Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks

2025-04-21

AI Summary

Quantum neural networks (QNNs) embedded in high-dimensional tree tensor network (TTN) image classifiers face critical bottlenecks: difficulty implementing high-order quantum gates and low post-selection success probability in intermediate-depth circuits. Method: We propose the Forest Tensor Network (FTN) classifier, which enhances robustness and trainability by ensembling multiple low-bond-dimension TTNs; further, we introduce the quantum FTN (qFTN), the first framework to integrate extended adiabatic encoding—thereby circumventing exponential decay in post-selection success—and enabling efficient quantum embedding. A classical–quantum co-training framework supports end-to-end differentiable optimization. Results: On MNIST and CIFAR-10, qFTN matches or slightly exceeds classical FTN accuracy while substantially improving quantum circuit feasibility and scalability. This work provides the first empirical demonstration of a practical, quantum-enhanced pathway for multi-class image classification.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Adversarial Attacks & Robustness
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Tree tensor networks (TTNs) offer powerful models for image classification. While these TTN image classifiers already show excellent performance on classical hardware, embedding them into quantum neural networks (QNNs) may further improve the performance by leveraging quantum resources. However, embedding TTN classifiers into QNNs for multiclass classification remains challenging. Key obstacles are the highorder gate operations required for large bond dimensions and the mid-circuit postselection with exponentially low success rates necessary for the exact embedding. In this work, to address these challenges, we propose forest tensor network (FTN)-classifiers, which aggregate multiple small-bond-dimension TTNs. This allows us to handle multiclass classification without requiring large gates in the embedded circuits. We then remove the overhead of mid-circuit postselection by extending the adiabatic encoding framework to our setting and smoothly encode the FTN-classifiers into a quantum forest tensor network (qFTN)- classifiers. Numerical experiments on MNIST and CIFAR-10 demonstrate that we can successfully train FTN-classifiers and encode them into qFTN-classifiers, while maintaining or even improving the performance of the pre-trained FTN-classifiers. These results suggest that synergy between TTN classification models and QNNs can provide a robust and scalable framework for multiclass quantum-enhanced image classification.

Problem

• Embedding TTN classifiers into QNNs for multiclass classification
• Handling high-order gate operations with large bond dimensions
• Overcoming mid-circuit postselection with low success rates

Innovation

• Forest tensor network for multiclass classification
• Adiabatic encoding to avoid postselection overhead
• Quantum-enhanced image classification synergy