Related papers: Simulating quantum systems on the Bethe lattice by…
Projected entangled pair states (PEPS) on finite two-dimensional lattices are a natural ansatz for representing ground states of local many-body Hamiltonians, as they inherently satisfy the boundary law of entanglement entropy. In this…
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…
The transverse folding algorithm [Phys. Rev. Lett. 102, 240603] is a tensor network method to compute time-dependent local observables in out-of-equilibrium quantum spin chains that can sometimes overcome the limitations of matrix product…
We propose a novel tensor network method to achieve accurate and efficient simulations of Abelian lattice gauge theories (LGTs) in (2+1)D for both ground state and real-time dynamics. The first key is to identify a gauge canonical form…
An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable…
A projected entangled pair state (PEPS) with ancillas is evolved in imaginary time. This tensor network represents a thermal state of a 2D lattice quantum system. A finite temperature phase diagram of the 2D quantum Ising model in a…
We introduce a numerical approach to calculate the statistics of work done on 1D quantum lattice systems initially prepared in thermal equilibrium states. This approach is based on two tensor-network techniques: Time Evolving Block…
Regularized factorization is proposed to simulate time evolution for quantum lattice systems. Transcending the Trotter decomposition, the resulting compact structure of the propagator indicates a high-order Baker-Campbell-Hausdorff series.…
We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…
We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops…
We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite…
A promising application of neural-network quantum states is to describe the time dynamics of many-body quantum systems. To realize this idea, we employ neural-network quantum states to approximate the implicit midpoint rule method, which…
Tensor network methods are routinely used in approximating various equilibrium and non-equilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
We analyze the recently developed folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] to simulate the dynamics of infinite quantum spin chains, and relate its performance to the kind of entanglement produced under the evolution of…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
We study the antiferromagnetic kagome Heisenberg model with additional scalar-chiral interaction by using the infinite projected entangled-pair state (iPEPS) ansatz. We discuss in detail the implementation of optimization algorithm in the…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
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…
The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the Tensor Product Variational Formulation algorithm. The lattices are constructed by tessellation of congruent polygons with…