Qvine: Vine Structured Quantum Circuits for Loading High Dimensional Distributions

2026-04-28

AI Summary

This work addresses the challenges of quantum amplitude encoding for high-dimensional probability distributions—namely, the curse of dimensionality, limited expressivity of parameterized quantum circuits, and training difficulties. It introduces, for the first time, the classical Vine copula decomposition into quantum circuit design, proposing a Vine-structured quantum circuit (Qvine) that enables efficient and scalable distribution loading through structured factorization. The approach substantially reduces circuit depth: quadratic in the number of dimensions under a general R-vine structure, and merely linear under D-vine and practical R-vine configurations. Empirical results demonstrate that Qvine achieves high-fidelity loading for both 3–4 dimensional Gaussian distributions and real-world joint distributions of stock returns, confirming its effectiveness and practical utility.

Abstract

Loading high dimensional distributions is an important task for utilizing quantum computers on applications ranging from machine learning to finance. The high dimensionality leads to a curse of dimensionality, representing a d-dimensional distribution with k resolution requires dk qubits and an unstructured parameterized circuit would express a unitary in an exponential operator space in the number of qubits, leading to vanishing gradients and poor convergence guarantees even at high depth. Vine copula decompositions are widely used to represent high dimensional distributions classically, showing high quality approximation in many important applications, such as financial modeling. We present Qvine, a vine structured ansatz for quantum circuits, that mirrors the vine decomposition to construct scalable quantum circuits with efficient trainability while achieving similarly high quality approximation for amplitude encoding distributions. For regular vines (R-vines), we show that the circuit depth scales at most quadratic in the dimension of the distribution, while for D-vines, as well as many practical R-vines, the circuit depth scales linear in the dimension. For 3-dimensional and 4-dimensional Gaussians and empirical joint stock price return distributions for selected stocks, our experiments show Qvines achieve high quality loading.

Problem

• high-dimensional distributions
• quantum circuit loading
• curse of dimensionality
• amplitude encoding
• trainability

Innovation

• quantum circuit ansatz
• vine copula
• amplitude encoding
• high-dimensional distribution loading
• scalable quantum circuits