# Towards Quantum Machine Learning with Tensor Networks

**Authors:** William Huggins, Piyush Patel, K. Birgitta Whaley, E. Miles Stoudenmire  
**arXiv:** [1803.11537](https://arxiv.org/abs/1803.11537)  
**Date:** 2018-03-30  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1803.11537v1/

## Key points

- Authors explore potential of quantum computing in machine learning
- Acknowledge challenges of near-term quantum devices
- Propose innovative approaches using tensor networks for discriminative and generative learning
- Suggest utilizing tree and matrix product state tensor networks in quantum circuits
- Unified framework for classical and quantum computing leveraging shared advancements
- Train model classically before transferring to quantum setting for optimization
- Efficiency of tensor network circuits in terms of qubit usage
- Scalability depending on architecture, providing qubit-efficient solution
- Numerical experiments conducted on handwriting recognition model with noise resilience testing
- Research contributes insights into harnessing tensor networks for enhanced performance in quantum machine learning

## Summary

In their paper titled "Towards Quantum Machine Learning with Tensor Networks," authors William Huggins, Piyush Patel, K. Birgitta Whaley, and E. Miles Stoudenmire explore the potential of quantum computing in the field of machine learning. They acknowledge the challenges posed by near-term quantum devices, such as limited physical qubits and high error rates, but propose innovative approaches to both discriminative and generative learning using tensor networks. Drawing inspiration from the effectiveness of tensor networks in classical machine learning, the authors suggest utilizing tree and matrix product state tensor networks in quantum computing circuits. These circuits are designed to offer advantages for near-term quantum devices, creating a unified framework where classical and quantum computing can leverage shared theoretical and algorithmic advancements. One key aspect of their proposal is the ability to train a model classically before transferring it to the quantum setting for further optimization. This approach not only streamlines the training process but also demonstrates how classical and quantum systems can work synergistically in machine learning tasks. Furthermore, the authors highlight the efficiency of tensor network circuits in terms of qubit usage. Depending on the architecture employed, these circuits can scale logarithmically or independently with input or output data sizes, providing a qubit-efficient solution for quantum machine learning applications. To validate their proposals, numerical experiments were conducted by training a discriminative model for handwriting recognition using an optimization procedure suitable for execution on quantum hardware. The trained model was also tested for noise resilience, showcasing its robustness in real-world scenarios. Overall, this research contributes valuable insights into harnessing tensor networks for quantum machine learning, paving the way for enhanced performance and scalability in future quantum computing applications within the realm of artificial intelligence and data analysis.