Will Decoherence Kill Quantum Computing ?

Given the recent recipients of The Wolf Prize in Physics, a question must be asked:

Is Decoherence in QM too large an obstacle to overcome in the creation of significant viable quantum computers?

Currently we can build them in low numbers of qubits.

Briefly.

Before Decoherence sets in.

From Wikipedia:

A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons, whose world lines cross over 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. The smallest perturbations can cause a quantum particle to decohere and introduce errors in the computation, such small perturbations do not change the topological properties of the braids. 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) simply bumping into a wall. While the elements of a topological quantum computer originate in a purely mathematical realm, recent experiments indicate these elements can be created in the real world using semiconductors made of gallium arsenide near absolute zero and subjected to strong magnetic fields.