On 2/3/2016 2:34 PM, John Clark wrote:
A recent paper in Nature Communications gives more evidence that
Quantum Computers might produce as big a revolution as
Nanotechnology, Seth Lloyd, Silvano Garnerone and Paolo Zanardi have
found a Quantum algorithms for the topological analysis of data:
http://www.nature.com/ncomms/2016/160125/ncomms10138/full/ncomms10138.html
Seth Lloyd, the man who found the Quantum factoring algorithm some
years back
The one called Shor's algorithm?
Brent
says "In a topological description, basic features of the data (How
many holes does it have? How are the different parts connected?) are
considered the same no matter how much they are stretched, compressed,
or distorted. It is often these fundamental topological attributes
that are important in trying to reconstruct the underlying patterns in
the real world
that the data are supposed to represent. It doesn’t matter what kind
of data set is being analyzed. The topological approach of looking for
connections and holes works whether it’s an actual physical hole, or
the data represents a logical argument and there’s a hole in the
argument. This will find both kinds of holes.”
But Lloyd says the topological approach is too demanding for
conventional computers "Topological analysis represents a crucial way
of getting at the significant features of the data, but it’s
computationally very expensive. This is where quantum mechanics kicks
in. The new quantum-based approach could exponentially speed up such
calculations." Lloyd gives this example: "If you have a data set with
300 points, a conventional approach to analyzing all the topological
features in that system would require a computer the size of the
universe. That is, it would take 2300 (two to the 300th power)
processing units — approximately the number of all the particles in
the universe. In other words, the problem is simply not solvable in
that way. That’s where our algorithm kicks in. Solving the same
problem with the new system, using a quantum computer, would require
just 300 quantum bits — and a device this size may be achieved in the
next few years. Our algorithm shows that you don’t need a big quantum
computer to kick some serious topological butt.”
John K Clark
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