510 research outputs found
Geometrical phases for the G(4,2) Grassmannian manifold
We generalize the usual abelian Berry phase generated for example in a system
with two non-degenerate states to the case of a system with two doubly
degenerate energy eigenspaces. The parametric manifold describing the space of
states of the first case is formally given by the G(2,1) Grassmannian manifold,
while for the generalized system it is given by the G(4,2) one. For the latter
manifold which exhibits a much richer structure than its abelian counterpart we
calculate the connection components, the field strength and the associated
geometrical phases that evolve non-trivially both of the degenerate
eigenspaces. A simple atomic model is proposed for their physical
implementation.Comment: 7 pages, 1 figure, REVTEX, minor typos corrected, to appear in Jour.
Math. Phy
Stability of holonomic quantum computations
We study the stability of holonomic quantum computations with respect to
errors in assignment of control parameters. The general expression for fidelity
is obtaned. In the small errors limit the simple formulae for the fidelity
decrease rate is derived.Comment: 7 page
Quantum Holonomies for Quantum Computing
Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum
information processing. In the HQC strategy information is encoded in
degenerate eigen-spaces of a parametric family of Hamiltonians. The
computational network of unitary quantum gates is realized by driving
adiabatically the Hamiltonian parameters along loops in a control manifold. By
properly designing such loops the non-trivial curvature of the underlying
bundle geometry gives rise to unitary transformations i.e., holonomies that
implement the desired unitary transformations. Conditions necessary for
universal QC are stated in terms of the curvature associated to the non-abelian
gauge potential (connection) over the control manifold. In view of their
geometrical nature the holonomic gates are robust against several kind of
perturbations and imperfections. This fact along with the adiabatic fashion in
which gates are performed makes in principle HQC an appealing way towards
universal fault-tolerant QC.Comment: 16 pages, 2 figures, REVTE
(1+1)-Dimensional SU(N) Static Sources in E and A Representations
Here is presented a detailed work on the (1+1) dimensional SU(N) Yang-Mills
theory with static sources. By studying the structure of the SU(N) group and of
the Gauss' law we construct in the electric representation the appropriate wave
functionals, which are simultaneously eigenstates of the Gauss' operator and of
the Hamiltonian. The Fourier transformation between the A- and the
E-representations connecting the Wilson line and a superposition of our
solutions is given.Comment: 10 pages, no figures, REVTEX, as in Phys. Rev.
Quantum computation with abelian anyons on the honeycomb lattice
We consider a two-dimensional spin system that exhibits abelian anyonic
excitations. Manipulations of these excitations enable the construction of a
quantum computational model. While the one-qubit gates are performed
dynamically the model offers the advantage of having a two-qubit gate that is
of topological nature. The transport and braiding of anyons on the lattice can
be performed adiabatically enjoying the robust characteristics of geometrical
evolutions. The same control procedures can be used when dealing with
non-abelian anyons. A possible implementation of the manipulations with optical
lattices is developed.Comment: 4 pages, 3 figures, REVTEX, improved presentation and implementatio
The Coulomb Branch of Yang-Mills Theory from the Schroedinger Representation
The Coulomb branch of the potential between two static colored sources is
calculated for the Yang-Mills theory using the electric Schroedinger
representation.Comment: 4 pages, no figures, REVTEX, as in Phys. Lett.
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