A model of quantum computing where information is processed by braiding anyons, offering inherent error protection.Topological quantum computation is a model of quantum computing that uses anyons—quasiparticles that exist only in two-dimensional systems—to store and process information. Unlike ordinary particles, anyons have exotic statistics: when two are exchanged, their quantum state changes by a phase or a unitary transformation that depends on the topology of the exchange path, not the details of the trajectory. This topological property makes the information encoded in the braiding of anyons inherently robust against local perturbations, such as noise or decoherence, because the information is stored non-locally in the global structure of the braid.
The idea was proposed in the late 1990s by Alexei Kitaev and, independently, by Michael Freedman and collaborators, building on earlier work on anyons and topological quantum field theory. Kitaev's 1997 paper on fault-tolerant quantum computation with anyons laid the foundation, and the concept has since been developed theoretically and experimentally.
In a topological quantum computer, qubits are encoded in the collective state of a set of anyons, and quantum gates are performed by braiding the anyons around each other in a specific sequence. The result of a computation is determined by the topology of the braid, which is insensitive to small disturbances in the positions or interactions of the anyons. This provides a natural form of error correction: as long as the anyons are kept far apart and the temperature is low enough to prevent unwanted anyon pairs, the quantum information remains protected. The final readout is done by bringing anyons together and measuring their fusion outcomes, which reveals the result of the computation.
Topological quantum computation is a leading candidate for building fault-tolerant quantum computers, and it is being pursued by companies like Microsoft, which has invested in research on Majorana fermions—a type of anyon—in semiconductor-superconductor heterostructures.
The braiding of anyons in topological quantum computation is mathematically equivalent to the braid group, which is also used to describe how strands of hair or rope can be intertwined, but in this case, the braids perform logical operations.
