将经典张量网络分类器渐进式编码为量子电路，避免训练灾难
Adiabatic Encoding of Pre-trained MPS Classifiers into Quantum Circuits
- 先经典训练MPS分类器，再通过绝热过程转为量子电路
- 在100个量子比特上保持分类准确率，避免梯度消失问题
- 适合想绕过量子训练瓶颈的研究者和工程师
尽管量子神经网络（QNN）在分类任务中表现强大，但其训练面临两个主要障碍：梯度消失（barren plateaus）和局部极小值。一种有前景的解决方案是先在经典计算机上训练张量网络（TN）模型，再将其嵌入量子神经网络。然而，传统嵌入方法通常依赖后选择（postselection），其成功概率随系统尺寸指数衰减。本文提出一种绝热编码框架，将预训练的矩阵积态（MPS）分类器编码为量子矩阵积态（qMPS）电路，并在保持性能的前提下逐步移除后选择。我们证明，在特定人工数据集上从零开始训练qMPS分类器存在指数级困难，而本文方法有效规避了这一问题。在二分类MNIST上的数值实验也验证了该方法的鲁棒性。
原文摘要 · Abstract (English)
Although Quantum Neural Networks (QNNs) offer powerful methods for classification tasks, the training of QNNs faces two major training obstacles: barren plateaus and local minima. A promising solution is to first train a tensor-network (TN) model classically and then embed it into a QNN.\ However, embedding TN-classifiers into quantum circuits generally requires postselection whose success probability may decay exponentially with the system size. We propose an \emph{adiabatic encoding} framework that encodes pre-trained MPS-classifiers into quantum MPS (qMPS) circuits with postselection, and gradually removes the postselection while retaining performance. We prove that training qMPS-classifiers from scratch on a certain artificial dataset is exponentially hard due to barren plateaus, but our adiabatic encoding circumvents this issue. Additional numerical experiments on binary MNIST also confirm its robustness.
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