Related papers: Detecting topological order in a ground state wave…
Topologically ordered materials may serve as a platform for new quantum technologies such as fault-tolerant quantum computers. To fulfil this promise, efficient and general methods are needed to discover and classify new topological phases…
While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse…
In this work we provide a general methodology to directly measure topological order in cold atom systems. As an application we propose the realisation of a characteristic topological model, introduced by Haldane, using optical lattices…
Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…
We show how to generalize the concepts of identifying and classifying symmetry protected topological phases in 1D to the case of an arbitrary mixed state. The pure state concepts are reviewed using a concrete spin-1 model. For the mixed…
In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…
We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace,…
We propose and investigate a new algorithm for quantifying the topological properties of cosmological density fluctuations. We first motivate this algorithm by drawing a formal distinction between two definitions of relevant topological…
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…
Multi-wavefunction overlaps -- generalizations of the quantum mechanical inner product for more than two quantum many-body states -- are valuable tools for studying many-body physics. In this paper, we investigate the multi-wavefunction…
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: How much…
Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological…
A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it…
In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…
The string-net approach by Levin and Wen and the local unitary transformation approach by Chen, Gu and Wen provided ways to systematically label non-chiral topological orders in 2D. In those approaches, different topologically ordered…
The exact range of the joined values of several R\'{e}nyi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied. Like in the case when only two orders of R\'{e}nyi entropies…
Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. While various tomographic methods such as classical shadow and MPS tomography have shown…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
We consider 1d Hamiltonian systems whose ground states display symmetry protected topological order. We show that ground states within the topological phase cannot be connected with each other through LOCC between a bipartition of the…