unlike last night a genuinely interesting debate: caltech says yes while hebrew university says no...,

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-dimensionalspacetime (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, 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 infractional 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.