signal-to-noise ratio. Finally, we study coplanar waveguide resonators fabricated from NbN. We investigate the feasibility of integrating this type of resonator onto the same chip as the Si finFET quantum dots. We then develop a novel resonator readout technique by the interference of two microwave sidebands. We demonstrate the insensitivity of this technique to common-mode phase and amplitude noise both theoretically and experimentally. This technique is then used to study resonator noise arising from two-level system defects. These results highlight both the practical constraints and the potential for achieving high readout fidelities using resonator-based hole spin qubit readout. This work establishes a blueprint for mitigating resonator-induced crosstalk and enabling high-fidelity readout in lossy materials by incorporating a screening layer.