[ExI] Quantum Computers

John Clark johnkclark at gmail.com
Wed Feb 3 18:44:15 UTC 2016

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:


Seth Lloyd, the man who found the Quantum factoring algorithm some years
back 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 dataset 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 dataset 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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