  State preparation is a necessary component of many quantum algorithms. In
this work, we combine a method for efficiently representing smooth
differentiable probability distributions using matrix product states with
recently discovered techniques for initializing quantum states to approximate
matrix product states. Using this, we generate quantum states encoding a class
of normal probability distributions in a trapped ion quantum computer for up to
20 qubits. We provide an in depth analysis of the different sources of error
which contribute to the overall fidelity of this state preparation procedure.
Our work provides a study in quantum hardware for scalable distribution
loading, which is the basis of a wide range of algorithms that provide quantum
advantage.
