347 research outputs found

    Structured Error Recovery for Codeword-Stabilized Quantum Codes

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    Codeword stabilized (CWS) codes are, in general, non-additive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical non-linear codes. For an n-qubit quantum code correcting errors on up to t qubits, this brute-force approach consecutively tests different errors of weight t or less, and employs a separate n-qubit measurement in each test. In this paper, we suggest an error grouping technique that allows to simultaneously test large groups of errors in a single measurement. This structured error recovery technique exponentially reduces the number of measurements by about 3^t times. While it still leaves exponentially many measurements for a generic CWS code, the technique is equivalent to syndrome-based recovery for the special case of additive CWS codes.Comment: 13 pages, 9 eps figure

    Low-complexity quantum codes designed via codeword-stabilized framework

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    We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code. For codes that can be obtained from a given graph, we give several upper bounds on the distance of a generic (additive or non-additive) CWS code, and the lower Gilbert-Varshamov bound for the existence of additive CWS codes. We also consider additive cyclic CWS codes and show that these codes correspond to a previously unexplored class of single-generator cyclic stabilizer codes. We present several families of simple stabilizer codes with relatively good parameters.Comment: 12 pages, 3 figures, 1 tabl

    Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes

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    Quantum convolutional codes, like their classical counterparts, promise to offer higher error correction performance than block codes of equivalent encoding complexity, and are expected to find important applications in reliable quantum communication where a continuous stream of qubits is transmitted. Grassl and Roetteler devised an algorithm to encode a quantum convolutional code with a "pearl-necklace encoder." Despite their theoretical significance as a neat way of representing quantum convolutional codes, they are not well-suited to practical realization. In fact, there is no straightforward way to implement any given pearl-necklace structure. This paper closes the gap between theoretical representation and practical implementation. In our previous work, we presented an efficient algorithm for finding a minimal-memory realization of a pearl-necklace encoder for Calderbank-Shor-Steane (CSS) convolutional codes. This work extends our previous work and presents an algorithm for turning a pearl-necklace encoder for a general (non-CSS) quantum convolutional code into a realizable quantum convolutional encoder. We show that a minimal-memory realization depends on the commutativity relations between the gate strings in the pearl-necklace encoder. We find a realization by means of a weighted graph which details the non-commutative paths through the pearl-necklace. The weight of the longest path in this graph is equal to the minimal amount of memory needed to implement the encoder. The algorithm has a polynomial-time complexity in the number of gate strings in the pearl-necklace encoder.Comment: 16 pages, 5 figures; extends paper arXiv:1004.5179v

    SIC~POVMs and Clifford groups in prime dimensions

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    We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010

    On the connection between mutually unbiased bases and orthogonal Latin squares

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    We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the two problems and generates complete sets of MUBs in power-of-prime dimensions and three MUBs in dimension six. For these cases, every square from an augmented set of MOLS has a corresponding MUB. We show that this no longer holds for certain composite dimensions.Comment: 6 pages, submitted to Proceedings of CEWQO 200

    A small-angle neutron scattering study of sodium dodecyl sulfate-poly(propylene oxide) methacrylate mixed micelles

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    cited By 3International audienceMixed micelle of protonated or deuterated sodium dodecyl sulfate (SDS and SDSd25, respectively) and poly(propylene oxide) methacrylate (PPOMA) are studied by small-angle neutron scattering (SANS). In all the cases the scattering curves exhibit a peak whose position changes with the composition of the system. The main parameters which characterize mixed micelles, i.e., aggregation numbers of SDS and PPOMA, geometrical dimensions of the micelles and degree of ionisation are evaluated from the analysis of the SANS curves. The position qmax of the correlation peak can be related to the average aggregation numbers of SDS-PPOMA and SDSd25-PPOMA mixed micelles. It is found that the aggregation number of SDS decreases upon increasing the weight ratio PPOMA/SDS (or SDSd25). The isotopic combination, which uses the "contrast effect" between the two micellar systems, has allowed us to determine the mixed micelle composition. Finally, the SANS curves were adjusted using the RMSA for the structure factor S(q) of charged spherical particles and the form factor P(q) of spherical core-shell particle. This analysis confirms the particular core-shell structure of the SDS-PPOMA mixed micelle, i.e., a SDS "core" micelle surrounded by the shell formed by PPOMA macromonomers. The structural parameters of mixed micelles obtained from the analysis of the SANS data are in good agreement with those determined previously by conductimetry and fluorescence studies. © 2005 Elsevier Inc. All rights reserved

    The role of the blood group-related glycosyltransferases FUT2 and B4GALNT2 in susceptibility to infectious disease

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    The glycosylation profile of the gastrointestinal tract is an important factor mediating host-microbe interactions. Variation in these glycan structures is often mediated by blood group-related glycosyltransferases, and can lead to wide-ranging differences in susceptibility to both infectious- as well as chronic disease. In this review, we focus on the interplay between host glycosylation, the intestinal microbiota and susceptibility to gastrointestinal pathogens based on studies of two exemplary blood group-related glycosyltransferases that are conserved between mice and humans, namely FUT2 and B4GALNT2. We highlight that differences in susceptibility can arise due to both changes in direct interactions, such as bacterial adhesion, as well as indirect effects mediated by the intestinal microbiota. Although a large body of experimental work exists for direct interactions between host and pathogen, determining the more complex and variable mechanisms underlying three-way interactions involving the intestinal microbiota will be the subject of much-needed future research

    Gas/particle partitioning and global distribution of polycyclic aromatic hydrocarbons – A modelling approach

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    The global atmospheric distribution and long-range transport (LRT) potential of three polycyclic aromatic hydrocarbons (PAH) - anthracene, fluoranthene and benzo[a]pyrene - are studied. The model used is a global aerosol-chemistry-transport-model, which is based on an atmospheric general circulation model. The model includes an in-built dynamic aerosol model coupled to two-dimensional surface compartments. Several parameterisations of gas/particle partitioning and different assumptions of degradation in the aerosol particulate phase were tested. PAHs are mostly distributed in the source regions but reach the Arctic and the Antarctic. The Canadian Arctic is predicted to be significantly less affected by mid-latitude PAH emissions than the European Arctic. Re-volatilisation is significant for semivolatile PAHs. Accumulation of semivolatile PAHs in polar regions, however, is not indicated. The model study suggests that gas/particle partitioning in air drastically influences the atmospheric cycling, the total environmental fate (e.g. compartmental distributions) and the LRT potential of the substances studied. A parameterisation which calculates the gas/particle partitioning assuming absorption into organic matter and adsorption to black carbon (soot) agrees best with the observations at remote sites. The study provides evidence that the degradation in the particulate phase must be slower than that in the gas-phase. The predicted concentrations of the semivolatile PAHs anthracene and fluoranthene in near-ground air at remote sites in mid and high northern latitudes are in line with measured concentrations, if adsorption of the substances to soot combined with absorption in particulate organic matter is assumed to determine gas/particle partitioning, but cannot be explained by adsorption alone (Junge-Pankow parameterisation of gas/particle partitioning). The results suggest that PAHs absorbed in the organic matrix of particulate matter is shielded from the gas-phase. (C) 2009 Elsevier Ltd. All rights reserved. [References: 42

    On SIC-POVMs in Prime Dimensions

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    The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a "canonical" unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the same conjugacy class of the Clifford group and give a class representative for all such dimensions. It follows that if even one such SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them are (for a given such dimension). I also conjecture that in all dimensions d, the number of conjugacy classes is bounded above by 3 and depends only on d mod 9, and I support this claim with computer computations in all dimensions < 48.Comment: 6 pages, no figures. v3 Refs added, improved discussion of previous work. Ref to a proof of the main conjecture also adde

    Quantum Reed-Solomon Codes

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    After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model - the quantum erasure channel - is discussed. Finally, parameters of quantum BCH codes are provided.Comment: Summary only (2 pages), for the full version see: Proceedings Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-13), Lecture Notes in Computer Science 1719, Springer, 199
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