Related papers: Continuum limits of Matrix Product States
This paper addresses the following verification task: Given a graph transformation system and a class of initial graphs, can we guarantee (non-)reachability of a given other class of graphs that characterizes bad or erroneous states? Both…
The distribution of entangled states of light over long distances is a major challenge in the field of quantum information. Optical losses, phase diffusion and mixing with thermal states lead to decoherence and destroy the non-classical…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
Matrix product states (MPS) provide a powerful framework for characterizing one-dimensional symmetry-protected topological (SPT) phases of matter and for formulating Lieb-Schultz-Mattis (LSM)-type constraints. Here we generalize the MPS…
We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple…
We show in the example of a one-dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form. The corresponding algebra is quadratic and involves three different…
Finite-state transducers give efficient representations of many Natural Language phenomena. They allow to account for complex lexicon restrictions encountered, without involving the use of a large set of complex rules difficult to analyze.…
Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number…
A state space based design method is given to find strongly stabilizing controllers for multiple-input-multiple-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H-infinity controller in terms of…
We consider the question of the boundedness of matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from two sets of matrices, $A_{i}\in\mathscr{A}$ and $B_{i}\in\mathscr{B}$, due to an appropriate choice of matrices $\{B_{i}\}$. It…
Minimum-uncertainty squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
We revisit the finite time analysis of policy gradient methods in the one of the simplest settings: finite state and action MDPs with a policy class consisting of all stochastic policies and with exact gradient evaluations. There has been…
The steady states of three families of one-dimensional non-equilibrium models with open boundaries, first proposed in [22], are studied using a matrix product formalism. It is shown that their associated quadratic algebras have…
In this paper, we introduce the concept of several products of rough finite state machines. We establish their relationships through coverings and investigate some algebraic properties for these products.
Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and…
The Kosterlitz-Thouless transition is studied from the representation of the systems's ground state wave functions in terms of Matrix Product States for a quantum system on an infinite-size lattice in one spatial dimension. It is found…
For a given unconstrained dynamical system, input redundancy has been recently redefined as the existence of distinct inputs producing identical output for the same initial state. By directly referring to signals, this definition readily…