Related papers: Efficient Generative Modeling with Unitary Matrix …

Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose amplitudes can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the…

Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in…

Probabilistic inference is a fundamental task in modern machine learning. Recent advances in tensor network (TN) contraction algorithms have enabled the development of better exact inference methods. However, many common inference tasks in…

Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and…

Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…

We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…

We employ matrix product states (MPS) and tensor networks to study topological properties of the space of ground states of gapped many-body systems. We focus on families of states in one spatial dimension, where each state can be…

Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful…

Generative models have been successfully used for generating realistic signals. Because the likelihood function is typically intractable in most of these models, the common practice is to use "implicit" models that avoid likelihood…

A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for…

(Please refer to arXiv:1810.08050, which has completely different aims but contains all the main contents of this paper) In this work, we propose to access the information of criticality and excitations of one-dimensional quantum systems by…

Generative Adversarial Network (GAN) and its variants exhibit state-of-the-art performance in the class of generative models. To capture higher-dimensional distributions, the common learning procedure requires high computational complexity…

Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…

Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input…

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 propose a tensor network algorithm for the efficient sampling of quantum pure states belonging to a generalized microcanonical ensemble. The algorithm consists in an adaptation of the power method to a recently introduced ensemble of…

Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation,…

We focus on symmetries related to matrices and vectors appearing in the simulation of quantum many-body systems. Spin Hamiltonians have special matrix-symmetry properties such as persymmetry. Furthermore, the systems may exhibit physical…