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

X-ray line ratios and double-ratios to non-destructively probe surface gold enrichment in gold alloys

The presence of surface layers with altered chemical composition in gold alloys is investigated exploiting X-ray line ratios populated in energy-dispersive X-ray fluorescence investigations. We show that the use of the Ag (Lα/Kα) X-ray ratio and the Ag (Lα/Kα)/Au (Mα/Lα) double-ratio allows to ascertain surface gold enrichment that can be attributed to a depletion of silver concentration in a thin (<1μm) surface layer of the material. The formalism developed in this paper is exploited to probe the chemical composition of precious protohistoric gold findings belonging to the largest complex of Bronze Age gold ornaments ever found in Italy. The results support the findings of complementary micrography investigations, performed on the same collection, and are relevant to contribute to understanding techniques used in ancient metallurgy