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

arXiv: https://arxiv.org/abs/2504.14995 · HTML: https://mlsanity.com/paper/2504.14995/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 79 references that are in the map.
- First posted on arXiv 21 Apr 2025.

## Builds on (most cited first, 24 of 24)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Towards Understanding Regularization in Batch Normalization](https://mlsanity.com/paper/1809.00846/) (2018)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [Exponentially Many Local Minima in Quantum Neural Networks](https://mlsanity.com/paper/2110.02479/) (2021)
- [Quantum Neural Networks: Concepts, Applications, and Challenges](https://mlsanity.com/paper/2108.01468/) (2021)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [A Multi-Scale Tensor Network Architecture for Classification and Regression](https://mlsanity.com/paper/2001.08286/) (2020)
- [Efficient tensor network simulation of IBM's largest quantum processors](https://mlsanity.com/paper/2309.15642/) (2023)
- [Closing the "Quantum Supremacy" Gap: Achieving Real-Time Simulation of a Random Quantum Circuit Using a New Sunway Supercomputer](https://mlsanity.com/paper/2110.14502/) (2021)
- [Deep Tree Tensor Networks](https://mlsanity.com/paper/2502.09928/) (2025)
- [Number-State Preserving Tensor Networks as Classifiers for Supervised Learning](https://mlsanity.com/paper/1905.06352/) (2019)
- [Tensor tree learns hidden relational structures in data to construct generative models](https://mlsanity.com/paper/2408.10669/) (2024)
- [Adiabatic Encoding of Pre-trained MPS Classifiers into Quantum Circuits](https://mlsanity.com/paper/2504.09250/) (2025)

## Abstract (arXiv)

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.