Tensor Networks for Machine Learning

Edwin Miles Stoudenmire

Edwin Miles Stoudenmire

Edwin Miles Stoudenmire

Ding Liu, Yao, Jiaqi, Z. Jamie Yao +1 more

Tensor networks (TN) have found a wide use in machine learning, and in particular, TN and deep learning bear striking similarities. In this work, we propose the quantum-classical hybrid tensor networks (HTN) which combine tensor networks with classical neural networks in a uniform deep learning framework to overcome the limitations of regular tensor networks in machine learning. We first analyze the limitations of regular tensor networks in the applications of machine learning involving the representation power and architecture scalability. We conclude that in fact the regular tensor networks are not competent to be the basic building blocks of deep learning. Then, we discuss the performance of HTN which overcome all the deficiency of regular tensor networks for machine learning. In this sense, we are able to train HTN in the deep learning way which is the standard combination of algorithms such as Back Propagation and Stochastic Gradient Descent. We finally provide two applicable cases to show the potential applications of HTN, including quantum states classification and quantum-classical autoencoder. These cases also demonstrate the great potentiality to design various HTN in deep learning way.

Richik Sengupta, Soumik Adhikary, Ivan Valer'evich Oseledets +1 more

A tensor network is a type of decomposition used to express and approximate large arrays of data.A given dataset, quantum state, or higher-dimensional multilinear map is factored and approximated by a composition of smaller multilinear maps.This is reminiscent to how a Boolean function might be decomposed into a gate array: this represents a special case of tensor decomposition, in which the tensor entries are replaced by 0, 1 and the factorisation becomes exact.The associated techniques are called tensor network methods: the subject developed independently in several distinct fields of study, which have more recently become interrelated through the language of tensor networks.The tantamount questions in the field relate to expressability of tensor networks and the reduction of computational overheads.A merger of tensor networks with machine learning is natural.On the one hand, machine learning can aid in determining a factorisation of a tensor network approximating a data set.On the other hand, a given tensor network structure can be viewed as a machine learning model.Herein the tensor network parameters are adjusted to learn or classify a data-set.In this survey we review the basics of tensor networks and explain the ongoing effort to develop the theory of tensor networks in machine learning.1

Zhihui Song, Jinchen Xu, Xin Zhou +2 more

Abstract There have been numerous quantum neural networks reported, but they struggle to match traditional neural networks in accuracy. Given the huge improvement of the neural network models’ accuracy by two-dimensional tensor network (TN) states in classical tensor network machine learning (TNML), it is promising to explore whether its application in quantum machine learning can extend the performance boundary of the models. Here, we transform two-dimensional TNs into quantum circuits for supervised learning. Specifically, we encode two-dimensional TNs into quantum circuits through rigorous mathematical proofs for constructing model ansätze, including string-bond states, entangled-plaquette states and isometric TN states. In addition, we propose adaptive data encoding methods and combine with TNs. We construct a tensor-network-inspired quantum circuit (TNQC) supervised learning framework for transferring TNML from classical to quantum, and build several novel two-dimensional TN-inspired quantum classifiers based on this framework. Finally, we propose a parallel quantum machine learning method for multi-class classification to construct 2D TNQC-based multi-class classifiers. Classical simulation results on the MNIST benchmark dataset show that our proposed models achieve the state-of-the-art accuracy performance, significantly outperforming other quantum classifiers on both binary and multi-class classification tasks, and beat simple convolutional classifiers on a fair track with identical inputs. The noise resilience of the models makes them successfully run and work in a real quantum computer.