Entanglement-Based Feature Extraction by Tensor Network Machine Learning

Abstract

It is a hot topic how entanglement, a quantity from quantum information theory, can assist machine learning. In this work, we implement numerical experiments to classify patterns/images by representing the classifiers as matrix product states (MPS). We show how entanglement can interpret machine learning by characterizing the importance of data and propose a feature extraction algorithm. We show on the MNIST dataset that when reducing the number of the retained pixels to 1/10 of the original number, the decrease of the ten-class testing accuracy is only O (10–3), which significantly improves the efficiency of the MPS machine learning. Our work improves machine learning’s interpretability and efficiency under the MPS representation by using the properties of MPS representing entanglement.

Non-Separability of Physical Systems as a Foundation of Consciousness

“…To be clear, a classical computer can in principle simulate superposition or even entanglement, but will require an enormous amount of time and power to achieve that. In a classical limit, the situation may be less clear, but there are indications that even then non-separable systems offer substantial advantages over separable ones [ 132 , 133 , 134 , 135 , 136 , 137 ], e.g., in terms of computational power, time required to carry out computations, and efficiency of learning. Thus, it appears that, even in a classical case, a non-separable system realizes a seamlessly integrated many-dimensional ‘whole’, in which complex computations can occur in a more straightforward way than in a separable system.…”

Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks

“…The latter features one tensor (usually in the center) containing a dangling leg representing the resulting prediction of the model, e.g., the class probabilities. So far most applications of MPS-based machine learning involved supervised learning tasks such as classification [50,70,[79][80][81], or unsupervised learning tasks such as generative modeling [51,82,83], sequence modeling [84,85], and anomaly detection [86]. Recently, MPS have also been utilized as a feature map for classical data in a quantum reinforcement learning (RL) framework [44].…”

A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom

“…Note that we shall not assume prior knowledge of quantum many-body physics, which is the most common application of tensor network algorithms. The skills and ideas that we introduce in this manuscript are intended to be general for the tensor network formalism, rather than for their use in a specific application, thus can also carry over to other area in which tensor networks have proven useful such as quantum chemistry [14][15][16][17][18], holography [19][20][21][22][23][24], machine learning [25][26][27][28][29], and the simulation of quantum circuits [30][31][32][33][34][35].…”

“…Tensor networks have been developed as a useful formalism for the theoretical understanding of quantum many-body wavefunctions [1][2][3][4][5][6][7][8][9][10], especially in regards to entanglement [11][12][13], and are also applied as powerful numeric tools and simulation algorithms. Although developed primarily for the description of quantum many-body systems, they have since found use in a plethora of other applications such as quantum chemistry [14][15][16][17][18], holography [19][20][21][22][23][24], machine learning [25][26][27][28][29] and the simulation of quantum circuits [30][31][32][33][34][35].…”