Quadratic Speedup for Spatial Search by Continuous-Time Quantum Walk.

Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a quadratic advantage over classical random walks has been an outstanding problem. Thus far, this advantage is obtained only for specific graphs or when a single node of the underlying graph is marked. In this Letter, we provide a new continuous-time quantum walk search algorithm that completely resolves this: our algorithm can find a marked node in any graph with any number of marked nodes, in a time that is quadratically faster than classical random walks. The overall algorithm is quite simple, requiring time evolution of the quantum walk Hamiltonian followed by a projective measurement. A key component of our algorithm is a purely analogue procedure to perform operations on a state of the form e^{-tH^{2}}|ψ⟩, which, for a given Hamiltonian H, only requires evolving H for time scaling as sqrt[t]. This allows us to quadratically fast-forward the dynamics of a continuous-time classical random walk. The applications of our Letter thus go beyond the realm of quantum walks and can lead to new analog quantum algorithms for preparing ground states of Hamiltonians or solving optimization problems.

Optimal Quantum Spatial Search on Random Temporal Networks.

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G(n,p), where p is the probability that any two given nodes are connected: After every time interval τ, a new graph G(n,p) replaces the previous one. We prove analytically that, for any given p, there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O(sqrt[n]), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

Publisher's Note: Spatial Search by Quantum Walk is Optimal for Almost All Graphs [Phys. Rev. Lett. 116, 100501 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.100501.

Spatial Search by Quantum Walk is Optimal for Almost all Graphs.

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work, we prove that for Erdös-Renyi random graphs, i.e., graphs of n vertices where each edge exists with probability p, search by CTQW is almost surely optimal as long as p≥log^{3/2}(n)/n. Consequently, we show that quantum spatial search is in fact optimal for almost all graphs, meaning that the fraction of graphs of n vertices for which this optimality holds tends to one in the asymptotic limit. We obtain this result by proving that search is optimal on graphs where the ratio between the second largest and the largest eigenvalue is bounded by a constant smaller than 1. Finally, we show that we can extend our results on search to establish high fidelity quantum communication between two arbitrary nodes of a random network of interacting qubits, namely, to perform quantum state transfer, as well as entanglement generation. Our work shows that quantum information tasks typically designed for structured systems retain performance in very disordered structures.

Disorder-assisted quantum transport in suboptimal decoherence regimes.

We investigate quantum transport in binary tree structures and in hypercubes for the disordered Frenkel-exciton Hamiltonian under pure dephasing noise. We compute the energy transport efficiency as a function of disorder and dephasing rates. We demonstrate that dephasing improves transport efficiency not only in the disordered case, but also in the ordered one. The maximal transport efficiency is obtained when the dephasing timescale matches the hopping timescale, which represent new examples of the Goldilocks principle at the quantum scale. Remarkably, we find that in weak dephasing regimes, away from optimal levels of environmental fluctuations, the average effect of increasing disorder is to improve the transport efficiency until an optimal value for disorder is reached. Our results suggest that rational design of the site energies statistical distributions could lead to better performances in transport systems at nanoscale when their natural environments are far from the optimal dephasing regime.

Systematic Dimensionality Reduction for Quantum Walks: Optimal Spatial Search and Transport on Non-Regular Graphs.

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that confine the dynamics to a smaller subspace of the full Hilbert space. In this work, we use invariant subspace methods, that can be computed systematically using the Lanczos algorithm, to obtain the reduced set of states that encompass the dynamics of the problem at hand without the specific knowledge of underlying symmetries. First, we apply this method to obtain new instances of graphs where the spatial quantum search algorithm is optimal: complete graphs with broken links and complete bipartite graphs, in particular, the star graph. These examples show that regularity and high-connectivity are not needed to achieve optimal spatial search. We also show that this method considerably simplifies the calculation of quantum transport efficiencies. Furthermore, we observe improved efficiencies by removing a few links from highly symmetric graphs. Finally, we show that this reduction method also allows us to obtain an upper bound for the fidelity of a single qubit transfer on an XY spin network.

Análise epidemiológica dos traumas bucomaxilofaciais de um serviço de emergência / Epidemiological analysis of maxillofacial trauma of an emergency service

Objetivo: Analisar a epidemiologia dos traumas bucomaxilofaciais de um serviço de emergência. Metodologia: Estudo retrospectivo de corte longitudinal histórico realizado por meio da análise de prontuários de pacientes atendidos no serviço de emergência da Santa Casa de Misericórdia de Barretos, São Paulo, Brasil, no período de março de 2004 a abril de 2009. Resultados: Foram analisados 250 prontuários, sendo a maioria do gênero masculino (85%; n=213). Quanto a faixa etária, (36%; n=90) dos traumatismos bucomaxilofaciais ocorreram entre 26 a 40 anos de idade. Trinta e cinco por cento (n=87) dos pacientes foram vítimas de acidentes de trânsito. As agressões físicas corresponderam a (24%; n=60) das emergências realizadas. Vinte e dois por cento (n=55) dos traumas se enquadraram em "outros", 15% (n=38) dos traumas foram provocados por acidentes domésticos e 3% (n=8) por acidentes laborais. Um por cento (n=2) foi relacionado a acidente por arma de fogo. Conclusão: Os traumas bucomaxilofaciais são frequentes nos serviços de emergência e os acidentes de trânsito e a violência urbana são os principais fatores etiológicos desta epidemia... (AU)

Objective: To analyze the epidemiology of maxillofacial trauma of an emergency service. Methodology: A retrospective study of historical longitudinal conducted through analysis of medical records of patients seen in the emergency department of the "Santa Casa de Misericórdia de Barretos", São Paulo, Brazil, from March 2004 to April 2009. Results: We analyzed 250 records, mostly male (85.0%, n=213). As for the age group (36.0%, n=90) of maxillofacial injuries occurred between 26 and 40 years old. Thirty five percent (n=87) of patients were victims of traffic accidents. The assaults accounted for (24.0%, n=60) performed emergencies. Twenty two percent (n=55) of trauma not fit in "other", (15.0%, n=38) of the injuries were caused by home accidents and (3.0%, n=8) for industrial accidents. One percent (n=2) was related to the accident by firearms. Conclusion: The maxillofacial trauma are common in emergency services and traffic accidents and urban violence are major etiological factors of this epidemic... (AU)

Linfoma não-Hodgkin de células t na mandíbula. relato de caso / T-cell non-Hodgkin lymphoma in the mandible: a case report

o linfoma não-Hodgkin de células T é uma doença rara, complexa, e que, de acordo com estudos recentes, vem aumentando na população, nos últimos anos. Pacientes com alterações imunológicas estão mais suscetíveis aos linfomas e, recentemente, pacientes acometidos por algumas doenças virais também foram incluídos no grupo de risco para o linfoma não-Hodgkin. o objetivo deste trabalho foi o de relatar um caso raro de linfoma não-Hodgkin de células T com manifestação na mandíbula, diagnosticado em um paciente jovem e destacar a importância dos profissionais de saúde no reconhecimento das neoplasias maxilomandibulares.

T-cell non-Hodgkin lymphoma is a rare, complex disease, and the population affected has been increasing in recent years according to recent studies. Patients with immunologic abnormalities are more susceptible to lymphomas and, recently, some patients affected by viral diseases have also been included in the risk group for non-Hodgkin lymphoma. The aim of this study was to report a rare case of non-Hodgkin T-cell expression in the jaw diagnosed in a young patient and to highlight the important role of health professionals in the recognition of maxillomandibular neoplasms.

Multibiomarker approach in fish to assess the impact of pollution in a large Brazilian river, Paraiba do Sul.

This article examines the advantages of the use of biomarkers as environmental indicators by applying it to Paraiba do Sul watershed, one of the most important Brazilian water bodies, which is in a critical environmental situation. We use a multibiomarker approach in fish as an integrated strategy to assess the impact of pollution. It comprehends a general biomarker of fish health, the condition factor (CF), and specific biomarkers of contaminant exposure such as metallothionein (MT), acetylcholinesterase (AChE) activity and biliary polycyclic aromatic hydrocarbons (PAH) metabolites. Our results revealed different effects in the fish from diverse locations with varying degrees of pollution. Furthermore, fish located just upstream of the water-treatment plant of the metropolitan area of Rio de Janeiro has shown to be affected by metals. This study indicates the usefulness of integrating a set of biomarkers to define the effects of anthropogenic inputs in aquatic bodies under complex polluted situations.