310 research outputs found

### (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 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

### Static Colored SU(2) Sources in (1+1)-Dimensions - An Analytic Solution in the Electric Representation

Within the Schroedinger Electric Representation we analytically calculate the
complete wave functional obeying Gauss' law with static SU(2) sources in
(1+1)-dimensions. The effective potential is found to be linear in the distance
between the sources as expected.Comment: 10 pages, 4 figs, REVTE

### Mixed state non-Abelian holonomy for subsystems

Non-Abelian holonomy in dynamical systems may arise in adiabatic transport of
energetically degenerate sets of states. We examine such a holonomy structure
for mixtures of energetically degenerate quantal states. We demonstrate that
this structure has a natural interpretation in terms of the standard
Wilczek-Zee holonomy associated with a certain class of Hamiltonians that
couple the system to an ancilla. The mixed state holonomy is analysed for
holonomic quantum computation using ion traps.Comment: Minor changes, journal reference adde

### Realization of Arbitrary Gates in Holonomic Quantum Computation

Among the many proposals for the realization of a quantum computer, holonomic
quantum computation (HQC) is distinguished from the rest in that it is
geometrical in nature and thus expected to be robust against decoherence. Here
we analyze the realization of various quantum gates by solving the inverse
problem: Given a unitary matrix, we develop a formalism by which we find loops
in the parameter space generating this matrix as a holonomy. We demonstrate for
the first time that such a one-qubit gate as the Hadamard gate and such
two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier
transformation can be obtained with a single loop.Comment: 8 pages, 6 figure

### Quantum computation with trapped ions in an optical cavity

Two-qubit logical gates are proposed on the basis of two atoms trapped in a
cavity setup. Losses in the interaction by spontaneous transitions are
efficiently suppressed by employing adiabatic transitions and the Zeno effect.
Dynamical and geometrical conditional phase gates are suggested. This method
provides fidelity and a success rate of its gates very close to unity. Hence,
it is suitable for performing quantum computation.Comment: 4 pages, 5 figures, REVTEX, second part modified, typos correcte

### Entanglement of two qubits in a relativistic orbit

The creation and destruction of entanglement between a pair of interacting
two-level detectors accelerating about diametrically opposite points of a
circular path is investigated. It is found that any non-zero acceleration has
the effect of suppressing the vacuum entanglement and enhancing the
acceleration radiation thereby reducing the entangling capacity of the
detectors. Given that for large accelerations the acceleration radiation is the
dominant effect, we investigate the evolution of a two detector system
initially prepared in a Bell state using a perturbative mater equation and
treating the vacuum fluctuations as an unobserved environment. A general
function for the concurrence is obtained for stationary and symmetric
worldlines in flatspace. The entanglement sudden death time is computed.Comment: v2: Some typo's fixed, figures compressed to smaller filesize and
added some references

### Refocusing schemes for holonomic quantum computation in presence of dissipation

The effects of dissipation on a holonomic quantum computation scheme are
analyzed within the quantum-jump approach. We extend to the non-Abelian case
the refocusing strategies formerly introduced for (Abelian) geometric
computation. We show how double loop symmetrization schemes allow one to get
rid of the unwanted influence of dissipation in the no-jump trajectory.Comment: 4 pages, revtex

### Decoherence-free dynamical and geometrical entangling phase gates

It is shown that entangling two-qubit phase gates for quantum computation
with atoms inside a resonant optical cavity can be generated via common laser
addressing, essentially, within one step. The obtained dynamical or geometrical
phases are produced by an evolution that is robust against dissipation in form
of spontaneous emission from the atoms and the cavity and demonstrates
resilience against fluctuations of control parameters. This is achieved by
using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903
(2002)] and employing entangling Raman- or STIRAP-like transitions that
restrict the time evolution of the system onto stable ground states.Comment: 10 pages, 9 figures, REVTEX, Eq. (20) correcte

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