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...

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

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

intrinsic topological insulator behavior in actual experiments. Topological quantum computer Topological quantum field theory Topological quantum number Photonic...

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

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...

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

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...

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

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...

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

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

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

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

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

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

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

invariants in mathematics. Topological quantum field theories (TQFTs) applicable to the frontier research of topological quantum matters include Chern-Simons-Witten...

category that plays a role in the areas of topological quantum field theory, conformal field theory, and quantum algebra. Modular tensor categories were...

signal conduction within neurons as pressure solitons. A topological soliton, also called a topological defect, is any solution of a set of partial differential...

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

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

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

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

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

fermionic topological phases. Since 2021 Kitaev has worked with Google Quantum AI on their experimental effort of realizing fault-tolerant quantum computation...

Alexei Kitaev's topological quantum codes, introduced in 1997 as the toric code, and the more general idea of a topological quantum computer are the...