发表机构
Mälardalen University（马尔默达尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究波函数流的量子模拟，提出将QNN融入相位反冲框架替换QROM，实现了流模型在量子计算机上的高效、精确执行，降低了电路资源消耗。
AI 中文摘要
流模型通过求解由速度场定义的常微分方程，生成从初始分布到目标分布的轨迹；流匹配通过建模两个分布间的传输动力学来学习该速度场；波函数流通过引入连续哈密顿量，建立了流模型与量子动力学间的形式联系，该哈密顿量驱动量子态的薛定谔演化。本文研究波函数流的精确高效量子模拟，以在量子计算机上高效实现流模型。首先，利用基于量子只读存储器（QROM）的相位反冲框架进行波函数流模拟，生成的概率密度与对应传统流模型产生的概率密度高度匹配。为解决量子电路资源成本高的问题，进一步将训练好的量子神经网络（QNN）融入相位反冲框架，替换QROM用于数据编码。数值实验表明，所提方法在量子计算机上实现流模型的效率更高，与基于QROM的框架相比，其保持了波函数流模拟的精度，且显著降低了量子电路资源消耗。
英文摘要
Flow models generate trajectories from an initial distribution to a target distribution by solving an ordinary differential equation defined by a velocity field. Flow matching learns this velocity field by modeling the transport dynamics between the two distributions. Wavefunction flow establishes a formal connection between flow models and quantum dynamics by introducing a continuity Hamiltonian, which drives the Schrödinger evolution of quantum states. In this paper, we investigate accurate and efficient quantum simulation of the wavefunction flow, thereby realizing the efficient implementation of flow models on quantum computers. We first leverage a quantum read-only memory (QROM)-based phase kickback framework for the wavefunction flow simulation, generating probability densities that closely match those produced by the corresponding conventional flow model. To address the high circuit-resource cost, we further incorporate a trained quantum neural network (QNN) into the phase kickback framework, replacing QROM for data encoding. Numerical experiments demonstrate that our proposed method implements flow models on quantum computers more efficiently, since it maintains the accuracy of wavefunction flow simulation compared with the QROM-based framework, and significantly reduces the circuit resources.
