Related papers: State Diagrams to determine Tree Tensor Network Op…
Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of…
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,…
This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…
Dynamics of open quantum systems with structured reservoirs can often be simulated efficiently with tensor network influence functionals. The standard variants of the time-evolving matrix product operator (TEMPO) method are applicable when…
We present a new variational tree tensor network state (TTNS) ansatz, the three-legged tree tensor network state (T3NS). Physical tensors are interspersed with branching tensors. Physical tensors have one physical index and at most two…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective low-rank structure that emerges after tensorization of discretized…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
We answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor…
We describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of…
Predicting and analyzing global behaviour of complex systems is challenging due to the intricate nature of their component interactions. Recent work has started modelling complex systems using networks endowed with multiway interactions…
Mesoscopic quantum systems exhibit complex many-body quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, non-interacting theories display a rich landscape of…
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
We introduce a non-interacting boson model to investigate topological structure of complex networks in the present paper. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important…
We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…
Tensor network formalisms have emerged as powerful tools for simulating quantum state evolution. While widely applied in the study of optical quantum circuits, such as Boson Sampling, existing tensor network approaches fail to address the…
This paper proposes a novel approach to Hamiltonian simulation using Decision Diagrams (DDs), which are an exact representation based on exploiting redundancies in representations of quantum states and operations. While the simulation of…
The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional…
Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…
Tensor networks are an efficient platform to represent interesting quantum states of matter as well as to compute physical observables and information-theoretic quantities. We present a general protocol to construct fixed-point tensor…