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.

状态准备是许多量子算法的必要组成部分。在这项工作中，我们将一种使用矩阵乘积状态有效表示平滑可微概率分布的方法与最近发现的用于初始化量子态以近似矩阵乘积状态的技术相结合。利用它，我们可以在捕获离子量子计算机中生成最多 20 个量子位的编码一类正态概率分布的量子态。我们对不同的误差源进行了深入分析，这些误差源有助于该状态准备过程的整体保真度。我们的工作提供了对可扩展分布加载的量子硬件的研究，这是提供量子优势的各种算法的基础。