Cryogenic Thermal Modeling of Microwave High Density Signaling

Abstract

Superconducting quantum computers require microwave control lines running from room temperature to the mixing chamber of a dilution refrigerator. Adding more lines without preliminary thermal modeling to make predictions risks overwhelming the cooling power at each thermal stage. In this paper, we investigate the thermal load of SC-086/50-SCN-CN semi-rigid coaxial cable, which is commonly used for the control and readout lines of a superconducting quantum computer, as we increase the number of lines to a quantum processor. We investigate the makeup of the coaxial cables, verify the materials and dimensions, and experimentally measure the total thermal conductivity of a single cable as a function of the temperature from cryogenic to room temperature values. We also measure the cryogenic DC electrical resistance of the inner conductor as a function of temperature, allowing for the calculation of active thermal loads due to Ohmic heating. Fitting this data produces a numerical thermal conductivity function used to calculate the static heat loads due to thermal transfer within the wires resulting from a temperature gradient. The resistivity data is used to calculate active heat loads, and we use these fits in a cryogenic model of a superconducting quantum processor in a typical Bluefors XLD1000-SL dilution refrigerator, investigating how the thermal load increases with processor sizes ranging from 100 to 225 qubits. We conclude that the theoretical upper limit of the described architecture is approximately 200 qubits. However, including an engineering margin in the cooling power and the available space for microwave readout circuitry at the mixing chamber, the practical limit is approximately 140 qubits.

Figures (8)

• Figure 1: (a) Depiction of the layers (not to scale) of an SC-086/50-SCN-CN coaxial cable (Coax Co., Ltd.) with materials and dimensions taken from the manufacturer's website sc-08650. (b) The SEM cross-section of an SC-086/50-SCN-CN coaxial cable sample from Coax Co., Ltd. has measured dimensions that agree with the reported dimensions in \ref{['fig:cross-section']}(a). Measured dimensions and scale are enlarged for readability. (c) A higher magnification image of the inner conductor of an SC-086/50-SCN-CN coax cable sample. The measured silver coating is approximately 3 $\mu m$ thick, which agrees with the nominal thickness coaxcocomm. Measured dimensions and scale are enlarged for readability. (d) An enlarged portion of \ref{['fig:cross-section']}(c) to make the dimension of the silver coating readable. A larger decimal point was digitally added to the image for clarity.
• Figure 2: The cupronickel outer conductor of an SC-086/50-SCN-CN coaxial cable mounted on the PPMS TTO measurement system. From left to right, we see the sample heater, which produces a time-dependent thermal gradient across the sample, two thermometers, and then thermal anchoring of the sample to the right-hand end.
• Figure 3: Thermal conductivity versus temperature for silver-coated cupronickel inner conductor, cupronickel outer conductor, and PTFE. Due to the challenge in accurately modeling the radiative correction above 300 K, the raw data was processed to exclude points above 300 K; the curves shown fit the processed data. The PTFE function displayed is the Teflon model from the NIST Cryogenics Index of Material Properties database marquardt2002bradleyp.e.2006.
• Figure 4: The fraction of the estimated cooling powers at each stage taken up by static heat loads of a Bluefors XLD1000-SL system outfitted with the maximum number of cables ($N = 1008$). The different refrigerator temperature stages on the x-axis are, as before, denoted as follows: "50K" for the 50K plate, "4K" for the 4K plate, "Still" for the still stage, "CP" for the cold plate, and "MXC" for the mixing chamber.
• Figure 5: DC electrical resistivity versus temperature for the silver-coated cupronickel inner conductor. The data was scaled by the cross-sectional area and length of the cable to give resistivity values.