Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

The Study of Magnesium Substitution Effect on Physicochemical Properties of Hydroxyapatite

In the present study, pure and Mg-substitutedhydroxyapatite powders made up of needle-like and plate-likeparticles, respectively, have been synthesized by wet chemicalprecipitation of CaO, MgO and H3PO4. The influence of differentamounts of MgO addition into synthesis media on properties ofas-synthesized and sintered powders has been evaluated.Through the phase and chemical composition analysis it hasbeen determined that the prepared powders contain variousamounts of Mg (in the range between 0.21–4.72 wt%). Thesubstitution of Mg promoted the decomposition ofhydroxyapatite to β-tricalcium phosphate