The position states of the harmonic oscillator describe the location of a particle moving on the real line. Similarly, the phase difference between two superconductors on either side of a Josephson junction takes values in the configuration space of a particle on a circle. More generally, many physical systems can be described by a basis of "position states," describing a particle moving on a more general configuration or state space. Most of this space is usually ignored due to the energy cost required to pin a particle to a precise "position". However, as our control over quantum systems improves, utilizing more of this higher-energy space harbors benefits for protecting quantum information and probing quantum matter. I will discuss quantum applications taking advantage of state spaces associated with the harmonic oscillator, as well as molecular rotational and nuclear states.
