Quantum Counting on the Complete Bipartite Graph

Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover's algorithm because its non-trivial eigenvalues are dependent on the number of marked elements. Since Grover's algorithm can be viewed as a quantum walk on a complete graph, a natural way to extend quantum counting is to use the evolution operator of quantum-walk-based search on non-complete graphs instead of Grover's operator. In this paper, we explore this extension by analyzing the coined quantum walk on the complete bipartite graph with an arbitrary number of marked vertices. We show that some eigenvalues of the evolution operator depend on the number of marked vertices and using this fact we show that the quantum phase estimation can be used to obtain the number of marked vertices. The time complexity for estimating the number of marked vertices in the bipartite graph with our algorithm aligns closely with that of the original quantum counting algorithm.Comment: 12 pages, 3 figures, title changed, references adde

Portuguese colonial architectural archives at the Arquivo Histórico Ultramarino, mid 19th century - 1975

The Arquivo Histórico Ultramarino (AHU - Overseas Historical Archive) holds Portuguese architectural and also engineering archival records created and managed by the Colonial Public Offices seated in Lisbon, dating back to the end of the 16th century to 1975. The archives from the offices that performed duties in the Portuguese colonies remained there, even after their independence from Portugal. Until recently, records dated from the mid 19th century onwards were poorly identified, a panorama that changed over the last decade. These records are related to Angola, Cabo Verde, Guinea-Bissao, São Tomé and Príncipe, Mozambique, previous Portugese possessions in India, Macao and East Timor. The AHU hosted two funded projects by the Portuguese Foundation to Science and Technology (FCT) submitted by the Centre for Socioeconomic and Territorial Studies from the Lisbon University Institute (DINÂMIA'CET-IUL). The participation of the AHU in both projects allowed processing these records bulk. The first one was “The Colonial Urbanization Offices”, a three year project which benefited from the collaboration of five archival fellowships during nearly two years. The second project is the “Coast to Coast”, has a similar duration to the previous and will be ongoing until December 2019, with the contribution of an archival fellowship. Two archivists of the AHU participated in these projects as well, supervising the archival processing as researchers.info:eu-repo/semantics/publishedVersio

Mixing Times in Quantum Walks on Two-Dimensional Grids

Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an exact expression for the stationary distribution of the coherent walk over odd-sided lattices is obtained after solving the eigenproblem for the evolution operator for this particular graph. The limiting distribution and mixing time of a quantum walk with a coin operator modified as in the abstract search algorithm are obtained numerically. On the basis of these results, the relation between the mixing time of the modified walk and the running time of the corresponding abstract search algorithm is discussed.Comment: 11 page

Colheita de girassol com plataforma de milho adaptada.

Adaptações feitas na plataforma de milho; Funcionamento da plataforma de milho adaptada; Vantagens da plataforma de milho adaptada; Indicações técnicas para a colheita de girassol.bitstream/item/60603/1/Folder-06-2005.pdf1 folder