  We present quantum algorithms for the loading of probability distributions
using Hamiltonian simulation for one dimensional Hamiltonians of the form
${\hat H}= \Delta + V(x) \mathbb{I}$. We consider the potentials $V(x)$ for
which the Feynman propagator is known to have an analytically closed form and
utilize these Hamiltonians to load probability distributions including the
normal, Laplace and Maxwell-Boltzmann into quantum states. We also propose a
variational method for probability distribution loading based on constructing a
coarse approximation to the distribution in the form of a `ladder state' and
then projecting onto the ground state of a Hamiltonian chosen to have the
desired probability distribution as ground state. These methods extend the
suite of techniques available for the loading of probability distributions, and
are more efficient than general purpose data loading methods used in quantum
machine learning.
