Related papers: Efficient 2D Tensor Network Simulation of Quantum …
Tensor network contraction is a fundamental mathematical operation that generalizes the dot product and matrix multiplication. It finds applications in numerous domains, such as database systems, graph theory, machine learning, probability…
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 establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions, and that…
Graph states are a class of important multiparty entangled states, of which bell pairs are the special case. Realizing a robust and fast distribution of arbitrary graph states in the downstream layer of the quantum network can be essential…
We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
This work introduces SpinGlassPEPS$.$jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction…
We determine the computational power of isometric tensor network states (isoTNS), a variational ansatz originally developed to numerically find and compute properties of gapped ground states and topological states in two dimensions. By…
We have applied a variational algorithm based on Projected Entangled Pair States (PEPS) to a two dimensional frustrated spin system, the spin-1/2 antiferromagnetic Heisenberg model on the Shastry-Sutherland lattice. We use the class of PEPS…
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…
An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for 2D wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the…
Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor…
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…
Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate? We answer this question by presenting a method to extract geometrically $k$-local conserved operators that…
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.…
Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While MPS are comprehensively understood, in…
Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via…
Matrix product states (MPS), a tensor network designed for one-dimensional quantum systems, has been recently proposed for generative modeling of natural data (such as images) in terms of `Born machine'. However, the exponential decay of…
Owing to their great expressivity and versatility, neural networks have gained attention for simulating large two-dimensional quantum many-body systems. However, their expressivity comes with the cost of a challenging optimization due to…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…