Fault-tolerant quantum computation with long-range correlated noise

We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r(D).     

Word-Representable Graphs: a Survey

Letters x and y alternate in a word w if after deleting all letters but x and y in w we get either a word xyxy... or a word yxyx... (each of these words can be of odd or even length). A graph G = (V,E) is word-representable if there is a finite word w over an alphabet V such that the letters x and y alternate in w if and only if xy ∈ E. The word-representable graphs include many important graph classes, in particular, circle graphs, 3-colorable graphs and comparability graphs. In this paper we present the full survey of the available results on the theory of word-representable graphs and the most recent achievements in this field.     

Detecting non-Abelian statistics with an electronic Mach-Zehnder interferometer

Fractionally charged quasiparticles in the quantum Hall state with a filling factor nu=5/2 are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by transport measurements in an electronic Mach-Zehnder interferometer. The tunneling current through the interferometer exhibits a characteristic dependence on the magnetic flux and a nonanalytic dependence on the tunneling amplitudes which can be controlled by gate voltages.     

The structure of some benzylideneamino-pyridinium iodides

The UV, IR, and PMR spectra of a number of m- and p-substituted N-(benzylideneamino)-pyridinium iodides confirm the structure of hydrazonium compounds proposed for them previously. On the basis of physicochemical data, a hypothesis has been put forward of the participation of the pyridinium ring in an intramolecular interaction of the conjugation type. Charge-transfer bands are observed in the UV spectra of some of these compounds.Communication XXXVIII of the series Hydrazones, for Communication XXXVII, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1219–1223, September, 1973.     

Quadratic transformations for the sixth Painlevé equation

A new type of transformation is found for the Painlevé six equation which can be considered as an analog of the well-known quadratic transformations for hypergeometric functions.