Related papers: Contracting projected entangled pair states is ave…
In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…
Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in entanglement entropy area law. In this…
A typical quantum state obeying the area law for entanglement on an infinite 2D lattice can be represented by a tensor network ansatz -- known as an infinite projected entangled pair state (iPEPS) -- with a finite bond dimension $D$. Its…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
We propose a pair of approximations that allows the leading order computational cost of contracting an infinite projected entangled-pair state (iPEPS) to be reduced from $\mathcal{O}(\chi^3D^6)$ to $\mathcal{O}(\chi^3D^3)$ when using a…
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…
Matrix product states (MPS) and matrix product operators (MPOs) are one dimensional tensor networks that underlie the modern density matrix renormalization group (DMRG) algorithm. The use of MPOs accounts for the high level of generality…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
In recent years, the variational Monte Carlo (VMC) calculations of projected entangled pair states (PEPS) has emerged as a competitive method for computing the ground states of many-body quantum systems. This method is particularly…
Due to the unfavorable scaling of tensor network methods with the refinement parameter M, new approaches are necessary to improve the efficiency of numerical simulations based on such states in particular for gapless, strongly entangled…
Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…
In general the calculation of robustness of entanglement for the mixed entangled quantum states is rather difficult to handle analytically. Using the the convex semi-definite programming method, the robustness of entanglement of some mixed…
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We…
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
The Hamiltonian for a system of itinerant particles on a two-dimensional lattice in a uniform magnetic field reduces the translational symmetry to a magnetic translation group, because of the need to choose a particular gauge for the vector…
Infinite projected entangled pair states (iPEPS), the tensor network ansatz for two-dimensional systems in the thermodynamic limit, already provide excellent results on ground-state quantities using either imaginary-time evolution or…
Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already…
We review different descriptions of many--body quantum systems in terms of tensor product states. We introduce several families of such states in terms of known renormalization procedures, and show that they naturally arise in that context.…
One of the main challenges of quantum many-body physics is that the dimensionality of the Hilbert space grows exponentially with the system size, which makes it extremely difficult to solve the Schr\"{o}dinger equations of the system. But…