Kempe
Le Mercredi 7 Juin 2000 à 10h30
au LRI, salle 101
University of California, Berkeley
Universal quantum computation on irreducible subspaces
Résumé/Abstract :
The discovery that quantum information encoded over quantum systems can exhibit
unexpected computational and information theoretic properties (eg. Shor's
factoring algorithm, quantum-teleportation) has led to an explosion of interest
in understanding and exploiting the "quantumness" of nature. To proceed beyond
mere theoretical concepts to the realm of testable and viable implementation
quantum coherences have to be protected against noise arising from the coupling
of a physical system to the environment. To this end the theory of
error-correcting codes has been successfully applied and it has been shown that
fault-tolerant quantum computing on encoded quantum states is possible. As an
alternative approach Decoherence Free Subsystems (DFS) have been developed as a
passive way to escape decoherence. They are a "quiet" corner in quantum
state-space (Hilbert-space) unaffected by noise and as such are ideal to store
quantum information. In order to use them for quantum computation, however, it
has to be shown that quantum gates - general unitary operations - can be
implemented fault-tolerantly and out of small constituents (gates that affect
one or two quantum-bits only). In this talk I will show how to achieve
universal computation on DFSs making use of tools of representation theory of
SU(2). As interesting by-products I will show how one single gate - the
exchange interaction - is "asymptotically" universal (even outside the
framework of DFS) and how we can operate many DFS quantum-computers "in
parallel".