Related papers: Local tensor network for strongly correlated proje…
Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…
With the advances in high resolution neuroimaging, there has been a growing interest in the detection of functional brain connectivity. Complex network theory has been proposed as an attractive mathematical representation of functional…
Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…
Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…
Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the…
Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space…
We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory. We provide…
Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…
Large-scale quantum networks have been employed to overcome practical constraints of transmissions and storage for single entangled systems. Our goal in this article is to explore the strong entanglement distribution of quantum networks. We…
Despite multipartite entanglement being a global property of a quantum state, a number of recent works have made it clear that it can be quantified using only local measurements. This is appealing because local measurements are the easiest…
The restricted Boltzmann machine (RBM) is one of the fundamental building blocks of deep learning. RBM finds wide applications in dimensional reduction, feature extraction, and recommender systems via modeling the probability distributions…
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…
The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…
Recently developed tensor network methods demonstrate great potential for addressing the quantum many-body problem, by constructing variational spaces with polynomially, instead of exponentially, scaled parameters. Constructing such an…
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…
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.
We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected…
We compute the quantum maximal correlation for bipartite Gaussian states of continuous-variable systems. Quantum maximal correlation is a measure of correlation with the monotonicity and tensorization properties that can be used to study…
The study of local models using finite shared randomness originates from the consideration about the cost of classically simulating entanglement in composite quantum systems. We construct explicitly two families of local-hidden-state (LHS)…
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…