A coffeecup can be deformed into a donut without changing its ‘topology’. The topological state of a Möbius ring remains unaffected under deformations, the ring needs to be cut and untwisted for the state to change. In general, it takes something severe in order to change topology. Such protection against changes is exactly what one is looking for in quantum technology.
Quantum states are fragile and tend to decohere quickly. This decoherence would be suppressed if the quantum state would somehow be stored in a topological variable. The roadmap “Topological Quantum Computing” aims at such topological protection. The five-year objective of the Topological Roadmap is the realization of a topological qubit encoding a quantum state that is protected for at least a second. As building blocks we use pairs of Majoranas that emerge in semiconductor nanowires in contact with a superconductor. A small circuit with Majoranas enables to demonstrate non-Abelian statistics. This involves exchanging, or braiding, Majoranas around each other. Braiding can change the quantum state in a controlled manner which consitutes a quantum gate operation. We will test the stability of this quantum gate and aim to demonstrate that conventional decoherence plays no role in topologically protected states. The Topological Roadmap is in close collaboration with Microsoft Research Station Q, located in Santa Barbara and headed by Dr. Michael Freedman.