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On-Chip Microwave Filters for High-Impedance Resonators with Gate-Defined Quantum Dots

Patrick Harvey-Collard, Guoji Zheng, Jurgen Dijkema, Nodar Samkharadze, Amir Sammak, Giordano Scappucci, Lieven M. K. Vandersypen

Published Jan 1, 2020• 27 citations

Abstract

Circuit quantum electrodynamics (QED) employs superconducting microwave resonators as quantum buses. In circuit QED with semiconductor quantum-dot-based qubits, increasing the resonator impedance is desirable as it enhances the coupling to the typically small charge dipole moment of these qubits. However, the gate electrodes necessary to form quantum dots in the vicinity of a resonator inadvertently lead to a parasitic port through which microwave photons can leak, thereby reducing the quality factor of the resonator. This is particularly the case for high-impedance resonators, as the ratio of their total capacitance over the parasitic port capacitance is smaller, leading to larger microwave leakage than for 50-x resonators. Here, we introduce an implementation of on-chip filters to suppress the microwave leakage. The filters comprise a high-kinetic-inductance nanowire inductor and a thin-film capacitor. The filter has a small footprint and can be placed close to the resonator, confining microwaves to a small area of the chip. The inductance and capacitance of the filter elements can be varied over a wider range of values than their typical spiral inductor and interdigitated capacitor counterparts. We demonstrate that the total linewidth of a 6.4 GHz and approximately 3-kx resonator can be improved down to 540 kHz using these filters.

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Circuit quantum electrodynamics (QED) employs superconducting microwave resonators as quantum buses. In circuit QED with semiconductor quantum-dot-based qubits, increasing the resonator impedance is desirable as it enhances the coupling to the typically small charge dipole moment of these qubits. However, the gate electrodes necessary to form quantum dots in the vicinity of a resonator inadvertently lead to a parasitic port through which microwave photons can leak, thereby reducing the quality factor of the resonator. This is particularly the case for high-impedance resonators, as the ratio of their total capacitance over the parasitic port capacitance is smaller, leading to larger microwave leakage than for 50-x resonators. Here, we introduce an implementation of on-chip filters to suppress the microwave leakage. The filters comprise a high-kinetic-inductance nanowire inductor and a thin-film capacitor. The filter has a small footprint and can be placed close to the resonator, confining microwaves to a small area of the chip. The inductance and capacitance of the filter elements can be varied over a wider range of values than their typical spiral inductor and interdigitated capacitor counterparts. We demonstrate that the total linewidth of a 6.4 GHz and approximately 3-kx resonator can be improved down to 540 kHz using these filters.

Circuit quantum electrodynamics with qubits based on semiconductor quantum dots can enable long-range two-qubit gates between distant spins, or improve gate-based charge sensing for readout. Compared to conventional resonators, high-impedance resonators improve the coupling to the qubits, but their losses to the quantum dot's leads are also larger. This study implements on-chip filtering using high-kinetic-inductance nanowires and thin-film capacitors to mitigate this source of losses. These filters are very compact and easily extended to a large number of leads, all while preserving state-of-the-art resonator quality factors.

Spin-photon coupling presents an enticing opportunity for the long-range coupling of spin qubits. The spin-photon coupling rate,

{g}_{s}

, is proportional to the charge-photon coupling rate,

{g}_{c}

. To move deeper into the strong-coupling regime,

{g}_{c}

can be enhanced by fabricating high-impedance cavities using high-kinetic-inductance films. Here, we report dc transport and microwave response investigations of niobium nitride (

\mathrm{Nb}\mathrm{N}

) films of different thicknesses. The kinetic inductance increases rapidly as the film thickness is reduced below 50 nm and for 15-nm

\mathrm{Nb}\mathrm{N}

films we measure a sheet kinetic inductance

{L}_{k,S}=41.2\phantom{\rule{0.2em}{0ex}}\text{pH}/◻

. As an application of the high-kinetic-inductance films, we fabricate compact

LC

filters that are commonly used to reduce microwave leakage in circuit quantum electrodynamics (cQED) devices. These filters feature up to 60 dB of attenuation near typical cavity resonance frequencies of

{f}_{c}=8

GHz.

We develop an engineered microwave environment for coupling high Q superconducting resonators to quantum dots using a multilayer fabrication stack for dot control wiring. Analytical and numerical models are presented, which show that high resonator quality factors can be attained by either minimizing the parasitic coupling capacitance to the leads or creating a low effective environmental impedance at the cavity frequency. We implement the later approach by fabricating low characteristic impedance (Zg≈10 Ω) microstrips on-chip for the dot bias wiring and show resonator quality factors of 8140 that can be attained without the addition of explicit filtering. Using this approach, we demonstrate single electron occupation in double and triple dots detected via dipole or quadrupole coupling to a superconducting resonator. Additionally, by using multilayer fabrication, we are able to improve ground plane integrity and keep microwave crosstalk below −20 dB out to 18 GHz while maintaining high wire density, which will be necessary for future circuit quantum electrodynamics quantum dot processors.

Circuit quantum electrodynamics (cQED) architecture enables long-range qubit coupling and nondemolition readout, with a key requirement of a small resonator photon leakage rate, κ. Several types of low-pass on-chip LC filter designs have been proposed to mitigate κ. However, the non-flat frequency response in the passband introduces waveform distortion, which may degrade qubit performance. In this work, we develop an on-chip compact Chebyshev filter for semiconductor quantum dots in cQED architecture. It exhibits a flat passband up to a 2 GHz cutoff frequency with microwave attenuation <−30 dB at 7 GHz, without observing the sign of damping oscillations induced by waveform distortion. We also analyze the integration of the filter with the cQED architecture and demonstrate that microwave attenuation meets the need for integration. The developed Chebyshev filter paves the way for the precise control of semiconductor quantum dots in cQED architecture with a low photon leakage rate.

We present a design of a tunable on-chip resonator that can benchmark the nonlinear kinetic inductance (KI) properties of various superconducting thin films in the W-band (75-110 GHz), for quantum device applications. Our design uses a quarter-wavelength microstrip resonator with ground plane cutout for transmission measurements, WR10 input & output ports, DC bias line and radial-stub notch filters to suppress RF leakage into the bias lines. Our resonator design procedure uses simulations with perfect electric conductors as an initial reference case, which will be later replaced by finite-impedance material to include the effect of sheet inductance.

High quality on-chip microwave resonators have recently found prominent new applications in quantum optics and quantum information processing experiments with superconducting electronic circuits, a field now known as circuit quantum electrodynamics (QED). They are also used as single photon detectors and parametric amplifiers. Here we analyze the physical properties of coplanar waveguide resonators and their relation to the materials properties for use in circuit QED. We have designed and fabricated resonators with fundamental frequencies from 2 to 9 GHz and quality factors ranging from a few hundreds to a several hundred thousands controlled by appropriately designed input and output coupling capacitors. The microwave transmission spectra measured at temperatures of 20 mK are shown to be in good agreement with theoretical lumped element and distributed element transmission matrix models. In particular, the experimentally determined resonance frequencies, quality factors, and insertion losses are fully and consistently explained by the two models for all measured devices. The high level of control and flexibility in design renders these resonators ideal for storing and manipulating quantum electromagnetic fields in integrated superconducting electronic circuits.