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Knots, World-Lines, and Quantum Computation

Professor Steve Simon ( Department of Physics, University of Oxford )
In certain two dimensional "topological" phases of matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, particle world lines in space-time can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link.  While sounding rather exotic, we believe that such phases of matter not only exist, but have actually been observed in quantum Hall experiments, and could provide a uniquely practical route to building a quantum computer.  Possibilities have also been proposed for creating similar physics in systems ranging from superfluid helium to strontium ruthenate to spin systems to cold atoms.

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