Performance of high impedance resonators in dirty dielectric environments

High-impedance resonators are a promising contender for realizing long-distance entangling gates between spin qubits. As material system for the qubits, semiconductor nanowires with strong spin-orbit interaction are often employed, working towards a large-scale spin-qubit quantum processor. Inherently, the fabrication of nanowire based qubits relies on the use of gate dielectrics which are detrimental to the quality of the resonator. Here, we investigate loss mechanisms of high-impedance NbTiN resonators in the vicinity of thermally grown SiO$_2$ and of Al$_2$O$_3$ fabricated by atomic layer deposition. We benchmark the resonator performance in elevated magnetic fields and at elevated temperatures and find that the internal quality factors are limited by the coupling between the resonator and two-level systems of the employed oxides. Nonetheless, we measure the internal quality factors of high-impedance resonators to exceed $10^3$ in all investigated oxide configurations. Because these oxides are commonly used for nanowire-device fabrication, our results allow for straightforward integration of high-impedance resonators into a nanowire-based quantum processor. Hence, these experiments pave the way for large-scale quantum computers based on semiconductor nanowires.