Talk abstract:
The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously. This coherence is lost as a quantum system interacts with its environment.
In classical computing one can assemble computers that are much more reliable than any of their individual components by exploiting error correcting codes. In quantum computing this was thought to be precluded by the Heisenberg Uncertainty Principle as recently as 2 years ago. But the development of quantum error correcting codes has completely turned this around.
This talk will describe a beautiful group theoretic framework that simplifies the presentation of known quantum error correcting codes and greatly facilitates the construction of new examples.
Sources
Below are the materials used during the talk.
Early work of Rolf Landauer and Charles Bennett of IBM T.J. Watson Research Lab on the physics of information processing circuits. Every 2 years for the past 50 years computers have become twice as fast while components have become twice as small.
As the components of computer circuits become very small their description must be given by quantum mechanics. Today experimental physicists are demonstrating control over the kind of events where one or two atoms are manipulated with one or two photons.
Early 1980s: Paul Benioff of Argonne Natl. Lab and David Deutsch of the Univ. of Oxford begin to model quantum computers to find out how they might differ from classical computers.
1994: Peter Shor of AT&T Labs exploits quantum coherence to find fast algorithms for factoring integers on a quantum computer. The first example of an important problem that a quantum computer can solve faster than a classical computer.
Why is this problem important?
If we look back 25 years it was generally believed that private communication over a public channel was impossible unless the two parties had agreed beforehand on some random secret information noone else knew. The invention of public key cryptography in 1976 completely changed this picture and made electronic commerce a real possibility, but the security of RSA rests on the presumed intractability of factoring.
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