Cryogenic Thermal Modeling of Microwave High Density Signaling

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.

💡 Research Summary

The paper presents a comprehensive thermal analysis of the SC‑086/50‑SCN‑CN semi‑rigid coaxial cable, which is widely used for microwave control and readout lines in superconducting quantum computers. The authors first verify the cable’s construction: a C7150 cupronickel outer conductor, a PTFE dielectric, and a silver‑plated C7150 inner conductor with a nominal 3‑4 µm coating. Energy‑dispersive X‑ray spectroscopy confirms the Cu:Ni ratio (~62.5:37.5) and the PTFE stoichiometry.

Thermal conductivity measurements are performed on the separated outer and inner conductors using a Physical Property Measurement System (PPMS) equipped with the Thermal Transport Option. The measurements span from 4 K to 300 K, and radiative losses are accounted for by experimentally estimating the emissivity of each component. The PTFE dielectric’s conductivity is taken from the NIST Cryogenics Index. The resulting k(T) data are fitted with multi‑term polynomial functions, providing continuous conductivity curves for use in thermal modeling.

In parallel, the DC resistance of the inner conductor is measured across the same temperature range. The resistivity ρ(T) is fitted to a polynomial that captures the normal‑metal behavior at high temperature and the rapid drop near the superconducting transition of the silver coating (~7 K). This resistivity model enables calculation of active (Ohmic) heating for any current flowing through the line.

The static heat load of a single cable is calculated by integrating the conductivity of each material layer (outer conductor, inner conductor, dielectric) over the temperature gradients between the refrigerator stages (300 K → 50 K → 4 K → 1.4 K → 0.2 K → mixing chamber). The cable lengths for each stage are taken from the Bluefors XLD1000‑SL specifications (e.g., ~0.3 m between 300 K and 50 K). The three parallel thermal paths are summed to obtain the total static load per cable, which amounts to tens of microwatts per stage.

Active heating is evaluated for four categories of microwave lines used in a typical transmon‑based processor: XY drive lines, flux‑bias lines for qubits, flux‑bias lines for tunable couplers, and readout lines. Each category employs a different attenuator chain, resulting in distinct current profiles. The Ohmic power P = I²R(T) is computed for each line, with the flux‑bias and coupler lines carrying constant DC currents, thus contributing significantly to the low‑temperature stages despite the low resistance at cryogenic temperatures.

The authors embed both static and active loads into a system‑level model of the Bluefors XLD1000‑SL dilution refrigerator. Stage‑by‑stage cooling powers (e.g., 0.02 W at the mixing chamber, 0.2 W at 0.2 K, etc.) are compared against the cumulative heat influx from 100, 150, 200, and 225‑qubit processors, assuming one cable per control line per qubit. The model shows that a 100‑qubit system comfortably fits within the cooling budget, while a 200‑qubit system approaches the limit of the mixing‑chamber stage. Including a 10‑15 % engineering margin and accounting for the limited physical space for microwave components at the mixing chamber, the practical upper bound is estimated at roughly 140 qubits.

The study’s key contributions are: (1) providing experimentally validated thermal conductivity and resistivity data for a commercially available semi‑rigid coaxial cable, including the often‑neglected silver‑plated inner conductor; (2) developing a detailed thermal model that separates static conductive loads from active Ohmic heating; (3) applying this model to realistic dilution‑refrigerator specifications to quantify the scaling limits of microwave‑based control architectures. The authors suggest that beyond the identified practical limit, alternative routing strategies—such as optical‑to‑RF transducers, cryogenic CMOS switches, or the adoption of higher‑performance pulse‑tube configurations—will be required to sustain further qubit scaling. Future work is proposed to extend the methodology to other high‑density cable families and to explore dynamic temperature‑feedback control schemes for active heat mitigation.