Effects of imperfections for Shor's factorization algorithm

We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor's algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show that the width of peaks, which frequencies allow to determine the factors, grow exponentially with the number of qubits. However, the algorithm remains operational up to a critical coupling strength $\epsilon_c$ which drops only polynomially with $\log_2 N$. The numerical dependence of $\epsilon_c$ on $\log_2 N$ is explained by analytical estimates that allows to obtain the scaling for functionality of Shor's algorithm on realistic quantum computers with a large number of qubits.Comment: 10 pages, 10 figures, 1 table. Added references and new data. Erratum added as appendix. 1 Figure and 1 Table added. Research is available at http://www.quantware.ups-tlse.fr

On groups with the same character degrees as almost simple groups with socle the Mathieu groups

Let $G$ be a finite group and $cd(G)$ denote the set of complex irreducible character degrees of $G$. In this paper, we prove that if $G$ is a finite group and $H$ is an almost simple group whose socle is Mathieu group such that $cd(G) =cd(H)$, then there exists an Abelian subgroup $A$ of $G$ such that $G/A$ is isomorphic to $H$. This study is heading towards the study of an extension of Huppert's conjecture (2000) for almost simple groups.Comment: arXiv admin note: text overlap with arXiv:1108.0010 by other author

Measuring compulsive buying behaviour: Psychometric validity of three different scales and prevalence in the general population and in shopping centres

Due to the problems of measurement and the lack of nationally representative data, the extent of compulsive buying behaviour (CBB) is relatively unknown. Methods: The validity of three different instruments was tested: Edwards Compulsive Buying Scale (ECBS; Edwards, 1993), Questionnaire About Buying Behavior (QABB; Lejoyeux & Adès, 1994) and Richmond Compulsive Buying Scale (RCBS; Ridgway, et. al., 2008) using two independent samples. One was nationally representative of the Hungarian population (N=2710) while the other comprised shopping mall customers (N=1447). Results: A new, four-factor solution for the ECBS was developed (ECBS-R), and confirmed the other two measures. Additionally, cut-off scores were defined for all measures. Results showed that the prevalence of CBB is 1.85% (with QABB) in the general population but significantly higher in shopping mall customers (8.7% with ECBS-R, 13.3% with QABB and 2.5% with RCBS-R). Conclusions: Due to the diversity of content, each measure identifies a somewhat different CBB group

Pacific Hake length frequencies at California ports, 1963-70

Since 1966, enlargement of specialized United States and Soviet hake fisheries led to scientific meetings and fishing agreements with provisions for exchanges of biological data by statistical areas where the catch exceeds 100 metric tons. While California area landings have not approached the qualifying level for data exchange, measurement data are presented in this report to complement other data for the hake resource. Hake in animal food samples were measured at Santa Barbara, Morro Bay, Fort Bragg, and Eureka. The majority of measurements were obtained at Santa Barbara where a declining trend in average sizes was noted for quarterly periods and for annual periods from 1966 to 1970. (23pp.