Efficient quantum gate teleportation in higher dimensions

The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and ‘nearly diagonal’ semi-Clifford gates are particularly important: they admit efficient gate teleportation protocols that implement these gates with fewer ancillary quantum resources such as magic states. Despite the practical importance of these sets of gates, many questions about their structure remain open; this is especially true in the higher-dimensional qudit setting. Our contribution is to leverage the discrete Stone–von Neumann theorem and the symplectic formalism of qudit stabilizer theory towards extending the results of Zeng et al . (2008) and Beigi & Shor (2010) to higher dimensions in a uniform manner. We further give a simple algorithm for recursively enumerating all gates of the Clifford hierarchy, a simple algorithm for recognizing and diagonalizing semi-Clifford gates, and a concise proof of the classification of the diagonal Clifford hierarchy gates due to Cui et al . (2016) for the single-qudit case. We generalize the efficient gate teleportation protocols of semi-Clifford gates to the qudit setting and prove that every third-level gate of one qudit (of any prime dimension) and of two qutrits can be implemented efficiently. Numerical evidence gathered via the aforementioned algorithms supports the conjecture that higher-level gates can be implemented efficiently.

A community-acquired Legionnaires’ disease outbreak caused by Legionella pneumophila serogroup 2: an uncommon event, Italy, August to October 2018

In September 2018 in Brescia province, northern Italy, an outbreak of Legionnaires' disease (LD) caused by Legionella pneumophila serogroup 2 (Lp2) occurred. The 33 cases (two fatal) resided in seven municipalities along the Chiese river. All cases were negative by urinary antigen test (UAT) and most were diagnosed by real-time PCR and serology. In only three cases, respiratory sample cultures were positive, and Lp2 was identified and typed as sequence type (ST)1455. In another three cases, nested sequence-based typing was directly applied to respiratory samples, which provided allelic profiles highly similar to ST1455. An environmental investigation was undertaken immediately and water samples were collected from private homes, municipal water systems, cooling towers and the river. Overall, 533 environmental water samples were analysed and 34 were positive for Lp. Of these, only three samples, all collected from the Chiese river, were Lp2 ST1455. If and how the river water could have been aerosolised causing the LD cases remains unexplained. This outbreak, the first to our knowledge caused by Lp2, highlights the limits of UAT for LD diagnosis, underlining the importance of adopting multiple tests to ensure that serogroups other than serogroup 1, as well as other Legionella species, are identified.

Event History and Topological Data Analysis

Persistent homology is used to track the appearance and disappearance of features as we move through a nested sequence of topological spaces. Equating the nested sequence to a filtration and the appearance and disappearance of features to events, we show that simple event history methods can be used for the analysis of topological data. We propose a version of the well known Nelson-Aalen cumulative hazard estimator for the comparison of topological features of random fields and for testing parametric assumptions. We suggest a Cox proportional hazards approach for the analysis of embedded metric trees. The Nelson-Aalen method is illustrated on globally distributed climate data and on neutral hydrogen distribution in the Milky Way. The Cox method is use to compare vascular patterns in fundus images of the eyes of healthy and diabetic retinopathy patients.

Eccentric tidal disruption event discs around supermassive black holes: dynamics and thermal emission

ABSTRACT After the tidal disruption event (TDE) of a star around a supermassive black hole (SMBH), if the stellar debris stream rapidly circularizes and forms a compact disc, the TDE emission is expected to peak in the soft X-ray or far ultraviolet (UV). The fact that many TDE candidates are observed to peak in the near UV and optical has challenged conventional TDE emission models. By idealizing a disc as a nested sequence of elliptical orbits that communicate adiabatically via pressure forces, and are heated by energy dissipated during the circularization of the nearly parabolic debris streams, we investigate the dynamics and thermal emission of highly eccentric TDE discs, including the effect of general-relativistic apsidal precession from the SMBH. We calculate the properties of uniformly precessing, apsidally aligned, and highly eccentric TDE discs, and find highly eccentric disc solutions exist for realistic TDE properties (SMBH and stellar mass, periapsis distance, etc.). Taking into account compressional heating (cooling) near periapsis (apoapsis), we find our idealized eccentric disc model can produce emission consistent with the X-ray and UV/optical luminosities of many optically bright TDE candidates. Our work attempts to quantify the thermal emission expected from the shock-heating model for TDE emission, and finds stream–stream collisions are a promising way to power optically bright TDEs.

A Characterization of Strong Completeness in Fuzzy Metric Spaces

Here, we deal with the concept of fuzzy metric space ( X , M , ∗ ) , due to George and Veeramani. Based on the fuzzy diameter for a subset of X , we introduce the notion of strong fuzzy diameter zero for a family of subsets. Then, we characterize nested sequences of subsets having strong fuzzy diameter zero using their fuzzy diameter. Examples of sequences of subsets which do or do not have strong fuzzy diameter zero are provided. Our main result is the following characterization: a fuzzy metric space is strongly complete if and only if every nested sequence of close subsets which has strong fuzzy diameter zero has a singleton intersection. Moreover, the standard fuzzy metric is studied as a particular case. Finally, this work points out a route of research in fuzzy fixed point theory.

Dual Graded Graphs and Bratteli Diagrams of Towers of Groups

An $r$-dual tower of groups is a nested sequence of finite groups, like the symmetric groups, whose Bratteli diagram forms an $r$-dual graded graph. Miller and Reiner introduced a special case of these towers in order to study the Smith forms of the up and down maps in a differential poset. Agarwal and the author have also used these towers to compute critical groups of representations of groups appearing in the tower. In this paper I prove that when $r=1$ or $r$ is prime, wreath products of a fixed group with the symmetric groups are the only $r$-dual tower of groups, and conjecture that this is the case for general values of $r$. This implies that these wreath products are the only groups for which one can define an analog of the Robinson-Schensted bijection in terms of a growth rule in a dual graded graph.

Algorithm-based fault recovery of adaptively refined parallel multilevel grids

On future extreme scale computers, it is expected that faults will become an increasingly serious problem as the number of individual components grows and failures become more frequent. This is driving the interest in designing algorithms with built-in fault tolerance that can continue to operate and that can replace data even if part of the computation is lost in a failure. For fault-free computations, the use of adaptive refinement techniques in combination with finite element methods is well established. Furthermore, iterative solution techniques that incorporate information about the grid structure, such as the parallel geometric multigrid method, have been shown to be an efficient approach to solving various types of partial different equations. In this article, we present an advanced parallel adaptive multigrid method that uses dynamic data structures to store a nested sequence of meshes and the iteratively evolving solution. After a fail-stop fault, the data residing on the faulty processor will be lost. However, with suitably designed data structures, the neighbouring processors contain enough information so that a consistent mesh can be reconstructed in the faulty domain with the goal of resuming the computation without having to restart from scratch. This recovery is based on a set of carefully designed distributed algorithms that build on the existing parallel adaptive refinement routines, but which must be carefully augmented and extended.

Strong approximation of Black-Scholes theory based on simple random walks

A basic model in financial mathematics was introduced by Black, Scholes and Merton in 1973. A classical discrete approximation in distribution is the binomial model given by Cox, Ross and Rubinstein in 1979. In this work we give a strong (almost sure, pathwise) discrete approximation of the BSM model using a suitable nested sequence of simple, symmetric random walks. The approximation extends to the stock price process, the value process, the replicating portfolio, and the greeks. An important tool in the approximation is a discrete version of the Feynman-Kac formula as well. Our aim is to show that from an elementary discrete approach, by taking simple limits, one may get the continuous versions. We think that such an approach can be advantageous for both research and applications. Moreover, it is hoped that this approach has pedagogical merits as well: gives insight and seems suitable for teaching students whose mathematical background may not contain e.g. measure theory or stochastic analysis.

Combined use of real-time PCR and nested sequence-based typing in survey of humanLegionellainfection

SUMMARYLegionnaires’ disease (LD) is a globally distributed systemic infectious disease. The burden of LD in many regions is still unclear, especially in Asian countries including China. A survey ofLegionellainfection using real-time PCR and nested sequence-based typing (SBT) was performed in two hospitals in Shanghai, China. A total of 265 bronchoalveolar lavage fluid (BALF) specimens were collected from hospital A between January 2012 and December 2013, and 359 sputum specimens were collected from hospital B throughout 2012. A total of 71 specimens were positive forLegionellaaccording to real-time PCR focusing on the 5S rRNA gene. Seventy of these specimens were identified asLegionella pneumophilaas a result of real-time PCR amplification of thedotA gene. Results of nested SBT revealed high genetic polymorphism in theseL. pneumophilaand ST1 was the predominant sequence type. These data revealed that the burden of LD in China is much greater than that recognized previously, and real-time PCR may be a suitable monitoring technology for LD in large sample surveys in regions lacking the economic and technical resources to perform other methods, such as urinary antigen tests and culture methods.