Related papers: Contracting projected entangled pair states is ave…
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…
Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence…
A projected entangled pair state (PEPS) with ancillas can be evolved in imaginary time to obtain thermal states of a strongly correlated quantum system on a 2D lattice. Every application of a Suzuki-Trotter gate multiplies the PEPS bond…
We analyze the problem of high-order polynomial approximation from a many-body physics perspective, and demonstrate the descriptive power of entanglement entropy in capturing model capacity and task complexity. Instantiated with a…
We introduce a new paradigm for scaling simulations with projected entangled-pair states (PEPS) for critical strongly-correlated systems, allowing for reliable extrapolations of PEPS data with relatively small bond dimensions $D$. The key…
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 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 states and parton wave functions are two pivotal methods for studying quantum many-body systems. This work connects these two subjects as we demonstrate that a variety of parton wave functions, such as projected Fermi sea and…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
Generalizations of the density-matrix renormalization group method have long been sought after. In this paper, we assess the accuracy of projected entangled-pair states on infinite lattices by comparing with Quantum Monte Carlo results for…
Quantum entanglement and its paradoxical properties hold the key to an information processing revolution. Much attention has focused recently on the challenging problem of characterizing entanglement. Entanglement for a two qubit system is…
Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Random quantum circuits are outstanding candidates to demonstrate quantum supremacy, which could be implemented on a quantum…
We adapt and optimize the projected-pair-entangled-state (PEPS) algorithm on finite lattices (fPEPS) for two-dimensional Hubbard models and apply the algorithm to the Hubbard model with nearest-neighbor hopping on a square lattice. In…
A natural way to generalise tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product…
We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently…
It is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states - a conjecture frequently stated in the context of numerical simulations…
The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
Tensor network states form a variational ansatz class widely used, both analytically and numerically, in the study of quantum many-body systems. It is known that if the underlying graph contains a cycle, e.g. as in projected entangled pair…
Gauge theories form the basis of our understanding of modern physics - ranging from the description of quarks and gluons to effective models in condensed matter physics. In the non-perturbative regime, gauge theories are conventionally…