Related papers: Tensor network representations from the geometry o…
We propose a method for constructing multi-qubit entangled quantum states representing weighted tripartite graphs. An expression for the entanglement distance for multi-qubit states corresponding to arbitrary tripartite graph structures is…
We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…
Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix product states, choosing a canonical form is a powerful tool,…
We consider entanglement-based quantum networks, where multipartite entangled resource states are distributed and stored among the nodes and locally manipulated upon request to establish the desired target configuration. Separating the…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
Topological quantum field theories (TQFT) encode properties of quantum states in the topological features of abstract manifolds. One can use the topological avatars of quantum states to develop intuition about different concepts and…
Periodic networks serve as models for the structural organisation of biological and chemical crystalline systems. Single or multiple networks can have different configurations in space, where entanglement may arise due to the way the…
An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$.…
Tensor network states are expected to be good representations of a large class of interesting quantum many-body wave functions. In higher dimensions, their utility is however severely limited by the difficulty of contracting the tensor…
Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this work we discuss quantum correlations in networks from the perspective of the underlying quantum…
The dynamics of plasmas are governed by a set of non-linear differential equations which remain challenging to solve directly for large 2D and 3D problems. Here we investigate how tensor networks could be applied to plasmas described by the…
The ability to selectively measure, initialize, and reuse qubits during a quantum circuit enables a mapping of the spatial structure of certain tensor-network states onto the dynamics of quantum circuits, thereby achieving dramatic resource…
Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…
Conventional holographic tensor networks can be described as toy holographic maps constructed from many small linear maps acting in a spatially local way, all connected together with ``background entanglement'', i.e. links of a fixed state,…
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 consider a frustrated anti-ferromagnetic triangular lattice Hamiltonian and show that the properties of the manifold of its degenerated ground state are represented by a novel type of tensor networks. These tensor networks are not based…
We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Although tensor network states constitute a broad range of exotic quantum states, their realization is challenging and often requires resources whose depth scales with system size. In this work, we explore criteria on the local tensors for…