Phononic Bragg Reflectors for Thermal Insulation Between Cryogenic Control Electronics and Qubits

The integration of cryogenic electronics near semiconductor spin qubits is crucial for controlling the millions of qubits needed in practical quantum computing. However, these qubits perform best below 1 K, which challenges the limited cooling capacity of cryostats and restricts the power budget of control electronics to a few milliwatts. Slightly raising the operating temperature of these electronics could alleviate this limitation, but would also benefit from thermal insulation to protect the qubits.

We propose a thermal insulator composed of alternating layers with a high acoustic impedance mismatch to optimize destructive phonon interference, effectively forming a Distributed Bragg Reflector (DBR). This stack maintains electrical connectivity through superconducting vias, enabling electronics to operate at higher temperatures without compromising the qubit environment. Simulations indicate that an optimized DBR can reduce thermal power transmission to below 1 mW/cm², assuming coherent phononic transport is dominant. Initial experiments on 600-nm-thick DBRs of Ta and SiO₂ on Si show significant thermal insulation at 100 mK, confirming the DBR's potential as an effective cryogenic insulator.