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Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…
In this paper we show how tensor networks help in developing explainability of machine learning algorithms. Specifically, we develop an unsupervised clustering algorithm based on Matrix Product States (MPS) and apply it in the context of a…
The cone of positive-semidefinite (PSD) matrices is fundamental in convex optimization, and we extend this notion to tensors, defining PSD tensors, which correspond to separable quantum states. We study the convex optimization problem over…
A brief pedagogical overview of recent advances in tensor network state methods are presented that have the potential to broaden their scope of application radically for strongly correlated molecular systems. These include global fermionic…
Towards the efficient simulation of near-term quantum devices using tensor network states, we introduce an improved real-space parallelizable matrix-product state (MPS) compression method. This method enables efficient compression of all…
Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors.…
In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
Quantum optimal control (QOC) provides a systematic framework for achieving high-fidelity operations in quantum systems and plays a central role in tasks such as gate synthesis, state transfer, and pulse design. Existing QOC methods broadly…
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding…
Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…
Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only tree-like tensor networks such as…
We present an algorithm for supervised learning using tensor networks, employing a step of preprocessing the data by coarse-graining through a sequence of wavelet transformations. We represent these transformations as a set of tensor…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
Tensor networks have recently found applications in machine learning for both supervised learning and unsupervised learning. The most common approaches for training these models are gradient descent methods. In this work, we consider an…
The rapid pace of recent advancements in numerical computation, notably the rise of GPU and TPU hardware accelerators, have allowed tensor network (TN) algorithms to scale to even larger quantum simulation problems, and to be employed more…