  With adiabatic techniques, it is possible to create quantum superposition
states with high fidelity while exercising limited control over the parameters
of a system. However, because these techniques are slow compared to other
timescales in the system, they are usually not suitable for creating highly
unstable states or performing time-critical processes. Both of these situations
arise in quantum information processing, where entangled states may only be
isolated from the environment for a short time and where quantum computers
require high-fidelity operations to be performed quickly. Recently it has been
shown that techniques like optimal control and shortcuts to adiabaticity may be
used to prepare quantum states non-adiabatically with high fidelity. Here we
present two examples of how these techniques can be used to create maximally
entangled many-body NOON states in one-dimensional Tonks--Girardeau gases.
