Related papers: Supervised Learning with Projected Entangled Pair …
We discuss the geometry of a class of tensor network states, called projected entangled pair states in the Physics literature. We provide initial results towards a question of Verstraete and Rizzi regarding the tensor network state of an $M…
Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems…
Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in…
Tensor networks such as matrix product states (MPS) and projected entangled pair states (PEPS) are commonly used to approximate quantum systems. These networks are optimized in methods such as DMRG or evolved by local operators. We provide…
We present a general graph-based Projected Entangled-Pair State (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural-matrix which…
Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the…
Entanglement, which quantifies non-local correlations in quantum mechanics, is the fascinating concept behind much of aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is…
Two dimensional tensor networks such as projected entangled pairs states (PEPS) are generally hard to contract. This is arguably the main reason why variational tensor network methods in 2D are still not as successful as in 1D. However,…
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…
Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…
Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and…
We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the…
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…
Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…
Deep neural networks as image priors have been recently introduced for problems such as denoising, super-resolution and inpainting with promising performance gains over hand-crafted image priors such as sparsity and low-rank. Unlike learned…
Semi-supervised learning aims to boost the accuracy of a model by exploring unlabeled images. The state-of-the-art methods are consistency-based which learn about unlabeled images by encouraging the model to give consistent predictions for…
We present an approach to identify topological order based on unbiased infinite projected entangled-pair states (iPEPS) simulations, i.e. where we do not impose a virtual symmetry on the tensors during the optimization of the tensor network…
We present a quantum algorithm to prepare injective PEPS on a quantum computer, a class of open tensor networks representing quantum states. The run-time of our algorithm scales polynomially with the inverse of the minimum condition number…
Tensors offer a natural representation for many kinds of data frequently encountered in machine learning. Images, for example, are naturally represented as third order tensors, where the modes correspond to height, width, and channels.…
With the advent of quantum and quantum-inspired machine learning, adapting the structure of learning models to match the structure of target datasets has been shown to be crucial for obtaining high performance. Probabilistic models based on…