Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits
This addresses the data encoding bottleneck for quantum machine learning practitioners, offering a scalable intermediary between classical data and quantum processors, though it is incremental as it builds on existing tensor network methods.
The paper tackles the exponential cost of amplitude encoding in quantum machine learning by introducing a pre-trained tensor-train encoding network that reduces computational complexity to polynomial time, achieving substantial gains in encoding efficiency on datasets like MNIST and semiconductor quantum dots while maintaining competitive classification performance.
Data encoding remains a fundamental bottleneck in quantum machine learning, where amplitude encoding of high-dimensional classical vectors into quantum states incurs exponential cost. In this work, we propose a pre-trained tensor-train (TT) encoding network (Pre-TT-Encoder) that significantly reduces the computational complexity of amplitude encoding while preserving essential data structure. The Pre-TT-Encoder exploits low-rank TT decompositions learned from classical data, enabling polynomial-time state preparation in the number of qubits and TT-ranks. We provide a theoretical analysis of the encoding complexity and establish fidelity bounds that quantify the trade-off between TT-rank and approximation error. Empirical evaluations on classical (MNIST) and quantum-native (semiconductor quantum dot) datasets demonstrate that our approach achieves substantial gains in encoding efficiency over direct amplitude encoding and PCA-based dimensionality reduction, while maintaining competitive performance in downstream variational quantum circuit classification tasks. The proposed method highlights the role of tensor networks as scalable intermediaries between classical data and quantum processors.