In physics, a topological quantum number (also called topological charge) is any quantity, in a physical theory, that takes on only one of a discrete...

to topological field theory. In condensed matter physics, topological quantum field theories are the low-energy effective theories of topologically ordered...

suggest a quantum information origin of elementary particles; (4) topological entanglement entropy that reveals the entanglement origin of topological order...

A topological quantum computer is a type of quantum computer. It utilizes anyons, a type of quasiparticle that occurs in two-dimensional systems. The...

group in 2D topological insulators in 2007. Later sets of theoretical models for the 2D topological insulator (also known as the quantum spin Hall insulators)...

In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in...

idea of topological quantum field theory. There are two main versions of topological string theory: the topological A-model and the topological B-model...

perturbations. Topological degeneracy can be used to protect qubits which allows topological quantum computation. It is believed that topological degeneracy...

classified by the winding number or topological charge (topological invariant and/or topological quantum number). A point's winding number with respect to a polygon...

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

linking number is determined by the homology class of the other curve. In physics, the linking number is an example of a topological quantum number. Given...

and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms...

map from space to some order parameter set) is one example of a topological quantum number. The simplest and most important case is the degree of a continuous...

algebraic theory of topological quantum information is a collection of algebraic techniques developed and applied to topological aspects of condensed...

These topological sectors correspond to the robustly quantized phases. The quantum Hall transitions can then be understood by looking at the topological excitations...

with topological spaces that allow tensor products. Topological entanglement involving linking and braiding can be intuitively related to quantum entanglement...

macroscopic quantum phenomena are superfluidity and superconductivity; other examples include the quantum Hall effect, Josephson effect and topological order...

The periodic table of topological insulators and topological superconductors, also called tenfold classification of topological insulators and superconductors...

quantum algorithms include phase kick-back, phase estimation, the quantum Fourier transform, quantum walks, amplitude amplification and topological quantum...

; Samajdar, R.; Omran, A. (2021-12-03). "Probing topological spin liquids on a programmable quantum simulator". Science. 374 (6572): 1242–1247. arXiv:2104...

which arises out of topological properties of the material band structure. These effects are observed in systems called quantum anomalous Hall insulators...

The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type. It was discovered first by mathematical physicist Albert...

"minimum". Neuromorphic quantum computing and quantum computing share similar physical properties during computation. A topological quantum computer decomposes...

Z2 spin liquid, is proposed, which realizes the simplest topological order – Z2 topological order. Both chiral spin state and Z2 spin liquid state have...

considerations. A topological group is a locally compact group if the underlying topological space is locally compact and Hausdorff; a topological group is abelian...

statistics. The fractional quantum Hall effect continues to be influential in theories about topological order. Certain fractional quantum Hall phases appear...

the winding number, the topological charge (although it is unrelated to 'charge' in the electrical sense), the topological quantum number (although it...

and most well studied of the quantum double models. It is also the simplest example of topological order—Z2 topological order (first studied in the context...

Andreas P.; Ryu, Shinsei (August 31, 2016). "Classification of topological quantum matter with symmetries". Reviews of Modern Physics. 88 (3): 035005...

implement topological quantum error correction. Topological cluster state computation is closely related to Kitaev's toric code, as the 3D topological cluster...