Experimental Loading of Normal Probability Distributions to Quantum States

State preparation is a necessary component of many quantum algorithms, and in particular is fundamental in quantum sampling algorithms such as quantum Monte Carlo integration. 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 variety of algorithms that provide quantum advantage.