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IEEE Transactions on Instrumentation and Measurement

Calibrated Two-Port Microwave Measurement up to 26.5 GHz for Wide Temperature Range From 4 to 300 K

Tomonori Arakawa, Seitaro Kon

Published Jan 1, 2023• 13 citations
Publisher

Abstract

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.

DOI
10.1109/tim.2023.3315393

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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.
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.
Multi-port microwave devices operating at cryogenic temperatures are used in quantum computing to enable complex quantum operations. These components need to be precisely characterized at their operating temperature to ensure adequate overall system performance. In this work, an S-parameter measurement system to characterize the performance of coaxial connectorized microwave devices having up to four ports at temperatures of 3 K and above is presented. A four-port calibration setup is implemented at the 3 K temperature stage inside a dilution refrigerator. Measurement results for devices under test at 3 K are presented and the performance of the measurement system is evaluated.
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.
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.
Designing large-scale superconducting quantum circuits involves complex microwave engineering to minimize loss, spurious reflections, and signal crosstalk. Essential for engineering more complex circuits is precise knowledge of devices’ microwave performance, which can be characterized by measuring its calibrated scattering parameters (S-parameters) at mK temperatures. In this work, we introduce a full 2-port calibrated S-parameter measurement setup which can characterize superconducting quantum integrated circuits and other RF integrated circuits operating at mK temperatures. The design and architecture of the measurement system consisting of in-house developed microwave calibration unit (MCU) housing the newly designed cryogenic calibration standards and the device under test (DUT) is discussed in detail. The measurement setup is then used to demonstrate the first calibrated S-parameter measurements of an in-house developed superconducting qubit integrated circuit at mK temperature.
Recent developments in microwave-based quantum computing technologies have motivated the need for the development of new and improved cryogenic microwave devices packaged in coaxial connectorized technology, and for their performance to be accurately characterized through S-parameter measurements made at cryogenic operating temperatures. To facilitate such accurate characterization, S-parameter measurement systems utilizing in-situ calibration techniques at cryogenic temperatures have been developed. This required use of cryogenic RF switches inside cryostats to select between calibration standards and devices to perform calibration and measurement in a single cooling cycle. However, this caused significant measurement errors due to non-identical signal paths due to differences in switch paths limiting the measurement accuracy of such measurement systems. In this work, a new technique is proposed to significantly improve the accuracy of cryogenic S-parameter measurements of coaxial connectorized devices by accounting for non-ideal effects in such switch-based cryogenic calibration units. The technique is demonstrated at room temperature (296 K) and cryogenic temperature (1.5 K) through S-parameter measurements of coaxial devices with up to two ports.