Introduction to Quantum Error Correction

In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied for fault tolerance. Considering the capabilities of currently available quantum technology, the requirements appear daunting. But the idea of ``subsystems'' shows that these requirements can be met in many different, and often unexpected ways.Comment: 44 pages, to appear in LA Science. Hyperlinked PDF at http://www.c3.lanl.gov/~knill/qip/ecprhtml/ecprpdf.pdf, HTML at http://www.c3.lanl.gov/~knill/qip/ecprhtm

Spectroscopic study of early-type multiple stellar systems II. New binary subsystems

Context. This work is part of a long-term spectroscopic study of a sample of 30 multiple stars with early-type components. In this second paper we present the results of six multiple systems in which new stellar components have been detected. Aims. The main aim is to increase the knowledge of stellar properties and dynamical structure of early-type multiple stellar systems. Methods. Using spectroscopic observations taken over a time baseline of more than 5 years we measured RVs by cross-correlations and applied a spectral disentangling method to double-lined systems. Besides the discovery of objects with double-lined spectra, the existence of new spectroscopic subsystems have been inferred from the radial velocity variations of single-lined components and through the variation of the barycentric velocity of double-lined subsystems. Orbital elements have been calculated when possible. Results. Seven new stellar components and two members that we expect to confirm with new observations have been discovered in the six studied multiples. We present orbital parameters for two double-lined binaries and preliminary orbits for three single-lined spectroscopic binaries. Five of the six analysed systems are quadruples, while the remaining has five components distributed in four hierarchical levels. These multiplicity orders are in fact lower limits, since these systems lack high-resolution visual observations and additional hierarchical level might exist in that separation range. Conclusions. The six analysed systems have greater multiplicity degree and a more complex hierarchical structure than previously known, which suggests that high-order multiple systems are significantly more frequent that it is currently estimated. The long term spectroscopic monitoring of multiple systems has shown to be useful for the detection of companions in intermediate hierarchical levels.Comment: 13 pages, 9 figures. Accepted by Astronomy and Astrophysic