A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions). These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable. Small, cumulative perturbations can cause quantum states to decohere and introduce errors in the computation, but such small perturbations do not change the braids’ topological properties. This is like the effort required to cut a string and reattach the ends to form a different braid, as opposed to a ball (representing an ordinary quantum particle in four-dimensional spacetime) bumping into a wall. Alexei Kitaev proposed topological quantum computation in 1997. While the elements of a topological quantum computer originate in a purely mathematical realm, experiments in fractional quantum Hall systems indicate these elements may be created in the real world using semiconductors made of gallium arsenide at a temperature of near absolute zero and subjected to strong magnetic fields.

Elements of quantum mechanics

Basics of QM on the way to topological quantum computing.

The qubit

About the qubit on the way to topological quantum computing.

States and operators

Some more about state representation and operators on qubits on the way to topological quantum computing.

Quantum gates

Quantum gates as qubit computations on the way to topological quantum computing.

The Deutsch-Josza quantum algorithm

A simple demonstration of the Deutsch-Josza algorithm demonstrating the potential of quantum computing in machine learning and AI.

Simon's quantum algorithm

Simon's algorithm helps to discover periodicity in functions and does so exponentially faster than any classic algorithm.

Superdense coding

How to use a single qubit to send two bits.

Quantum teleportation

One cannot copy/paste a qubit but you can cut/paste it.