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The geometric entanglement per lattice site, as a holistic measure of the multipartite entanglement, serves as a universal marker to detect quantum phase transitions in quantum many-body systems. However, it is very difficult to compute the…
We investigate creation of optimal entanglement in symmetric networks. The proposed network is one in which the connections are organized by a group table in other words a group association scheme. We show that optimal entanglement can be…
Tensor Network States (TNS) offer an efficient representation for the ground state of quantum many body systems and play an important role in the simulations of them. Numerous TNS are proposed in the past few decades. However, due to the…
The optimal use of quantum and classical computational techniques together is important to address problems that cannot be easily solved by quantum computations alone. This is the case of the ground state problem for quantum many-body…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
Characterizing the ground-state properties of disordered systems, such as spin glasses and combinatorial optimization problems, is fundamental to science and engineering. However, computing exact ground states and counting their…
In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…
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…
Quantum entanglement detection and characterization are crucial for various quantum information processes. Most existing methods for entanglement detection rely heavily on a complete description of the quantum state, which requires numerous…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Reliable detection and quantification of quantum entanglement, particularly in high-spin or many-body systems, present significant computational challenges for traditional methods. This study examines the effectiveness of ensemble machine…
We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to…
We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…
In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules. This method allows us to display quantum correlations…
Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…
Quantum entanglement plays a pivotal role in various quantum information processing tasks. However, there still lacks a universal and effective way to detecting entanglement structures, especially for high-dimensional and multipartite…
Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory…
Large-scale quantum networks, necessary for distributed quantum information processing, are posited to have quantum entangled systems between distant network nodes. The extent and quality of distributed entanglement in a quantum network,…
Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally…