Validity of rotating wave approximation in non-adiabatic holonomic quantum computation

We examine the validity of the rotating wave approximation (RWA) in non-adiabatic holonomic single-qubit gates [New J. Phys. {\bf 14}, 103035 (2012)]. We demonstrate that the adoption of RWA may lead to a sharp decline in fidelity for rapid gate implementation and small energy separation between the excited and computational states. The validity of the RWA in the recent experimental realization [Nature (London) {\bf 496}, 482 (2013)] of non-adiabatic holonomic quantum computation for a superconducting qubit is examined.Comment: Changes, old figure replaced two new figures, journal reference adde

A Numerical Approach to Modeling Submoons and Investigating Stability Regions

The recent discovery of the Neptune-sized exomoon candidate Kepler-1625bi (Teachey et al. 2018) has prompted a wave of research into the possibility of such a large satellite hosting its own moons, or submoons. These submoons have a lot in common with moons, and lessons from moon stability calculations can help to understand submoon behavior and stability. Past submoon research has focused on determining stability regions for these submoons using simplified models of the body’s tidal evolution (Reid 1973, Conrad 1985, Kollmeier and Raymond 2019). In order to provide a more detailed understanding of submoon behavior, a Fortran N-Body code was used to calculate all gravitational interactions in the system and track the resulting motion of each body. This code has in the past been used to model planet formation, moon formation, and planet migration and was modified to include submoon behavior. It was found to provide a detailed picture of submoon behavior, and it lays the groundwork for future submoon research. Preliminary results show that stability depends highly on the initial location of the submoon as well as showing a general lack of submoon stability around the Earth’s moon or Kepler-1625bi. Future research searching the parameter space for stable submoon orbits and investigating other factors including the effects of other bodies and formation methods is highly encouraged