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arXiv:1808.09612 · Superconductor Science and Technology

High speed flux sampling for tunable superconducting qubits with an embedded cryogenic transducer

B Foxen, J Y Mutus, E Lucero, E Jeffrey, D Sank, R. Barends, K Arya, B Burkett, Yu Chen, Zijun Chen, B Chiaro, A Dunsworth, Austin G. Fowler, C Gidney, M Giustina, R Graff, T Huang, J Kelly, P Klimov, A Megrant, O Naaman, M. Neeley, C Neill, C Quintana, P Roushan, A Vainsencher, J Wenner, T C White, John M. Martinis

Published Nov 12, 2018• 20 citations
arXivHTMLPDF

Abstract

We develop a high speed on-chip flux measurement using a capacitively shunted SQUID as an embedded cryogenic transducer and apply this technique to the qualification of a near-term scalable printed circuit board (PCB) package for frequency tunable superconducting qubits. The transducer is a flux-tunable LC resonator where applied flux changes the resonant frequency. We apply a microwave tone to probe this frequency and use a time-domain homodyne measurement to extract the reflected phase as a function of flux applied to the SQUID. The transducer response bandwidth is 2.6 GHz with a maximum gain of 1200°/Φ 0 allowing us to study the settling amplitude to better than 0.1%. We use this technique to characterize on-chip bias line routing and a variety of PCB-based packages and demonstrate that step response settling can vary by orders of magnitude in both settling time and amplitude depending on if normal or superconducting materials are used. By plating copper PCBs in aluminum we measure a step response consistent with the packaging used for existing high-fidelity qubits.

DOI
10.1088/1361-6668/aaf048

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We develop a high speed on-chip flux measurement using a capacitively shunted SQUID as an embedded cryogenic transducer and apply this technique to the qualification of a near-term scalable printed circuit board (PCB) package for frequency tunable superconducting qubits. The transducer is a flux-tunable LC resonator where applied flux changes the resonant frequency. We apply a microwave tone to probe this frequency and use a time-domain homodyne measurement to extract the reflected phase as a function of flux applied to the SQUID. The transducer response bandwidth is 2.6 GHz with a maximum gain of 1200°/Φ 0 allowing us to study the settling amplitude to better than 0.1%. We use this technique to characterize on-chip bias line routing and a variety of PCB-based packages and demonstrate that step response settling can vary by orders of magnitude in both settling time and amplitude depending on if normal or superconducting materials are used. By plating copper PCBs in aluminum we measure a step response consistent with the packaging used for existing high-fidelity qubits.
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We present a design and implementation of a frequency-tunable superconducting resonator. The resonance frequency tunability is achieved by flux-coupling a superconducting LC loop to a current-biased feedline; the resulting screening current leads to a change of the kinetic inductance and shift in the resonance frequency. The thin-film aluminum resonator consists of an interdigitated capacitor and thin line inductors forming a closed superconducting loop. The magnetic flux from the nearby niobium current feedline induces Meissner shielding currents in the resonator loop leading to a change in the kinetic part of the total inductance of the resonator. We demonstrate continuous frequency tuning within 160 MHz around the resonant frequency of 2.7 GHz. We show that: (1) frequency up-conversion is achieved when a kilohertz ac modulation signal is superimposed onto the dc bias resulting in sidebands to the resonator tone; (2) three-wave mixing is attained by parametrically pumping the nonlinear kinetic inductance using a strong rf pump signal in the feedline. The simple architecture is amenable to large-array multiplexing and on-chip integration with other circuit components. The concept could be applied in flux magnetometers, up-converters, and parametric amplifiers operating above 4 K when alternative high-critical-temperature material with high kinetic inductance is used.
We report the development of flux memory for use with superconducting circuits. This technology stores persistent currents in superconducting loops on-chip to be used to provide flux biasing for superconducting circuits, like qubits. We developed three types of flux memory and draw comparisons among them for circuit design. We demonstrate the utility of flux memory by using an in-situ flux detector and characterize each approach and further demonstrate that once flux is set in a memory cell, benchtop DC control sources can be powered off, leaving the on-chip flux bias in place. We propose that flux memory can be arranged in a two-dimensional configuration to multiplex control signals and reduce how line counts scale (N^2 devices -> 2N control lines), and our experimental results pave the path to the proposed scalability. We demonstrate the use of flux memory to flux bias a transmon qubit and show the tunability of the qubit state to a target frequency which remained stable on-chip for 20 hours.
We present a Rapid Single Flux Quantum (RSFQ) microwave controller for superconducting qubits. Applying microwaves from room temperature sources is the conventional approach to excite quantum state transitions. Finding a method to apply short microwave bursts with a narrow linewidth is a challenge for on-chip Josephson based oscillators. We present a scheme containing an RSFQ pulse generator, ultra narrowband filter, SQUID based resonator and coupler. The operating frequency of the designed controller is 3-6 GHz. The unique feature of this design is a SQUID based resonator. By varying magnetic field in the SQUID, the\nresonance length can be varied between λ/4 and λ/2. The\nresonator is added as a shunt between the filter and coupler. Transmission of microwave signals from the filter to the output is determined by the shunt resonance. RSFQ T flip-flop circuit is designed to control the magnetic field applied to the SQUID in the resonator. Miniaturization of the coupler of 2-10 GHz has been done using a quasi-lumped element designed. We present the simulations results for the frequency response of\ndifferent resonance lengths of the modulator.
Precise gravitational measurements are vital for geophysics and inertial navigation, but compact gravimeters with high measurement bandwidth remain difficult to realize. We propose and analyze a chip-scale superconducting gravimeter in which a flux-tunable transmon qubit is coupled to a high quality factor (QmQ_mQm​) nanomechanical beam. The beam is embedded in a SQUID loop placed in parallel with the qubit's flux-tunable SQUID; gravity induced beam displacement therefore modulates the qubit frequency through the SQUID flux and is mapped onto the qubit's geometric phase. A stroboscopic readout at mechanical revival times suppresses qubit mechanics dephasing, yielding a projected sensitivity of 10210^2102--103 nGal/Hz10^3\,\mathrm{nGal}/\sqrt{\mathrm{Hz}}103nGal/Hz​ with sub-millisecond interrogation times. Electrical \emph{in situ} tunability and microwave-based calibration make this architecture a practical route toward compact, high-bandwidth on-chip gravimetry.
Predictable frequency trimming of superconducting resonators at liquid-helium temperatures requires a tuning element whose usable range remains well defined despite screening currents and hysteresis. Here, we realize flux-controlled λ/4 coplanar-waveguide resonators terminated by two-junction DC superconducting quantum interference devices (SQUIDs) fabricated in a standard Nb/Al-AlOx/Nb multilayer process. Integrated on-chip flux-bias lines allow the resonant frequency to be controlled at 4.2 K. RF measurements show periodic frequency modulation with applied flux, with a maximum shift of δfr=8.63 MHz and a single-valued tuning interval of δfr0=2.85 MHz. Near half-integer flux quanta, the response exhibits hysteretic jumps caused by the finite SQUID loop inductance, so that the usable single-valued tuning interval is smaller than the full modulation range. We develop a semi-analytical model of the frequency–flux response, supported by numerical simulations and 3D electromagnetic extraction of the device parameters, which reproduces the measured hysteretic branches and identifies the SQUID loop inductance and junction critical current as the main parameters limiting the usable tuning range. These results provide a quantitative design framework for MHz-scale frequency trimming of Nb superconducting resonators in 4 K cryogenic readout circuits.