Efficient utility-scale encoding of data and distributions on a Quantum Computer

Data loading is a crucial initial step in practical quantum computations, especially in finance where precise representation of complex probability distributions is vital. Most common methods for encoding these distributions tend to result in exponentially deep quantum circuits, rendering them impractical on current noisy hardware. We introduce an improved algorithm that constructs efficient, provably linear-depth shallow quantum circuits for encoding data and probability distributions, including heavy-tailed distributions such as Lévy distributions. This approach significantly reduces circuit depth, thus reducing hardware noise impact, and enhancing feasibility for real-world applications. We have validated our method on both simulated and real IBM quantum devices, including the 127-qubit Heron Quantum Processing Unit, demonstrating efficiency and scalability.