Related papers: Contracting projected entangled pair states is ave…
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…
The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit an enormously rich…
The tensor network algorithm, a family of prevalent numerical methods for quantum many-body problems, aptly captures the entanglement properties intrinsic to quantum systems, enabling precise representation of quantum states. However, its…
Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems. Their expressive and computational power is characterized by an underlying…
Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…
We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…
Genuine multipartite entanglement of a given multipartite pure quantum state can be quantified through its geometric measure of entanglement, which, up to logarithms, is simply the maximum overlap of the corresponding unit tensor with…
Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…
The experimental realization of increasingly complex synthetic quantum systems calls for the development of general theoretical methods, to validate and fully exploit quantum resources. Quantum-state tomography (QST) aims at reconstructing…
A projected entangled pair state (PEPS) with ancillas is evolved in imaginary time. This tensor network represents a thermal state of a 2D lattice quantum system. A finite temperature phase diagram of the 2D quantum Ising model in a…
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
We propose an algorithm to convert a projected entangled pair state (PEPS) into a canonical form, analogous to the well-known canonical form of a matrix product state. Our approach is based on a variational gauging ansatz for the QR tensor…
We develop tangent space methods for projected entangled-pair states (PEPS) that provide direct access to the low-energy sector of strongly-correlated two-dimensional quantum systems. More specifically, we construct a variational ansatz for…
We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
Algorithms to simulate the ring-exchange models using the projected entangled pair states (PEPS) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange…
We study Projected Entangled Pair States (PEPS) with continuous virtual symmetries, i.e., symmetries in the virtual degrees of freedom, through an elementary class of models with SU(2) symmetry. Discrete symmetries of that kind have…
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.