Related papers: Matrix product states, geometry, and invariant the…
A matrix modeling formulation for translation-invariant noncommutative gauge theories is given in the setting of differential graded algebras and quantum groups. Translation-invariant products are discussed in the setting of…
We demonstrate the use of matrix product state (MPS) models for discriminating quantum data on quantum computers using holographic algorithms, focusing on classifying a translationally invariant quantum state based on $L$ qubits of quantum…
We present a novel framework for learning cost-efficient latent representations in problems with high-dimensional state spaces through nonlinear dimension reduction. By enriching linear state approximations with low-order polynomial terms…
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…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…
We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
We report on a systematic implementation of su(2) invariance for matrix product states (MPS) with concrete computations cast in a diagrammatic language. As an application we present a variational MPS study of $su(2)$ invariant quantum spin…
Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key…
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…
In one spatial dimension, families of short-range entangled many-body quantum states, parameterized over some parameter space, can be topologically distinguished and classified by topological invariants built from the higher Berry phase --…
We reconstruct a matrix product state (MPS) in reduced spaces using density matrix. This scheme applies to a MPS built on a blocked quantum lattice. Each block contains $N$ physical sites that have a local space of rank $R$. The simulation…
Using the matrix product ansatz, we obtain solutions of the steady-state distribution of the two-species open one-dimensional zero range process. Our solution is based on a conventionally employed constraint on the hop rates, which…
We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We…
A generalization of matrix product states (MPS) is introduced which is suitable for describing interacting quantum systems in two and three dimensions. These scale-renormalized matrix-product states (SR-MPS) are based on a course-graining…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
Identifying variational wave functions that efficiently parametrize the physically relevant states in the exponentially large Hilbert space is one of the key tasks towards solving the quantum many-body problem. Powerful tools in this…
In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of…
These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular…
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports…