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.