Direct Application of the Phase Estimation Algorithm to Find the Eigenvalues of the Hamiltonians

The eigenvalue of a Hamiltonian, $\mathcal{H}$, can be estimated through the phase estimation algorithm given the matrix exponential of the Hamiltonian, $exp(-i\mathcal{H})$. The difficulty of this exponentiation impedes the applications of the phase estimation algorithm particularly when $\mathcal{H}$ is composed of non-commuting terms. In this paper, we present a method to use the Hamiltonian matrix directly in the phase estimation algorithm by using an ancilla based framework: In this framework, we also show how to find the power of the Hamiltonian matrix-which is necessary in the phase estimation algorithm-through the successive applications. This may eliminate the necessity of matrix exponential for the phase estimation algorithm and therefore provide an efficient way to estimate the eigenvalues of particular Hamiltonians. The classical and quantum algorithmic complexities of the framework are analyzed for the Hamiltonians which can be written as a sum of simple unitary matrices and shown that a Hamiltonian of order $2^n$ written as a sum of $L$ number of simple terms can be used in the phase estimation algorithm with $(n+1+logL)$ number of qubits and $O(2^anL)$ number of quantum operations, where $a$ is the number of iterations in the phase estimation. In addition, we use the Hamiltonian of the hydrogen molecule as an example system and present the simulation results for finding its ground state energy.Comment: 10 pages, 3 figure

Greater Anis (Crotophaga major) Commensal Foraging with Freshwater Fish in the Pantanal Floodplain, Brazil

Foraging associations between birds and other groups of animals have been widely reported in the literature. I report the first observation of a foraging tactic involving a flock of Greater Ani (Crotophaga major), which deliberately followed fish along an artificial ditch in the Pantanal wetlands, feeding on animals flushed by the movement of the vegetation on the ditch banks. Further observations of the feeding behavior and foraging tactics of Greater Anis are necessary to ascertain if this type of behavior is a frequent event or merely sporadic. Received 22 June 2010. Accepted 11 October 2010

Predation of herps by spiders (Araneae) in the Brazilian Cerrado.

Two events of predation of herps by spiders in the Brazilian Cerrado are reported here. A lizard Micrablepharus atticolus (Sauria: Gymnophthalmidae) was found being preyed upon by Lycosa erythrognatha (Araneae: Lycosidae) and a frog Physalaemus cuvieri (Anura: Leiuperidae) was seen being preyed upon by Ancylometes sp. (Araneae: Ctenidae)

Contribuição ao Conhecimento da Distribuição Geográfica do Tatu-de-Rabo-Mole-Grande Cabassous tatouay no Brasil: Revisão, Status e Comentários sobre a Espécie

The greater naked-tailed armadillo Cabassous tatouay is one of the least-known armadillo species. Field records are rare, if not controversial, and only few specimens exist in scientific collections in Brazil. This species is listed in the Brazilian Red List of Threatened Species as well as in six official Brazilian state Red Lists. Fieldwork was performed between 2005 and 2008 to monitor wildlife in the central-western region of São Paulo State. Cabassous tatouay was registered in three opportunities, in the municipalities of Agudos, Borebi and Avare, and ecological and morphometrical data were registered. Although this species tolerates altered habitats, the scarce field records may be related to its habits and have led to the lack of basic information on greater naked-tailed armadillos. This communication provides important ecological and biogeographical information about C. tatouay