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arXiv:2112.05152 · Applied Physics Letters

Microwave calibration of qubit drive line components at millikelvin temperatures

Slawomir Simbierowicz, V. Yu. Monarkha, Suren Singh, Nizar Messaoudi, Philip Krantz, Russell E. Lake

Published Jan 31, 2022• 22 citations
arXivHTMLPDF

Abstract

Systematic errors in qubit state preparation arise due to non-idealities in qubit control lines such as impedance mismatch. Using a data-based methodology of short-open-load calibration at a temperature of 30 mK, we report calibrated 1-port scattering parameter data of individual qubit drive line components. At 5 GHz, cryogenic return losses of a 20-dB-attenuator, a 10-dB-attenuator, a 230-mm-long 0.86-mm silver-plated cupronickel coaxial cable, and a 230-mm-long 0.86-mm NbTi coaxial cable were found to be 35−2+3 dB, 33−2+3 dB, 34−2+3 dB, and 29−1+2 dB, respectively. For the same frequency, we also extract cryogenic insertion losses of 0.99−0.04+0.04 dB and 0.02−0.04+0.04 dB for the coaxial cables. We interpret the results using master equation simulation of all XY gates performed on a single qubit. For example, we simulate a sequence of two 5 ns gate pulses (X and Y) through a two-element Fabry–Pérot cavity with 276-mm path length directly preceding the qubit and establish that the return loss of its reflective elements must be >9.7 dB (>14.7 dB) to obtain 99.9% (99.99%) gate fidelity.

DOI
10.1063/5.0081861

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Systematic errors in qubit state preparation arise due to non-idealities in qubit control lines such as impedance mismatch. Using a data-based methodology of short-open-load calibration at a temperature of 30 mK, we report calibrated 1-port scattering parameter data of individual qubit drive line components. At 5 GHz, cryogenic return losses of a 20-dB-attenuator, a 10-dB-attenuator, a 230-mm-long 0.86-mm silver-plated cupronickel coaxial cable, and a 230-mm-long 0.86-mm NbTi coaxial cable were found to be 35−2+3 dB, 33−2+3 dB, 34−2+3 dB, and 29−1+2 dB, respectively. For the same frequency, we also extract cryogenic insertion losses of 0.99−0.04+0.04 dB and 0.02−0.04+0.04 dB for the coaxial cables. We interpret the results using master equation simulation of all XY gates performed on a single qubit. For example, we simulate a sequence of two 5 ns gate pulses (X and Y) through a two-element Fabry–Pérot cavity with 276-mm path length directly preceding the qubit and establish that the return loss of its reflective elements must be >9.7 dB (>14.7 dB) to obtain 99.9% (99.99%) gate fidelity.
We report calibrated microwave transmission and reflection measurements of a qubit sample holder at millikelvin temperatures. The methodology we present extends our previous work on one-port cryogenic short-open-load (SOL) calibration to a two-port SOLT measurement by implementing an unknown thru (T) standard. We report the resulting calibrated transmission and reflection at millikelvin temperatures through a printed circuit board that is installed into the sample holder. Finally, we consider a cascade of components at the end of a qubit drive line that includes (1) a cryogenic attenuator, (2) a coaxial cable, and (3) a qubit sample holder. Using experimentally determined parameters for return losses for all three components, we calculate the negligible state-preparation error in the frequency band of 5-7 GHz due to control pulse distortions arising from reflection at the coaxial launches. Taken together, our results highlight the utility of calibrated cryogenic scattering parameter measurements for the validation of qubit packaging and the wiring in its immediate vicinity.
To realize a quantum information processing system, it is necessary not only to increase the number of physical qubits but also to cooperatively operate a multitude of cryogenic microwave components such as cables, circulators, and amplifiers for controlling or reading them. Therefore, it is essential to develop metrological methods to precisely evaluate the microwave scattering parameters of each component at low temperatures. Here, we report a calibrated microwave measurement method for a wide temperature range of 4 K to 300 K. At each temperature, we performed a full two-port calibration, which enables us to precisely measure the scattering parameters of various cryogenic microwave components up to 26.5 GHz by using 3.5 mm connectors as the reference planes. We carefully verified the validity of the calibration impedance elements and demonstrated our method by evaluating the temperature-dependent characteristics of a coaxial cable and a circulator.
Development of RF and microwave metrology capabilities at cryogenic temperatures is critical for the development of high-performance microwave devices to facilitate commercialization of cryogenic quantum technologies. This article presents a broadband microwave S-parameter calibration scheme suitable for cryogenic environments operating at temperatures down to tens of milli-kelvin (mK). The technique is based on a weighted multi-line thru-reflect-line (TRL) calibration approach and is demonstrated using coaxial air line calibration standards. One-and two-port microwave devices commonly used in cryogenic quantum computing applications, a cryogenic 50 Ω~\Omega Ωmatched load and a cryogenic 6 dB attenuator, were measured. The measured results at mK temperatures indicate that when combined with calibration standards of appropriate electrical length, the weighted multi-line TRL calibration scheme allows broadband frequency coverage compared to conventional TRL calibration schemes utilizing a single line standard. The mechanical and electrical properties of the line standards at mK temperatures were investigated and discussed. These findings establish the feasibility of utilizing multiple off-the-shelf coaxial air lines to enhance the frequency range of calibrations at mK temperatures.
Quantum computing technologies utilise microwave components and interfaces at cryogenic temperatures during operation. This paper describes an S-parameter measurement system to characterise coaxial microwave devices at temperatures down to tens of milli-kelvin. The measurement system is calibrated using a Thru-reflect-line technique utilising a coaxial air-dielectric transmission line as the reference impedance standard. Various coaxial microwave devices having a wide range of reflection and transmission coefficient values are measured at both room temperature and mK temperature to investigate the calibration performance and understand the various error sources in the measurements.
Abstract Superconducting circuit testing and materials loss characterization requires robust and reliable methods for the extraction of internal and coupling quality factors of microwave resonators. A common method, imposed by limitations on the device design or experimental configuration, is the single-port reflection geometry, i.e. reflection-mode. However, impedance mismatches in cryogenic systems must be accounted for through calibration of the measurement chain while it is at low temperatures. In this paper, we demonstrate a data-based, single-port calibration using commercial microwave standards and a vector network analyzer with samples at millikelvin temperature in a dilution refrigerator, making this method useful for measurements of quantum phenomena. Finally, we cross reference our data-based, single-port calibration and reflection measurement with over-coupled 2D- and 3D-resonators against well established two-port techniques corroborating the validity of our method.
Large-scale cryogenic quantum systems are constrained by an input-output bottleneck between room-temperature electronics and millikelvin stages, particularly in superconducting qubit platforms. This bottleneck is most acute for output lines, where bulky and expensive microwave components limit scalability. A promising approach for scalable characterization and testing is to perform signal multiplexing directly at the qubit plane. We demonstrate a cryogenic CMOS (cryoCMOS) RF multiplexer operating at 10 millikelvin with record-low static power consumption of 200 pW. The device provides < 2 dB insertion loss and > 30 dB isolation across DC-8 GHz. Direct connection to transmon qubits marginally affects coherence times in the range of 100 microseconds, enabling multiplexing of readout, flux and, in principle, XY drive lines. This work introduces cryoCMOS multiplexers as valuable tools for scalable, high-throughput cryogenic characterization and testing, and advances co-integrated quantum-classical control for future large-scale quantum processors.