Related papers: Bridging Perturbative Expansions with Tensor Netwo…
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach…
The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of Tree Tensor Network (TTN) states to solve the…
Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…
In this paper, we introduce a tensor network (TN) scheme into the entanglement augmentation process of the synergistic optimization framework by Rudolph et al. [arXiv:2208.13673] to build its process systematically for inhomogeneous…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
We study entanglement percolation in qubit-based planar quantum network models of arbitrary topology, where neighboring nodes are initially connected by pure states with quenched disorder in their entanglement. To address this, we develop a…
We present an expression for the spectral gap, opening up new possibilities for performing and accelerating spectral calculations of quantum many-body systems. We develop and demonstrate one such possibility in the context of tensor network…
Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this work we discuss quantum correlations in networks from the perspective of the underlying quantum…
Teleportation of quantum information over long distances requires robust entanglement on the macroscopic scale. The construction of highly energetic eigenstates with tunable long-range entanglement can provide a new medium for information…
We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge…
We present a procedure to construct tensor-network representations of many-body Gaussian states efficiently and with a controllable error. These states include the ground and thermal states of bosonic and fermionic quadratic Hamiltonians,…
Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…
In this paper, we construct a tensor network representation of quantum causal histories, as a step towards directly representing states in quantum gravity via bulk tensor networks. Quantum causal histories are quantum extensions of causal…
While tensor networks have their traditional application in simulating quantum systems, in the recent decade they have gathered interest as machine learning models. We combine the experience from both fields and derive how quantum…
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…
Topological quantum many-body systems, such as Hall insulators, are characterized by a hidden order encoded in the entanglement between their constituents. Entanglement entropy, an experimentally accessible single number that globally…
Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…
We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum…
Tensor networks representations of many-body quantum systems can be described in terms of quantum channels. We focus on channels associated with the Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network that has been…