Quantum State Preparation of Normal Distributions using Matrix Product States
State preparation is a necessary component of many quantum algorithms, and in particular is fundamental in sampling routines such as those needed for quantum speedup of Monte Carlo methods. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with newly 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 the first study in quantum hardware for scalable distribution loading, which is the basis of a wide range of algorithms that provide quantum advantage.