用决策图构建可训练的量子态表示，突破传统变分量子电路局限
Variational decision diagrams for quantum-inspired machine learning applications
- 提出变分决策图（VDD），结合决策图结构与变分方法
- 在伊辛和海森堡模型中成功估算基态，未发现梯度消失现象
- 为量子机器学习提供新路径，适合研究量子算法设计者
决策图（DDs）因其能有效利用量子态与量子操作中的数据冗余，成为高效模拟量子电路的重要工具，可实现概率幅的快速计算。然而其在量子机器学习（QML）中的应用尚未被探索。本文提出变分决策图（VDD），一种新型图结构，融合了决策图的结构性优势与变分方法的可调性，用于高效表示量子态。我们通过将VDD应用于横向场伊辛和海森堡哈密顿量的基态估计问题，研究其可训练性。梯度方差分析表明，训练VDD是可行的，未出现梯度消失（即无空旷高原现象）。该工作为决策图在量子机器学习中的应用提供了新视角，可作为构造与训练变分族的新替代方案。
原文摘要 · Abstract (English)
Decision diagrams (DDs) have emerged as an efficient tool for simulating quantum circuits due to their capacity to exploit data redundancies in quantum states and quantum operations, enabling the efficient computation of probability amplitudes. However, their application in quantum machine learning (QML) has remained unexplored. This paper introduces variational decision diagrams (VDDs), a novel graph structure that combines the structural benefits of DDs with the adaptability of variational methods for efficiently representing quantum states. We investigate the trainability of VDDs by applying them to the ground state estimation problem for transverse-field Ising and Heisenberg Hamiltonians. Analysis of gradient variance suggests that training VDDs is possible, as no signs of vanishing gradients--also known as barren plateaus--are observed. This work provides new insights into the use of decision diagrams in QML as an alternative to design and train variational ansätze.
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