Related papers: TensorNetwork on TensorFlow: Entanglement Renormal…
The multi-scale entanglement renormalization ansatz (MERA) provides a natural description of the ground state of a quantum critical Hamiltonian on the lattice. From an optimized MERA, one can extract the scaling dimensions of the underlying…
Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…
Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here we put forward a variational Monte Carlo approach for the…
Hybrid tensor networks offer a promising route to enhance the expressivity of classical tensor network methods by incorporating quantum states prepared on a quantum computer. Existing approaches are limited by the variational optimization…
The Multiscale Entanglement Renormalization Ansatz (MERA) is a tensor network based variational ansatz that is capable of capturing many of the key physical properties of strongly correlated ground states such as criticality and topological…
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…
We extend the formalism of entanglement renormalization to the study of boundary critical phenomena. The multi-scale entanglement renormalization ansatz (MERA), in its scale invariant version, offers a very compact approximation to quantum…
The goal of this manuscript is to provide an introduction to the multi-scale entanglement renormalization ansatz (MERA) and its application to the study of quantum critical systems. Only systems in one spatial dimension are considered. The…
In this article two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is…
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 computations, with matrix multiplication being the primary operation, serve as the fundamental basis for data analysis, physics, machine learning, and deep learning. As the scale and complexity of data continue to grow rapidly, the…
There will be a fast-paced shift from conventional network systems to novel quantum networks that are supported by the quantum entanglement and teleportation, key technologies of the quantum era, to enable secured data transmissions in the…
Recursive neural networks have widely been used by researchers to handle applications with recursively or hierarchically structured data. However, embedded control flow deep learning frameworks such as TensorFlow, Theano, Caffe2, and MXNet…
The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA…
The use of entanglement renormalization in the presence of scale invariance is investigated. We explain how to compute an accurate approximation of the critical ground state of a lattice model, and how to evaluate local observables,…
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…
Tensor network (TN) states, including entanglement renormalization (ER), can encompass a wider variety of entangled states. When the entanglement structure of the quantum state of interest is non-uniform in real space, accurately…
Techniques for approximately contracting tensor networks are limited in how efficiently they can make use of parallel computing resources. In this work we demonstrate and characterize a Monte Carlo approach to the tensor network…
We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum field theories in the continuum. A key tool is "quantum circuit perturbation theory," which enables us to systematically construct…
We introduce a learning-based framework to optimize tensor programs for deep learning workloads. Efficient implementations of tensor operators, such as matrix multiplication and high dimensional convolution, are key enablers of effective…