7,811 research outputs found
Towards topological quantum computer
One of the principal obstacles on the way to quantum computers is the lack of
distinguished basis in the space of unitary evolutions and thus the lack of the
commonly accepted set of basic operations (universal gates). A natural choice,
however, is at hand: it is provided by the quantum R-matrices, the entangling
deformations of non-entangling (classical) permutations, distinguished from the
points of view of group theory, integrable systems and modern theory of
non-perturbative calculations in quantum field and string theory. Observables
in this case are (square modules of) the knot polynomials, and their pronounced
integrality properties could provide a key to error correction. We suggest to
use R-matrices acting in the space of irreducible representations, which are
unitary for the real-valued couplings in Chern-Simons theory, to build a
topological version of quantum computing.Comment: 14 page
On the Continuum Limit of the Conformal Matrix Models
The double scaling limit of a new class of the multi-matrix models proposed
in \cite{MMM91}, which possess the -symmetry at the discrete level, is
investigated in details. These models are demonstrated to fall into the same
universality class as the standard multi-matrix models. In particular, the
transformation of the W-algebra at the discrete level into the continuum one of
the paper \cite{FKN91a} is proposed, the corresponding partition functions
being compared. All calculations are demonstrated in full in the first
non-trivial case of -constraints.Comment: FIAN/TD-5/92, LaTeX, 32p
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