Non-Unitary Quantum Machine Learning: Fisher Efficiency Transitions from Distributed Quantum Expressivity

Abstract

Quantum machine learning has faced growing scrutiny over its practical advantages compared to classical approaches, particularly following dequantization results and large scale benchmarking studies that have challenged earlier optimistic claims. This work presents a systematic empirical evaluation of non unitary quantum machine learning implemented via the Linear Combination of Unitaries framework within hybrid quantum classical neural networks. Across more than 570 experiments spanning four domains digit classification MNIST, agricultural disease detection PlantVillage, molecular property regression QM9, and medical histopathology PathMNIST non unitary quantum layers are benchmarked against structurally identical unitary baselines. Consistent performance improvements are observed across all domains, with gains ranging from +0.2 percentage to +5.8 percentage depending on dataset complexity and qubit count. A particularly notable finding is a Fisher efficiency transition in medical imaging tasks, where parameter efficiency shifts from negative to positive as qubit count increases from 10 to 12, indicating a threshold dependent efficiency regime. Additionally, non unitary IQP circuit variants reach or exceed classical baselines at 10 qubits on CIFAR 10, demonstrating that circuits with established complexity theoretic hardness guarantees remain compatible with competitive learning performance under the LCU framework. These results offer a large scale, evidence based characterisation of the conditions under which non unitary QML yields measurable empirical benefits in near term settings.