Asymmetric quantum error correction via code conversion

In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the presence of such an error asymmetry, an appropriately asymmetric quantum code - that is, a code that can correct more phase errors than bit errors - will be more efficient than a traditional, symmetric quantum code. Here we construct fault tolerant circuits to convert between an asymmetric subsystem code and a symmetric subsystem code. We show that, for a moderate error asymmetry, the failure rate of a logical circuit can be reduced by using a combined symmetric asymmetric system and that doing so does not preclude universality.Comment: 5 pages, 8 figures, presentation revised, figures and references adde

Accuracy threshold for concatenated error detection in one dimension

Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical systems that are candidates for quantum computing possess this property. Here we study the performance of a concatenated error-detection code in a system that permits only nearest-neighbor interactions in one dimension. We make use of a new message-passing scheme that maximizes the number of errors that can be reliably corrected by the code. Our numerical results indicate that arbitrarily accurate universal quantum computation is possible if the probability of failure of each elementary physical operation is below approximately 10^{-5}. This threshold is three orders of magnitude lower than the highest known.Comment: 7 pages, 4 figures, now with error bar

Message passing in fault tolerant quantum error correction

Inspired by Knill's scheme for message passing error detection, here we develop a scheme for message passing error correction for the nine-qubit Bacon-Shor code. We show that for two levels of concatenated error correction, where classical information obtained at the first level is used to help interpret the syndrome at the second level, our scheme will correct all cases with four physical errors. This results in a reduction of the logical failure rate relative to conventional error correction by a factor proportional to the reciprocal of the physical error rate.Comment: 8 pages, 9 figure

Communities as Well Separated Subgraphs With Cohesive Cores: Identification of Core-Periphery Structures in Link Communities

Communities in networks are commonly considered as highly cohesive subgraphs which are well separated from the rest of the network. However, cohesion and separation often cannot be maximized at the same time, which is why a compromise is sought by some methods. When a compromise is not suitable for the problem to be solved it might be advantageous to separate the two criteria. In this paper, we explore such an approach by defining communities as well separated subgraphs which can have one or more cohesive cores surrounded by peripheries. We apply this idea to link communities and present an algorithm for constructing hierarchical core-periphery structures in link communities and first test results.Comment: 12 pages, 2 figures, submitted version of a paper accepted for the 7th International Conference on Complex Networks and Their Applications, December 11-13, 2018, Cambridge, UK; revised version at http://141.20.126.227/~qm/papers

Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co

Deterministic optical quantum computer using photonic modules

The optical quantum computer is one of the few experimental systems to have demonstrated small scale quantum information processing. Making use of cavity quantum electrodynamics approaches to operator measurements, we detail an optical network for the deterministic preparation of arbitrarily large two-dimensional cluster states. We show that this network can form the basis of a large scale deterministic optical quantum computer that can be fabricated entirely on chip.Comment: 9 pages, 10 figures, minor revision

Affectus Hispaniae en la historiografía del Alto Imperio

This paper analyses texts written by Greek and Latin High Empire historians dealing with Hispania. Some of the authors have a very positive view (Florus, Iustinus, Appian) while others are clearly negative (Veleius Paterculus, Valerius Maximus) though most of them show little interest, indifference or variety of opinions. When there is interest in the region or praise, it is because the author comes from Hispania or he is trying to please an emperor born in Hispania, but it could also be due to a universal conception of history revealing a critical attitude towards Roman imperialism, as in Appian. The praise found in Iustinus’s epitome should be attributed to the author of the epitome rather than to Pompeius Trogus. This can be taken as evidence for situating Iustinus’s life and work in the 2nd century A.D. Loathing of Hispania seems to have its origins in conservative, ‘optimate’ nationalist circles, who perceive the province as the ‘popular’ region that acclaimed and welcomed ‘seditious’ individuals such as Tiberius Gracchus and Sertorius.Se estudian en este trabajo los textos de historiadores del Alto Imperio, latinos y griegos, que tratan sobre Hispania. En algunos autores encontramos una visión muy positiva (Floro, Justino, Apiano) y en otros claramente negativa (Veleyo Patérculo, Valerio Máximo), aunque en la mayoría de los casos hay escasa atención, indiferencia o diversidad de opiniones. El interés por la región y los elogios pueden estar motivados por el origen hispánico del autor o su voluntad de agradar a algún emperador oriundo de Hispania, pero también por una concepción universal de la historia que denota en ocasiones una posición crítica con el imperialismo romano, como es el caso de Apiano. La alabanza que hallamos en el epítome de Justino creemos que debe atribuirse más al epitomador que a Pompeyo Trogo, lo que apoyaría una datación temprana de la vida y la obra de Justino (s. II d.C.). La aversión hacia Hispania parece haber surgido en medios conservadores, “optimates” nacionalistas, que ven la provincia como el territorio “popular”, que encumbró y acogió a “sediciosos” como Tiberio Graco y Sertorio

The TESS-Keck Survey II: An Ultra-Short Period Rocky Planet and its Siblings Transiting the Galactic Thick-Disk Star TOI-561

We report the discovery of TOI-561, a multi-planet system in the galactic thick disk that contains a rocky, ultra-short period planet (USP). This bright ($V=10.2$) star hosts three small transiting planets identified in photometry from the NASA TESS mission: TOI-561 b (TOI-561.02, P=0.44 days, $R_b = 1.45\pm0.11\,R_\oplus$), c (TOI-561.01, P=10.8 days, $R_c=2.90\pm0.13\,R_\oplus$), and d (TOI-561.03, P=16.3 days, $R_d=2.32\pm0.16\,R_\oplus$). The star is chemically ([Fe/H]$=-0.41\pm0.05$, [$\alpha$/H]$=+0.23\pm0.05$) and kinematically consistent with the galactic thick disk population, making TOI-561 one of the oldest ($10\pm3\,$Gyr) and most metal-poor planetary systems discovered yet. We dynamically confirm planets b and c with radial velocities from the W. M. Keck Observatory High Resolution Echelle Spectrometer. Planet b has a mass and density of $3.2\pm0.8\,M_\oplus$ and $5.5^{+2.0}_{-1.6}\,$g$\,$cm$^{-3}$, consistent with a rocky composition. Its lower-than-average density is consistent with an iron-poor composition, although an Earth-like iron-to-silicates ratio is not ruled out. Planet c is $7.0\pm2.3\,M_\oplus$ and $1.6\pm0.6\,$g$\,$cm$^{-3}$, consistent with an interior rocky core overlaid with a low-mass volatile envelope. Several attributes of the photometry for planet d (which we did not detect dynamically) complicate the analysis, but we vet the planet with high-contrast imaging, ground-based photometric follow-up and radial velocities. TOI-561 b is the first rocky world around a galactic thick-disk star confirmed with radial velocities and one of the best rocky planets for thermal emission studies.Comment: Accepted at The Astronomical Journal; 25 pages, 10 figure

Mechanisms of viral entry: sneaking in the front door

Recent developments in methods to study virus internalisation are providing clearer insights into mechanisms used by viruses to enter host cells. The use of dominant negative constructs, specific inhibitory drugs and RNAi to selectively prevent entry through particular pathways has provided evidence for the clathrin-mediated entry of hepatitis C virus (HCV) as well as the caveolar entry of Simian Virus 40. Moreover, the ability to image and track fluorescent-labelled virus particles in real-time has begun to challenge the classical plasma membrane entry mechanisms described for poliovirus and human immunodeficiency virus. This review will cover both well-documented entry mechanisms as well as more recent discoveries in the entry pathways of enveloped and non-enveloped viruses. This will include viruses which enter the cytosol directly at the plasma membrane and those which enter via endocytosis and traversal of internal membrane barrier(s). Recent developments in imaging and inhibition of entry pathways have provided insights into the ill-defined entry mechanism of HCV, bringing it to the forefront of viral entry research. Finally, as high-affinity receptors often define viral internalisation pathways, and tropism in vivo, host membrane proteins to which viral particles specifically bind will be discussed throughout