Related papers: Continuous Tensor Network States for Quantum Field…
Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to…
Recent work by Wu {\em et al.} [arXiv:1910.11011] proposed a numerical method, so-called matrix product operator-matrix product state (MPO-MPS) method, by which several types of quantum many-body wave functions, in particular, the projected…
Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor…
Tensor networks representations of many-body quantum systems can be described in terms of quantum channels. We focus on channels associated with the Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network that has been…
Traditional mean-field theory is a simple generic approach for understanding various phases. But that approach only applies to symmetry breaking states with short-range entanglement. In this paper, we describe a generic approach for…
We investigate the tensor network representations of fermionic crystalline symmetry-protected topological (SPT) phases on two-dimensional lattices. As a mapping from virtual indices to physical indices, projected entangled-pair state (PEPS)…
We investigate the topological character of lattice chiral Gaussian fermionic states in two dimensions possessing the simplest descriptions in terms of projected entangled-pair states (PEPS). They are ground states of two different kinds of…
We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of…
We point out that the MERA network for the ground state of a 1+1-dimensional conformal field theory has the same structural features as kinematic space---the geometry of CFT intervals. In holographic theories kinematic space becomes…
We show how to accurately study 2D quantum critical phenomena using infinite projected entangled-pair states (iPEPS). We identify the presence of a finite correlation length in the optimal iPEPS approximation to Lorentz-invariant critical…
The multi-scale entanglement renormalization ansatz (MERA) is a tensor network that can efficiently parameterize critical ground states on a 1D lattice, and also suggestively implement some aspects of the holographic correspondence of…
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 introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…
Size extensivity, defined as the correct scaling of energy with system size, is a desirable property for any many-body method. Traditional CI methods are not size extensive hence the error increases as the system gets larger. Coupled…
Numerical treatment of two dimensional strongly-correlated systems is both extremely challenging and of fundamental importance. Infinite projected entangled-pair states (PEPS), a class of tensor networks, have demonstrated cutting-edge…
As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from…
We propose an approach to study the ground state of quantum many-body systems in which Tensor Network States (TNS), specifically Projected Entangled Pair States (PEPS), and Green's function Monte Carlo (GFMC) are combined. PEPS, by design,…
We propose a generalized form of entangled coherent states (ECS) and apply them in a multi-arm optical interferometer to estimate multiple phase shifts. We obtain the quantum Cramer-Rao bounds for both the linear and nonlinear…
Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…
Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…