Related papers: Sequentially generated states for the study of two…
We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this…
We introduce a family of quantum spin chains with nearest-neighbor interactions that can serve to clarify and refine the classification of gapped quantum phases of such systems. The gapped ground states of these models can be described as a…
We give a classification of gapped quantum phases of one-dimensional systems in the framework of Matrix Product States (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states, and both in…
We characterize entanglement subject to its definition over real and complex, composite quantum systems. In particular, a method is established to assess quantum correlations with respect to a selected number system, illuminating the deeply…
Many-body entangled quantum states studied in condensed matter physics can be primary resources for quantum information, allowing any quantum computation to be realized using measurements alone, on the state. Such a universal state would be…
In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space…
Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states such as projected…
Entanglement is widely considered the cornerstone of quantum information and an essential resource for relevant quantum effects, such as quantum teleportation, quantum cryptography, or the speed-up of quantum computing, as in Shor's…
Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the "area law". In…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
A systematic and compact treatment of arbitrary $su(2)$ invariant spin-$s$ quantum chains with nearest-neighbour interactions is presented. The ground-state is derived in terms of matrix product states (MPS). The fundamental MPS…
We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…
We argue and demonstrate that projected entangled-pair states (PEPS) outperform matrix product states significantly for the task of generative modeling of datasets with an intrinsic two-dimensional structure such as images. Our approach…
Permutation symmetries of multipartite quantum states are defined only when the constituent subsystems are of equal dimensions. In this work we extend this notion of permutation symmetry to heterogeneous systems, that is, systems composed…
We determine which translationally invariant matrix product states have a continuum limit, that is, which can be considered as discretized versions of states defined in the continuum. To do this, we analyse a fine-graining renormalization…
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…
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…