Atomic ions quantum computation

Here, we rq>ort related trapped-ion research at NIST on (1) the study of the dynamics of a two-level atomic system coupled to harmonic atomic motion, (2) the creation and characterization of nonclassical states of motion such as Schrodinger-cat superposition states, and (3) quantum logic for the generation of highly entangled states and for the investigation of scaling in a quantum computer. 

The other approach, called molecular dynamics [249], is essentially based on Newton s mechanics utilized to describe the nuclear motions. Thus, quantum mechanics is discarded (at least for the moment), and classical mechanics is bravely applied to a system of atoms, ions, or molecules pretending these are not quantum objects. For molecules, such classical parametrizations go by the name force field methods, and they make up an important class of computational chemistry [58]. Given the knowledge of an atom s mass m and the force F(f) acting on it at some time t, the atom s acceleration a(t) is calculated according to F(f) = ma i) the force itself is the derivative of the potential energy V(r(f)) such that we have... 

Such a one-dimensional chain of ions where each ion can be selectively excited, can be used as the basis of a quantum computer [1247, 1248]. This can be seen as follows Every computer is based on the two bit states 0 and 1 . In the atomic quantum computer these bit states correspond to an atom in the ground state and in a long living excited state, e.g. a metastable electronic state or an excited hyperfine... 

Many systems are being studied to manipulate quantum information. Some make use of individual atoms cold trapped ions, neutral atoms in optical lattices, atoms in crystals. Other involve particle spins or photons in cavity QED or nonlinear optical setups as well as more exotic ones where geometric combinations of elementary excitations are defined as qubits, such as in topological quantum computing [8]. However, none of these systems has yet emerged as a definitive way to build a quantum information processor. A reason for this is that there is an essential dichotomy we need... 

The time evolution of such a system is described by a 2 °x2 °matrix This demonstrates the complexity of quantum mechanical time evolution. At the same time it becomes clear that quantum systems have - due to the fact that they describe the evolution of all possible states simultaneously - a sort of inner parallelism . Therefore, they will be an ideal medium for real parallel computations as soon as the dynamical behaviour of the quantum states can be controlled in isolation from the rest of the world (with which an interaction is only needed if one wants to read out the result). New experimental possibilities for realizing quantum computers, ranging from neutral atoms interacting with microwaves over optical cavities and nuclear spins to trapped ions, offer most promising perspectives [15]. The chapters by Tino Gramss and Thomas Pellizzari on the Theory of Quantum Computation and First Steps Towards a Realization of Quantum Computers, respectively, will introduce the reader to recent developments in this exciting field. 

Fig. 6.11 A quantum computer proposal in the context of optical cavity quantum electrodynamics. Atoms or ions are used to represent the qubits and are trapped within two mirrors so as to communicate with each other by photon exchange. The qubits have to be addressed individually by laser beams.

The electron distribution, p(r), has been computed by quantum mechanics for all neutral atoms and many ions and the values off(Q), as well as coefficients for a useful empirical approximation, are tabulated in the International Tables for Crystallography vol C [2]. In general,is a maximum equal to the nuclear charge, Z, lor Q = 0 and decreases monotonically with increasing Q. 

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