Related papers: Topological order and topological entropy in class…
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…
Topological order is a new type order that beyond Landau's symmetry breaking theory. The topological entanglement entropy provides a universal quantum number to characterize the topological order in a system. The topological entanglement…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
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,…
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 the concept of nested topological order in a class of exact quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry. The topological order present in the models can be partially destroyed by introducing a…
Concepts of information theory are increasingly used to characterize collective phenomena in condensed matter systems, such as the use of entanglement entropies to identify emergent topological order in interacting quantum many-body…
We introduce the concept of composite topological order in multicomponent systems. In such a state topological order appears only in higher-than-usual composites, with no topological order in elementary fields. We propose that such a state…
We determine the conditions under which topological order survives a rapid quantum quench. Specifically, we consider the case where a quantum spin system is prepared in the ground state of the Toric Code Model and, after the quench, it…
In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…
It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
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…
Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…
We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
Ordered phases of matter have close connections to computation. Two prominent examples are spin glass order, with wide-ranging applications in machine learning and optimization, and topological order, closely related to quantum error…
Topological ordered states are exotic quantum states of matter that defy the usual description in terms of symmetry breaking and local order parameters. The type or order they feature is of non-local, topological nature, and it allows such…
Topological way of thinking now goes beyond conventional solid materials, and topological characterization of classical mechanical systems governed by Newton's equation of motion begins to attract much attention. To have a deeper insight on…