这篇论文找到了混合量子神经网络训练不稳定的一个隐藏原因——测量值范围太小，并提出了一个简单的可学习缩放参数QMT来解决。实验在蛋白质分类和Fashion MNIST上都有效果。
标准Pauli测量下量子神经网络输出被约束在[-1,1]区间，导致交叉熵损失对logit差异敏感度不足，梯度被抑制。本文首次将这一效应定义为测量诱导logit收缩。提出可学习的量子测量温度（QMT）参数，在损失函数之前重新缩放量子测量输出，补偿物理测量范围限制。QMT不改变量子电路结构或测量算子。在荧光显微图像与六类Fashion MNIST实验中，QMT一致提升了logit分离度、梯度强度和训练稳定性，并提高了分类准确率。
Mitigating Measurement-Induced Training Instability in Hybrid Quantum Neural Networks for Protein Classification
Hybrid Quantum Neural Network (QNN) classifiers produce logits as expectation values of quantum measurement operators. For standard Pauli measurements, these outputs are intrinsically bounded to the interval [-1,1]. When such bounded logits are used directly with the cross-entropy loss applied to softmax-normalized logits for multi-class classification, the loss function operates in a regime of weak sensitivity to logit differences. As a consequence, parameter gradients are suppressed, leading to unstable optimization in variational quantum classifiers (VQCs). In this work, we identify this effect as measurement-induced logit contraction, a previously uncharacterized source of trainability degradation in hybrid QNNs. To address this limitation, we introduce a learnable scaling parameter, termed Quantum Measurement Temperature (QMT), which rescales quantum measurement outputs prior to the loss. Unlike post-hoc calibration, QMT acts during training and compensates for the physically imposed bounds on quantum measurement outputs. This rescaling increases gradient magnitude and variance, thereby improving loss sensitivity. The proposed mechanism is architecture-agnostic and does not modify the quantum ansatz, circuit depth, or measurement operators. Experiments on fluorescence microscopy images and a six-class variant of Fashion MNIST demonstrate that QMT consistently enhances logit separation, strengthens gradients, stabilizes training across random initializations, and improves classification accuracy, relative to unscaled measurement readouts. These results demonstrate that QMT enables stable and reliable training of hybrid QNNs for practical applications.