Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits

TL;DR

This paper introduces a pre-trained tensor-train encoding network that reduces the complexity of quantum data encoding, enabling efficient and scalable quantum machine learning with preserved data fidelity.

Contribution

It proposes a novel tensor-train based encoding method that lowers computational costs and maintains data quality, advancing quantum data encoding techniques.

Findings

Achieves polynomial-time state preparation in qubits and TT-ranks.

Outperforms direct amplitude encoding and PCA in efficiency.

Maintains competitive classification performance on classical and quantum datasets.

Abstract

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.