225 research outputs found
SU(3) Revisited
The ``'' matrices for all states of the two fundamental representations
and octet are shown in the generalized Euler angle parameterization. The
raising and lowering operators are given in terms of linear combinations of the
left invariant vector fields of the group manifold in this parameterization.
Using these differential operators the highest weight state of an arbitrary
irreducible representation is found and a description of the calculation of
Clebsch-Gordon coefficients is given.Comment: 22 pages LaTe
Geometric phases in dressed state quantum computation
Geometric phases arise naturally in a variety of quantum systems with
observable consequences. They also arise in quantum computations when dressed
states are used in gating operations. Here we show how they arise in these
gating operations and how one may take advantage of the dressed states
producing them. Specifically, we show that that for a given, but arbitrary
Hamiltonian, and at an arbitrary time {\tau}, there always exists a set of
dressed states such that a given gate operation can be performed by the
Hamiltonian up to a phase {\phi}. The phase is a sum of a dynamical phase and a
geometric phase. We illustrate the new phase for several systems.Comment: 4 pages, 2 figure
High Fidelity State Transfer Over an Unmodulated Linear XY Spin Chain
We provide a class of initial encodings that can be sent with a high fidelity
over an unmodulated, linear, XY spin chain. As an example, an average fidelity
of ninety-six percent can be obtained using an eleven-spin encoding to transmit
a state over a chain containing ten-thousand spins. An analysis of the magnetic
field dependence is given, and conditions for field optimization are provided.Comment: Replaced with published version. 8 pages, 5 figure
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