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Review of Scientific Instruments

Calibrated transmission and reflection from a multi-qubit microwave package

Slawomir Simbierowicz, V. Yu. Monarkha, Merlin von Soosten, Søren E. S. Andresen, Russell E. Lake

Published May 1, 2023• 7 citations
Publisher

Abstract

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.

DOI
10.1063/5.0144840

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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.
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.
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.
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.
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.
Accurate knowledge of the microwave power delivered to a cryogenic device under test (DUT) is essential for the characterization and operation of superconducting quantum circuits. However, this information is difficult to obtain inside dilution refrigerators because of distributed attenuation, impedance mismatch, switch-path repeatability, and temperature-dependent microwave components. This paper presents an in situ measurement method for RF power at the cryogenic device plane. The method uses a custom variable temperature stage (VTS) as a cryogenic thermal-transfer element. The TVS is alternately heated by a four-wire DC heater and by microwave power dissipated in a 20 dB pass-through attenuator. By fitting the thermal transients and comparing the corresponding steady-state temperatures, the absorbed microwave power is inferred from a directly measured DC electrical power through an AC/DC substitution procedure. The finite reflection and transmission of the attenuator are then accounted for by cryogenic two-port scattering-parameter measurements based on a switch-assisted Short--Open--Load--Reciprocal calibration, so that the result is referred to the DUT reference plane. The system is demonstrated in a dilution refrigerator with powers between -43 and -58 dBm at the DUT input plane. The demonstrated relative standard uncertainty ranges from about 2% at -43.9 dBm to about 40% at -57.6 dBm. The proposed approach combines thermal RF power transfer, cryogenic S-parameter correction, and uncertainty evaluation in a measurement architecture compatible with quantum-device experiments, providing a practical route toward traceable microwave-power calibration at millikelvin stages.
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.