Topological quantum computer
These anyons' world lines intertwine to form braids in a three-dimensional spacetime (one temporal and two spatial dimensions).
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.
As of 2022, Microsoft is the only major technology company with a history of research and development in topological quantum computing.
Thus, the world lines of two anyons cannot intersect or merge, which allows their paths to form stable braids in space-time.
Therefore, the quantum information which is stored in the state of the system is impervious to small errors in the trajectories.
[5] In 2005, Sankar Das Sarma, Michael Freedman, and Chetan Nayak proposed a quantum Hall device that would realize a topological qubit.
In 2005 Vladimir J. Goldman, Fernando E. Camino, and Wei Zhou[6] claimed to have created and observed the first experimental evidence for using a fractional quantum Hall effect to create actual anyons, although others have suggested their results could be the product of phenomena not involving anyons.
Non-abelian anyons, a species required for topological quantum computers, have yet to be experimentally confirmed.
Quanta Magazine stated in 2021 that "no one has convincingly shown the existence of even a single (Majorana zero-mode) quasiparticle",[9] although in 2023 a new article[10] by the magazine has covered some preprints by Google[11] and Quantinuum[12] claiming the realization of non-abelian anyons on quantum processors, the first used a toric code with twist defects as a topological degeneracy (or topological defect) while the second used a different but related protocol both of which can be understood as Majorana bound states in quantum error correction.
[13][14][15] They found that a conventional quantum computer device, given an error-free operation of its logic circuits, will give a solution with an absolute level of accuracy, whereas a topological quantum computing device with flawless operation will give the solution with only a finite level of accuracy.
However, any level of precision for the answer can be obtained by adding more braid twists (logic circuits) to the topological quantum computer, in a simple linear relationship.
In other words, a reasonable increase in elements (braid twists) can achieve a high degree of accuracy in the answer.
Actual computation [gates] are done by the edge states of a fractional quantum Hall effect.
Controlling these errors is simply a matter of separating the anyons to a distance where the rate of interfering strays drops to near zero.
[19] However, because we wish to encode these three anyon states as superpositions of 0 and 1, we need to limit the basis to a two-dimensional Hilbert space.
Similarly, we know that if we braid anyons around each-other a certain number of times, this will lead back to the same state.
[22] In 2023, Microsoft Quantum researchers published a paper in Physical Review that described a new device that can represent a logical qubit with hardware stability, measuring a phase of matter consistent with the observation of topological superconductivity and Majorana zero modes.
[23] The scientists reported that "such devices have demonstrated low enough disorder to pass the topological gap protocol, proving the technology is viable.
"[24] This publication has been criticized by other scientists for not providing sufficient evidence for Majorana modes as in previous papers.
