Quantum-inspired tensor networks in machine learning models

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most relevant dependencies. Due to the formal similarity between quantum entanglement and statistical correlations, tensor networks have recently been integrated in machine learning, operating both as alternative learning architectures and as decompositions of components of neural networks. The expectation is that the theoretical understanding of tensor networks developed within quantum many-body physics leads to novel methods that offer advantages in terms of computational efficiency, explainability, or privacy. Here we review the use of tensor networks in the context of machine learning, providing a critical assessment of the state of the art, the potential advantages, and the challenges that must be overcome.

Physics solutions for machine learning privacy leaks

Machine learning systems are becoming more and more ubiquitous in increasingly complex areas, including cutting-edge scientific research. The opposite is also true: the interest in better understanding the inner workings of machine learning systems motivates their analysis under the lens of different scientific disciplines. Physics is particularly successful in this, due to its ability to describe complex dynamical systems. While explanations of phenomena in machine learning based on physics are increasingly present, examples of direct application of notions akin to physics in order to improve machine learning systems are more scarce. Here we provide one such application in the problem of developing algorithms that preserve the privacy of the manipulated data, which is especially important in tasks such as the processing of medical records. We develop well-defined conditions to guarantee robustness to specific types of privacy leaks, and rigorously prove that such conditions are satisfied by tensor-network architectures. These are inspired by the efficient representation of quantum many-body systems, and have shown to compete and even surpass traditional machine learning architectures in certain cases. Given the growing expertise in training tensor-network architectures, these results imply that one may not have to be forced to make a choice between accuracy in prediction and ensuring the privacy of the information processed.

A gentle introduction to Quantum Natural Language Processing

The main goal of this master's thesis is to introduce Quantum Natural Language Processing (QNLP) in a way understandable by both the NLP engineer and the quantum computing practitioner. QNLP is a recent application of quantum computing that aims at representing sentences' meaning as vectors encoded into quantum computers. To achieve this, the distributional meaning of words is extended by the compositional meaning of sentences (DisCoCat model) : the vectors representing words' meanings are composed through the syntactic structure of the sentence. This is done using an algorithm based on tensor products. We see that this algorithm is inefficient on classical computers but scales well using quantum circuits. After exposing the practical details of its implementation, we go through three use-cases.