Related papers: Unitary network: Tensor network unitaries with loc…

The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have…

We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion…

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…

The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with…

Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…

The immediate past has witnessed an increased amount of interest in local algorithms, i.e., constant time distributed algorithms. In a recent survey of the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local algorithms…

Tensor networks are factorisations of high rank tensors into networks of lower rank tensors and have primarily been used to analyse quantum many-body problems. Tensor networks have seen a recent surge of interest in relation to supervised…

This paper addresses the following question of neural network identifiability: Does the input-output map realized by a feed-forward neural network with respect to a given nonlinearity uniquely specify the network architecture, weights, and…

An important result in the theory of quantum control is the "universality" of $2$-local unitary gates, i.e. the fact that any global unitary evolution of a system of $L$ qudits can be implemented by composition of $2$-local unitary gates.…

In this thesis I develop a formalism whereby a tensor network may be understood in terms of a unitary braided tensor category, and represented in a particularly efficient manner corresponding to the exploitation of this mathematical…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Community detecting is one of the main approaches to understanding networks \cite{For2010}. However it has been a longstanding challenge to give a definition for community structures of networks. Here we found that community structures are…

Deep neural networks can suffer from the exploding and vanishing activation problem, in which the networks fail to train properly because the neural signals either amplify or attenuate across the layers and become saturated. While other…

Entangled quantum networks provide great flexibilities and scalabilities for quantum information processing or quantum Internet. Most of results are focused on the nonlocalities of quantum networks. Our goal in this work is to explore new…

Constraining linear layers in neural networks to respect symmetry transformations from a group $G$ is a common design principle for invariant networks that has found many applications in machine learning. In this paper, we consider a…

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…

Matrix representations of quantum operators are computationally complete but often obscure the structural topology of information flow within a quantum circuit \cite{nielsen2000}. In this paper, we introduce a generalized graph-theoretic…

Matrix-product unitaries (MPU) are 1D tensor networks describing time evolution and unitary symmetries of quantum systems, while their action on states by construction preserves the entanglement area law. MPU which are formed by a single…

We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…

Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…