At the lowest temperatures, the noisy "creaking" of materials is related to defects within the material host that support (typically) electronic or acoustic low-energy excitations. These defects can take a wide variety of microscopic forms, broadly described using generic models such as the tunneling two-level systems (TLS) model. Although the details of TLS, and their impact on the low-temperature behavior of glassy materials have been studied since the 1970s, these states have recently taken on relevance in the field of quantum computing, where the limits to the coherence of superconducting microwave quantum circuits are dominated by TLS. In this talk I will describe recent experiments involving nanoscale acoustic cavities incorporating phononic bandgap shielding, the influence of which is to dramatically alter the behavior of TLS, and consequently the acoustic properties within the cavity. This ability to engineer the quantum noise in materials has a plethora of applications. I will explore one of the more exciting applications: the creation of hybrid acoustic and superconducting quantum circuits, where the small scale, reduced cross-talk, and ultralong coherence time of quantum acoustic devices may provide significant improvements in connectivity and performance of current quantum hardware.