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arXiv:2410.01053

Thermalization of a flexible microwave stripline measured by a superconducting qubit

Patrick Paluch, Martin Spiecker, Nicolas Gosling, Viktor Adam, Jakob Kammhuber, Kiefer Vermeulen, Daniël Bouman, Wolfgang Wernsdorfer, Ioan M. Pop

Published Oct 1, 2024• 0 citations
arXivHTMLPDF

Abstract

With the demand for scalable cryogenic microwave circuitry continuously rising, recently developed flexible microwave striplines offer the tantalyzing perspective of increasing the cabling density by an order of magnitude without thermally overloading the cryostat. We use a superconducting quantum circuit to test the thermalization of input flex cables with integrated $60\,$dB of attenuation distributed at various temperature stages. From the measured decoherence rate of a superconducting fluxonium qubit, we estimate a residual population of the readout resonator below $3.5\cdot10^{-3}$ photons and we measure a $0.28\,$ms thermalization time for the flexible stripline attenuators. Furthermore, we confirm that the qubit reaches an effective temperature of $26.4\,$mK, close to the base temperature of the cryostat, practically the same as when using a conventional semi-rigid coaxial cable setup.

DOI
10.48550/arxiv.2410.01053

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•Jan 1, 2026•0 citations
With the demand for scalable cryogenic microwave circuitry continuously rising, recently developed flexible microwave striplines offer the tantalyzing perspective of increasing the cabling density by an order of magnitude without thermally overloading the cryostat. We use a superconducting quantum circuit to test the thermalization of input flex cables with integrated 60 60\,60dB of attenuation distributed at various temperature stages. From the measured decoherence rate of a superconducting fluxonium qubit, we estimate a residual population of the readout resonator below 3.5⋅10−33.5\cdot10^{-3}3.5⋅10−3 photons and we measure a 0.28 0.28\,0.28ms thermalization time for the flexible stripline attenuators. Furthermore, we confirm that the qubit reaches an effective temperature of 26.4 26.4\,26.4mK, close to the base temperature of the cryostat, practically the same as when using a conventional semi-rigid coaxial cable setup.
With the demand for scalable cryogenic microwave circuitry continuously rising, recently developed flexible microwave striplines offer the tantalizing perspective of increasing the cabling density by an order of magnitude without thermally overloading the cryostat. We use a superconducting quantum circuit to test the thermalization of input flex cables with integrated 60 dB of attenuation distributed at various temperature stages. From the measured decoherence rate of a superconducting fluxonium qubit, we estimate a residual population of the readout resonator of (2.2±0.9)×10−3 photons and we measure a 0.28 ms thermalization time for the flexible stripline attenuators. Furthermore, we confirm that the qubit reaches an effective temperature of 26.4 mK, close to the base temperature of the cryostat, practically the same as when using a conventional semi-rigid coaxial cable setup.
We report a comparative study on microwave control lines for a transmon qubit using (i) flexible stripline transmission lines and (ii) semi-rigid coaxial cables. During each experiment, we performed repeated measurements of the energy relaxation and coherence times of a transmon qubit using one of the wiring configurations. Each measurement run spanned 70–250 h of the measurement time, and four separate cooldowns were performed so that each configuration could be tested twice. From these datasets, we observe that changing the microwave control lines from coaxial cables to flexible stripline transmission lines does not have a measurable effect on coherence compared to thermal cycling the system or random coherence fluctuations. Our results open up the possibility of large-scale integration of qubit control lines with integrated component with planar layouts on flexible substrate.
Since superconducting quantum computers use microwave signals to control and readout their qubits, microwave transmission lines and circuits that can be used under cryogenic conditions are required. For microwave transmission lines, thermal insulation is essential to enhance wiring density and to prevent parasitic heating that can lead to increased computational errors. Thus, here we design and characterize a scalable, thermally insulated microwave transmission line. The transmission line designed for superconducting qubit readout at 5 GHz band achieves both thermal insulation and low loss, by employing resonator-based impedance matching in a microstripline structure. A flexible cable including eight planar transmission lines was designed, fabricated and characterized using S-parameter measurement, demonstrating low crosstalk below 40dB and signal attenuation of -23.5±0.07dB; this coincides with electromagnetic simulations. These microwave properties remained stable across a wide temperature range from room temperature down to 4 K, including steep gradients. The integration of chip attenuators further reduces thermal noise and protects sensitive cryogenic components. Our approach offers a promising solution for compact, high-density microwave wiring using flat cables under thermal gradients, necessary for large scale quantum computing.
Improving qubit coherence times is fundamental to the development of quantum computing technology. In most experiments in circuit quantum electrodynamics, dephasing induced by residual thermal photons in the readout resonator limits the coherence times of superconducting qubits. The authors design and test a type of microwave cavity attenuator that can be well thermalized to the base stage of a dilution refrigerator. With these cavity attenuators, they reproducibly measure enhanced qubit coherence times and report very low thermal-photon populations in the readout mode. This invention is a useful addition to the toolbox for state-of-the-art quantum circuitry.
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.
The dream of universal quantum computing promises to revolutionize many fields due to its potential to drastically speed up certain calculations compared to classical computers. This has naturally attracted attention and investment. For example, in 2024, Google unveiled their Willow superconducting quantum processor, achieving a significant milestone by demonstrating quantum error correction below the surface code threshold. Despite these advances, the road to a fully fledged quantum computer is still uncharted, and current technology is not sufficient to get there. Therefore, unconventional materials hold great potential for addressing challenges faced by traditional approaches. This work focuses on fluxonium qubits made from the disordered superconductor granular aluminum (grAl), aiming to gain deeper insights into underlying loss mechanisms and noise sources. One of the main results of this work is the identification of inductive loss as the dominant decoherence mechanism in grAl fluxonium qubits with frequencies lower than 300 MHz at the half flux bias. The observed inductive loss tangent aligns with previously measured single-photon internal quality factors of grAl resonators, and the energy relaxation profiles are well described by a combination of inductive, dielectric, and Purcell loss. The study endeavors to deepen the understanding of decoherence by refining loss models via the quantum fluctuation-dissipation theorem and proposing an improved framework for Purcell loss. A comparison with other qubit materials underscores the universal nature of inductive loss in grAl fluxoniums, in contrast to well established Josephson junction array (JJA) based fluxoniums which show no such limitation at even lower qubit frequencies. The second outcome of this thesis is the validation of flexible striplines (`flexlines') for the use in future cryogenic microwave setups. This enables at least an order of magnitude increase in the density of microwave input circuitry without thermally overloading the cryostat, paving the way for increasingly complex superconducting detectors and quantum devices. The study found no significant differences in qubit performance between setups using flexlines and conventional coaxial cables. Passive heat load measurements indicated comparable photon shot noise-induced dephasing for both setups. The introduced heating pulse method demonstrated a faster thermalization time for flexlines compared to coaxial cables, and it can serve as a simple health check for other groups as well. An extended thermal model was developed to better understand the contributions of various attenuators in the input chains to the measured heat loads and to propose improved input chains. To further exploit the versatility of grAl for fluxonium qubits, the investigation of the microscopic origin of the limiting inductive loss is of interest to develop potential suppression methods. JJA-based fluxoniums could play a crucial role in this context, as particularly long arrays with increased plasma frequencies can emulate the properties of grAl while leveraging their better-understood behavior.