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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…
Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
Using quantum information geometry, I derive quantum generalizations of the Onsager rate equations, which model the dynamics of an open system near a steady state. The generalized equations hold for a flexible definition of the forces as…
Calculation of observables with three-dimensional projected entangled pair states is generally hard, as it requires a contraction of complex multi-layer tensor networks. We utilize the multi-layer structure of these tensor networks to…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
Quantum state tomography (QST) is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become…
In the out-of-equilibrium evolution induced by a quench, fast degrees of freedom generate long-range entanglement that is hard to encode with standard tensor networks. However, local observables only sense such long-range correlations…
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tensors may generate the very same state. A fundamental question…
Quantum dots are versatile systems for exploring quantum transport, electron correlations, and many-body phenomena such as the Kondo effect. While equilibrium properties are well understood through methods like the numerical renormalization…
Coexistence of different dynamical phases is a hallmark of glassy dynamics. This is well-studied in classical systems where the underlying theoretical framework is that of large deviation theory. The presence of a similar phase coexistence…
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…
Tensor network methods are incredibly effective for simulating quantum circuits. This is due to their ability to efficiently represent and manipulate the wave-functions of large interacting quantum systems. We describe the challenges faced…
In the long-standing quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to quantum information theory, such as entanglement, and constitutive features of…
Quantum networks are considered as a promising future platform for quantum information exchange and quantum applications, which have capabilities far beyond the traditional communication networks. Remote quantum entanglement is an essential…
The simulation of quantum transport in a realistic, many-particle system is a nontrivial problem with no quantitatively satisfactory solution. While real-time propagation has the potential to overcome the shortcomings of conventional…
Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor…