physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is...

In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed...

field of computer science, a pre-topological order or pre-topological ordering of a directed graph is a linear ordering of its vertices such that if there...

called the root of the arborescence. Topological sorting is the algorithmic problem of finding a topological ordering of a given DAG. It can be solved in...

to accept a proper class as a topological space, then the class of all ordinals is also a topological space for the order topology.) The set of limit points...

processors, the first used a toric code with twist defects as a topological degenerancy (or topological defect) while the second used a different but related protocol...

Symmetry-protected topological (SPT) order is a kind of order in zero-temperature quantum-mechanical states of matter that have a symmetry and a finite...

magnetic field. In this way, topological insulators are an example of symmetry-protected topological order. So-called "topological invariants", taking values...

invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension, which allows...

state. So the topological entanglement entropy links topological order with pattern of long range quantum entanglements. Given a topologically ordered state...