Finding flows in the one-way measurement model

The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform a unitary embedding between two Hilbert spaces is for the graph G, together with input/output vertices I, O \subset V(G), to have a flow in the sense introduced by Danos and Kashefi [quant-ph/0506062]. For the special case of |I| = |O|, using a graph-theoretic characterization, I show that such flows are unique when they exist. This leads to an efficient algorithm for finding flows, by a reduction to solved problems in graph theory.Comment: 8 pages, 3 figures: somewhat condensed and updated version, to appear in PR

Finding Optimal Flows Efficiently

Among the models of quantum computation, the One-way Quantum Computer is one of the most promising proposals of physical realization, and opens new perspectives for parallelization by taking advantage of quantum entanglement. Since a one-way quantum computation is based on quantum measurement, which is a fundamentally nondeterministic evolution, a sufficient condition of global determinism has been introduced as the existence of a causal flow in a graph that underlies the computation. A O(n^3)-algorithm has been introduced for finding such a causal flow when the numbers of output and input vertices in the graph are equal, otherwise no polynomial time algorithm was known for deciding whether a graph has a causal flow or not. Our main contribution is to introduce a O(n^2)-algorithm for finding a causal flow, if any, whatever the numbers of input and output vertices are. This answers the open question stated by Danos and Kashefi and by de Beaudrap. Moreover, we prove that our algorithm produces an optimal flow (flow of minimal depth.) Whereas the existence of a causal flow is a sufficient condition for determinism, it is not a necessary condition. A weaker version of the causal flow, called gflow (generalized flow) has been introduced and has been proved to be a necessary and sufficient condition for a family of deterministic computations. Moreover the depth of the quantum computation is upper bounded by the depth of the gflow. However, the existence of a polynomial time algorithm that finds a gflow has been stated as an open question. In this paper we answer this positively with a polynomial time algorithm that outputs an optimal gflow of a given graph and thus finds an optimal correction strategy to the nondeterministic evolution due to measurements.Comment: 10 pages, 3 figure

Solving frustration-free spin systems

We identify a large class of quantum many-body systems that can be solved exactly: natural frustration-free spin-1/2 nearest-neighbor Hamiltonians on arbitrary lattices. We show that the entire ground state manifold of such models can be found exactly by a tensor network of isometries acting on a space locally isomorphic to the symmetric subspace. Thus, for this wide class of models real-space renormalization can be made exact. Our findings also imply that every such frustration-free spin model satisfies an area law for the entanglement entropy of the ground state, establishing a novel large class of models for which an area law is known. Finally, we show that our approach gives rise to an ansatz class useful for the simulation of almost frustration-free models in a simple fashion, outperforming mean field theory.Comment: 5 pages, 1 figur

Generalized Flow and Determinism in Measurement-based Quantum Computation

We extend the notion of quantum information flow defined by Danos and Kashefi for the one-way model and present a necessary and sufficient condition for the deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the X-Y, X-Z and Y-Z planes. We apply both measurement calculus and the stabiliser formalism to derive our main theorem which for the first time gives a full characterization of the deterministic computation in the one-way model. We present several examples to show how our result improves over the traditional notion of flow, such as geometries (entanglement graph with input and output) with no flow but having generalized flow and we discuss how they lead to an optimal implementation of the unitaries. More importantly one can also obtain a better quantum computation depth with the generalized flow rather than with flow. We believe our characterization result is particularly essential for the study of the algorithms and complexity in the one-way model.Comment: 16 pages, 10 figure

Generalized Flow and Determinism in Measurement-based Quantum Computation

We extend the notion of quantum information flow defined by Danos and Kashefi for the one-way model and present a necessary and sufficient condition for the deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the X-Y, X-Z and Y-Z planes. We apply both measurement calculus and the stabiliser formalism to derive our main theorem which for the first time gives a full characterization of the deterministic computation in the one-way model. We present several examples to show how our result improves over the traditional notion of flow, such as geometries (entanglement graph with input and output) with no flow but having generalized flow and we discuss how they lead to an optimal implementation of the unitaries. More importantly one can also obtain a better quantum computation depth with the generalized flow rather than with flow. We believe our characterization result is particularly essential for the study of the algorithms and complexity in the one-way model.Comment: 16 pages, 10 figure

El federalismo cooperativo como factor catalizador de un Gobierno Abierto

Este artículo tiene como propósito articular un marco de análisis que justifica la importancia de la colaboración entre gobiernos, bajo el supuesto de que un sistema rígido de competencias tiende a fragmentar la solución de los asuntos públicos en las agendas de gobierno. Un federalismo cooperativo, en tanto variable productora de relaciones intergubernamentales, da forma a un contexto que favorece impulsar soluciones más integrales en torno a demandas inscritas en el plan de acción, elaborado como requisito de pertenencia a la Alianza Internacional por un Gobierno Abierto. La propuesta llevada a Brasilia por la representación de México en junio de 2012, con la idea de promover la apertura gubernamental en el plano subnacional y local, tendrá mayores posibilidades de éxito si previamente se establecen bases mínimas para un federalismo cooperativo que facilite la gestión de los asuntos públicos establecidos en el plan de acción

Edge centrality via the Holevo quantity

In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann entropy of the graph. We show that this can be computed in terms of the Holevo quantity, a well known quantum information theoretical measure. While computing the Von Neumann entropy and hence the Holevo quantity requires computing the spectrum of the graph Laplacian, we show how to obtain a simplified measure through a quadratic approximation of the Shannon entropy. This in turns shows that the proposed centrality measure is strongly correlated with the negative degree centrality on the line graph. We evaluate our centrality measure through an extensive set of experiments on real-world as well as synthetic networks, and we compare it against commonly used alternative measures

Incidence and determinants of new AIDS-defining illnesses after HAART initiation in a Senegalese cohort

<p>Abstract</p> <p>Background</p> <p>Although a dramatic decrease in AIDS progression has been observed after Highly Active Anti Retroviral Therapy (HAART) in both low- and high-resource settings, few data support that fact in low-resource settings.</p> <p>This study describes the incidence of AIDS-defining illnesses (ADI) after HAART initiation and analyzes their risk factors in a low-resource setting. A focus was put on CD4 cell counts and viral load measurements.</p> <p>Methods</p> <p>404 HIV-1-infected Senegalese adult patients were enrolled in a prospective observational cohort and data censored as of April 2008. A Poisson regression was used to model the incidence of ADIs over two periods and to assess its association with baseline variables, current CD4, current viral load, CD4 response, and virological response.</p> <p>Results</p> <p>ADI incidence declined from 20.5 ADIs per 100 person-years, 95% CI = [16.3;25.8] during the first year to 4.3, 95% CI = [2.3;8.1] during the fourth year but increased afterwards. Before 42 months, the decrease was greater in patients with clinical stage CDC-C at baseline and with a viral load remaining below 1000 cp/mL but was uniform across CD4 strata (p = 0.1). After 42 months, 293 patients were still at risk. The current CD4 and viral load were associated with ADI incidence (decrease of 21% per 50 CD4/mm³and of 61% for patients with a viral load < 1000 cp/mL).</p> <p>Conclusions</p> <p>During the first four years, a uniform decline of ADI incidence was observed even in patients with low CD4-cell counts at HAART initiation as long as the viral load remained undetectable. An increase was noted later in patients with immunologic and virological failures but also in patients with only virological failure.</p