đ€ AI Summary
This work identifies and formally names a previously unrecognized issue in hybrid quantum neural networksââmeasurement-induced logit contractionââwhere quantum measurement outputs, constrained to the interval [â1, 1], diminish the sensitivity of cross-entropy loss to logit differences, leading to vanishing gradients and unstable training. To address this, the authors propose a circuit-agnostic, learnable Quantum Measurement Temperature (QMT) mechanism that adaptively scales measurement outputs to enhance loss sensitivity without altering the underlying quantum circuit architecture. Experimental results demonstrate that QMT substantially improves logit separation, gradient magnitude, and training stability, yielding higher classification accuracy on both fluorescence microscopy images and a six-class Fashion-MNIST benchmark.
đ Abstract
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.