Variational Quantum Algorithms for Image Classification

Variational quantum algorithms are among the most widely studied approaches for applying near-term quantum devices to learning tasks. In this work we investigate a supervised quantum-autoencoder-style classifier that encodes images by amplitude encoding and predicts labels from a designated readout sub-register. Building on the quantum-autoencoder (QAE)-style classifier of Asaoka and Kudo, we make three contributions. First, we give a rigorous equivalence result showing that, for computational-basis label states, the original SWAP-test-based training objective can be estimated without ancilla and reference registers by directly measuring the readout subsystem. This simplification reduces circuit resources while preserving the same training signal. Second, we propose a lightweight hybrid extension: instead of using only the probability of the correct readout bitstring, we estimate the full readout distribution and apply a learnable temperature-and-bias post-processing followed by a softmax normalization. Across MNIST, KMNIST, and Fashion-MNIST (restricted to eight classes), this classical post-processing yields substantial and statistically significant improvements in evaluation accuracy, consistently across cross-entropy and mean-squared-error objectives. Finally, to interpret these gains we analyze Fisher-geometry summaries based on effective dimension and complementary Fisher-spectrum diagnostics for both the quantum models and the classical baselines. Empirically, the hybrid quantum model is associated with a more spectrally concentrated and anisotropic Fisher geometry, with Fisher mass concentrated in fewer dominant directions and with a substantially larger local Fisher scale after training.