Finding a marked node on any graph by continuous-time quantum walk

Spatial search by discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e.\ in a time that is in the square root of the hitting time of $P$. However, in the framework of continuous-time quantum walks, it was previously unknown whether such general speed-up is possible. In fact, in this framework, the widely used quantum algorithm by Childs and Goldstone fails to achieve such a speedup. Furthermore, it is not clear how to apply this algorithm for searching any Markov chain $P$. In this article, we aim to reconcile the apparent differences between the running times of spatial search algorithms in these two frameworks. We first present a modified version of the Childs and Goldstone algorithm which can search for a marked element for any ergodic, reversible $P$ by performing a quantum walk on its edges. Although this approach improves the algorithmic running time for several instances, it cannot provide a generic quadratic speedup for any $P$. Secondly, using the framework of interpolated Markov chains, we provide a new spatial search algorithm by continuous-time quantum walk which can find a marked node on any $P$ in the square root of the classical hitting time. In the scenario where multiple nodes are marked, the algorithmic running time scales as the square root of a quantity known as the extended hitting time. Our results establish a novel connection between discrete-time and continuous-time quantum walks and can be used to develop a number of Markov chain-based quantum algorithms.Comment: This version deals only with new algorithms for spatial search by continuous-time quantum walk (CTQW) on ergodic, reversible Markov chains. Please see arXiv:2004.12686 for results on the necessary and sufficient conditions for the optimality of the Childs and Goldstone algorithm for spatial search by CTQ

Environment-assisted analog quantum search

Two main obstacles for observing quantum advantage in noisy intermediate-scale quantum computers (NISQ) are the finite precision effects due to control errors, or disorders, and decoherence effects due to thermal fluctuations. It has been shown that dissipative quantum computation is possible in presence of an idealized fully-engineered bath. However, it is not clear, in general, what performance can be achieved by NISQ when internal bath degrees of freedom are not controllable. In this work, we consider the task of quantum search of a marked node on a complete graph of $n$ nodes in the presence of both static disorder and non-zero coupling to an environment. We show that, given fixed and finite levels of disorder and thermal fluctuations, there is an optimal range of bath temperatures that can significantly improve the success probability of the algorithm. Remarkably for a fixed disorder strength $\sigma$, the system relaxation time decreases for higher temperatures within a robust range of parameters. In particular, we demonstrate that for strong disorder, the presence of a thermal bath increases the success probability from $1/(n \sigma^2)$ to at least $1/2$. While the asymptotic running time is approximately maintained, the need to repeat the algorithm many times and issues associated with unitary over-rotations can be avoided as the system relaxes to an absorbing steady state. Furthermore, we discuss for what regimes of disorder and bath parameters quantum speedup is possible and mention conditions for which similar phenomena can be observed in more general families of graphs. Our work highlights that in the presence of static disorder, even non-engineered environmental interactions can be beneficial for a quantum algorithm

Complexity of Gaussian quantum optics with a limited number of non-linearities

It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide evidence that computing transition amplitudes of Gaussian processes with a single-layer of non-linearities is hard for classical computers. To do so, we show how an efficient algorithm to solve this problem could be used to efficiently approximate outcome probabilities of a Gaussian boson sampling experiment. We also extend this complexity result to the problem of computing transition probabilities of Gaussian processes with two layers of non-linearities, by developing a Hadamard test for continuous-variable systems that may be of independent interest. Given recent experimental developments in the implementation of photon-photon interactions, our results may inspire new schemes showing quantum computational advantage or algorithmic applications of non-linear quantum optical systems realizable in the near-term.Comment: 5 pages for the main file, 8 pages for the appendix, 3 figure

Com quantas cidades se faz a Pan-América? Dimensões político-urbanas dos Boletins da União Pan-Americana

This article intends to discuss the importance of the urban and the cities in the political projects of continental integration led by the Pan American Union. The analysis of some editions of the Bulletins of the Pan American Union and the historiography dedicated to Pan Americanism aims to underline the metonymic relationship between American nations and their cities. The holding of a series of congresses and conferences indicates how the institution, based in Washington D.C., brought together disciplines and practices in favor of mapping and cataloging the different traditions identified in the continent, appeased by the ideal of cooperation and the rhetoric of American solidarity. This conciliation was operated through liberalism, an assumption for Pan-Americanist practices, to which one is establish a critique. In the midst of this plot, architecture and architects occupied a privileged place and formulated professional perspectives that made use of this inter-American project to establish a network and guarantee the permanent debate of American cities within the scope of the Pan-American Congresses of Architects.Este artículo pretende discutir la importancia de lo urbano y de las ciudades en los proyectos políticos de integración continental liderados por la Unión Panamericana. El análisis de algunas ediciones de los Boletines de la Unión Panamericana y de la historiografía dedicada al panamericanismo pretende subrayar la relación metonímica entre las naciones americanas y sus ciudades. La realización de una serie de congresos y conferencias indica cómo la institución, con sede en Washington D.C., reunió disciplinas y prácticas a favor de mapear y catalogar las distintas tradiciones identificadas en el continente, apaciguadas desde el ideal de cooperación y la retórica de la solidaridad americana. Esta conciliación se operó a través del liberalismo, presupuesto de las prácticas panamericanistas, que se establece una crítica. En medio de esta trama, la arquitectura y los arquitectos ocuparon un lugar privilegiado y formularon perspectivas profesionales que aprovecharon este proyecto interamericano para establecer una red y garantizar el debate permanente sobre las ciudades americanas en el ámbito de los Congresos Panamericanos de Arquitectos.O presente artigo pretende debater a importância do urbano e das cidades nos projetos políticos de integração continental capitaneados pela União Pan-Americana. A análise de algumas edições dos Boletins da União Pan-Americana e da historiografia dedicada ao pan-americanismo tem como objetivo sublinhar a relação metonímica entre as nações americanas e suas cidades. A realização de uma série de congressos e conferências indica como a instituição, sediada em Washington D.C., congregou disciplinas e práticas em prol do mapeamento e catalogação das diferentes tradições identificadas no continente, apaziguadas a partir do ideal de cooperação e da retórica de solidariedade americana. Essa conciliação era operada por meio do liberalismo, pressuposto para as práticas pan-americanistas, ao qual pretende-se estabelecer uma crítica. Em meio a essa trama, a arquitetura e os arquitetos ocuparam um lugar privilegiado e formularam perspectivas profissionais que se valiam desse projeto interamericano para estabelecer uma rede e garantir o debate permanente sobre as cidades americanas no âmbito dos Congressos Pan-Americanos de Arquitetos

Los caballeros de la Politécnica: la regulación profesional, la metáfora y la política en el discurso Alexandre Albuquerque

The article aims to analyze the participation of Alexandre Albuquerque (1880-1940) on the debates about the professional regulation of architects in Brazil. From the construction of a mythology around the architect-engineer, originating in his speech as speaker of the graduating class at the Polytechnic School in 1905, his protagonism in unifying the interests of his professional class is constantly reiterated. Thus, this paper intends to analyze the context of production and transmition of the 1905 speech, in order to understand the distance between your formulation, your insertion in the debate about professional regulation and your conversion into mythology.O artigo objetiva analisar a participação de Alexandre Albuquerque (1880-1940) nos debates sobre a regulamentação profissional dos arquitetos no Brasil. A partir da construção de uma mitologia em torno do engenheiro-arquiteto, com origem em seu discurso enquanto orador da turma de formandos da Escola Politécnica em 1905, seu protagonismo como aglutinador dos interesses de sua classe profissional é constantemente reiterado. Dessa forma, o trabalho procura analisar o contexto de produção e transmissão do discurso de 1905 a fim de compreender a distância entre sua formulação, sua inserção no debate acerca da regulamentação profissional e sua conversão em mitologia.El artículo tiene como objetivo analizar la participación de Alexandre Albuquerque (1880-1940) en los debates sobre la regulación profesional de los arquitectos en Brasil. A partir de la construcción de una mitología alrededor del arquitecto-ingeniero, originario de su discurso como orador de la clase que se graduó en la Escuela Politécnica en 1905, su papel como unificador de los intereses de su clase profesional se reitera constantemente. De este modo, el artículo analiza el contexto de la producción y transmisión del discurso de 1905 con el fin de entender la distancia entre su formulación, su inclusión en el debate sobre la regulación profesional y su conversión en la mitología