Related papers: Automatic Structural Search of Tensor Network Stat…

We propose an entanglement-based algorithm of the tensor-network strong-disorder renormalization group (tSDRG) method for quantum spin systems with quenched randomness. In contrast to the previous tSDRG algorithm based on the energy…

Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multi-scale entanglement renormalization ansatz (MERA), a tensor network capable of efficiently…

I present an example of how to analytically optimize a multiscale entanglement renormalization ansatz for a finite antiferromagnetic Heisenberg chain. For this purpose, a quantum-circuit representation is taken into account, and we…

We use TensorNetwork [C. Roberts et al., arXiv: 1905.01330], a recently developed API for performing tensor network contractions using accelerated backends such as TensorFlow, to implement an optimization algorithm for the Multi-scale…

We introduce the multi-scale entanglement renormalization ansatz (MERA), an efficient representation of certain quantum many-body states on a D-dimensional lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive…

We propose a tensor network method for investigating strongly disordered systems that is based on an adaptation of entanglement renormalization [G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)]. This method makes use of the strong disorder…

Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume…

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…

We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)]…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…

The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…

Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…

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…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent…

We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…

We propose a second renormalization group method to handle the tensor-network states or models. This method reduces dramatically the truncation error of the tensor renormalization group. It allows physical quantities of classical…

Entanglement-based quantum networks exhibit a unique flexibility in the choice of entangled resource states that are then locally manipulated by the nodes to fulfill any request in the network. Furthermore, this manipulation is not uniquely…