Towards Quantum Machine Learning with Tensor Networks

TL;DR

This paper explores quantum machine learning using tensor network circuits, proposing methods suitable for near-term quantum devices, and demonstrating their effectiveness through numerical experiments in handwriting recognition.

Contribution

It introduces quantum tensor network circuits for discriminative and generative learning, enabling qubit-efficient schemes and bridging classical and quantum approaches.

Findings

Tensor network circuits can be trained for handwriting recognition.

Proposed methods are potentially implementable on near-term quantum hardware.

Models show resilience to noise in numerical tests.

Abstract

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.