Tailor Made Embeddings for Quantum Machine Learning

Quantum machine learning (QML) often struggles with the "curse of dimensionality" and the difficulty of embedding large classical datasets into quantum states. Standard methods like amplitude embedding require exponential resources for data recovery (tomography), while others lack the structure needed for effective learning. This paper asks: can we use a variational autoencoder (VAE) to learn task-specific, compact quantum embeddings that are both reconstructable and optimized for downstream quantum classification?

The authors propose a hybrid framework where a classical VAE is trained to compress data into a latent space that maps directly to quantum information. They define two primary modes: an Amplitude Encoder, which maps data to quantum state amplitudes, and an Ansatz Encoder, which maps data to rotation angles for variational circuits. By training the autoencoder to minimize reconstruction loss (using perceptual and adversarial losses), the model ensures that the resulting quantum representation retains essential structural information. Crucially, the autoencoder is trained independently of the quantum classifier, allowing for a clear evaluation of the quantum circuit's contribution.

The framework successfully compresses complex datasets, including ImageNet, into 13-qubit representations. On the MNIST (3 vs. 5) task, the learned amplitude encoder achieved 98.5% validation accuracy, significantly outperforming naive amplitude embedding by over 30 percentage points. The authors demonstrate that their approach replaces the exponential cost of full quantum state tomography with a polynomial measurement scheme. Furthermore, they validated the stability of these embeddings on real IBM quantum hardware, confirming that the learned representations remain robust under device noise.