Design of bent quantum waveguides via shortcuts to adiabaticity

Quantum waveguides are one of the key components in the developement of quantum technologies that experienced a new surge in popularity in recent years. In quantum computers, quantum particles have to be moved between different sites on a quantum chip through waveguides. The progressive miniaturization of quantum chips requires the waveguides to follow certain paths and so they need to be bent in order to be accomodated onto the chip. If the bending is too abrupt, instabilities are introduced in the system, possibly causing reflection and consequently data loss. This difficulty is usually overcome by adopting the adiabatic approach: the parameter representing the bending needs to vary gently along the waveguide, to prevent disruptive effects. This method, however, cannot be applied in many settings, in particular the ones that need a high degree of compactness. Thus, a new approach that would take into account all the different requirements is needed. ``Shortcuts to Adiabaticity" (STA) offers the right platform to improve on adiabatic processes and in this thesis we will apply a protocol based on STA to maximize particle transmission fidelity in geometries where the adiabatic approach cannot be employed