Phononic Bragg Reflectors for Thermal Insulation of Scalable Cryogenic Control Electronics from Qubits

Scaling solid-state architectures to the millions of qubits required for utility-scale quantum computing could benefit from the integration of control electronics in the immediate vicinity of the quantum layer. However, lithographically fabricated solid-state qubits perform best at temperatures well below 1 K, where available cooling power is limited, whereas the control electronics dissipate substantial power and therefore require the higher cooling power available at elevated temperatures. To address this challenge, we propose a cryopackaging concept that uses broadband phononic Distributed Bragg Reflectors (DBRs) as a thermal barrier between cryoelectronics and the qubit chip. As an experimental realization of this concept, we fabricate and characterize Ta/SiO$_2$ DBR structures. In this architecture, the DBR is intended to provide mechanical support for superconducting vias while offering substantially better thermal insulation than typical bulk materials. For a 600-nm-thick DBR consisting of 10 Ta/SiO$_2$ bilayers, we obtain a thermal conduction below 1 mW/cm$^2$ from 1.5 K to 100 mK. In a centimeter-scale architecture, this level of isolation is compatible with Watt-level cooling power for nearby electronics while maintaining a qubit temperature around 100 mK in commercially available dilution refrigerators.