The invariants of the Clifford groups

The automorphism group of the Barnes-Wall lattice L_m in dimension 2^m (m not 3) is a subgroup of index 2 in a certain ``Clifford group'' C_m (an extraspecial group of order 2^(1+2m) extended by an orthogonal group). This group and its complex analogue CC_m have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge's 1996 result that the space of invariants for C_m of degree 2k is spanned by the complete weight enumerators of the codes obtained by tensoring binary self-dual codes of length 2k with the field GF(2^m); these are a basis if m >= k-1. We also give new constructions for L_m and C_m: let M be the Z[sqrt(2)]-lattice with Gram matrix [2, sqrt(2); sqrt(2), 2]. Then L_m is the rational part of the mth tensor power of M, and C_m is the automorphism group of this tensor power. Also, if C is a binary self-dual code not generated by vectors of weight 2, then C_m is precisely the automorphism group of the complete weight enumerator of the tensor product of C and GF(2^m). There are analogues of all these results for the complex group CC_m, with ``doubly-even self-dual code'' instead of ``self-dual code''.Comment: Latex, 24 pages. Many small improvement

Experimental and numerical investigation on the impact response of CFRP under 3-point-bending

The strain rate-dependent material characteristic of carbon fiber reinforced plastics (CFRP) is widely known and has been investigated in detail at coupon level. In this study, for the first time the strain rate dependent characteristic of a three-dimensional CFRP structure was investigated. The evolution of the determined strain rate dependency was correlated with the results at coupon level. For this purpose two special 3-point-bending fixtures were developed to obtain the flexural impact response of the investigated T700S DT120 prepreg system at coupon and component (hat profile) level. The rectangular coupon specimens were loaded with quasi-static to intermediate impact velocities from 3.3x10$^{-5}$ to 10ms$^{-1}$ while the structural sub components were tested using impact velocities from 3.3x10$^{-5}$ to 1m s$^{-1}$ With increasing impact velocities, the experimental tests showed a significant increase in force at first failure and maximum deflection at coupon level. The increases in force were of 52% and 120%, respectively. However, the increase for structural hat profile components was just 12.4% due to a different failure mode. The observed initial failure modes were compressive failure provoked by fiber kinking for the coupon and interlaminar shear failure for the structural component. Regardless of the different failure modes this work proves the necessity of considering the strain rate dependency of a composite material to accurately predict the maximum load capacity of a CFRP structure during a dynamic load event. Additionally, the comparison of the experimental results restults to numerical results revealed weaknesses in the prediction accuracy of the currently used models

Qudit versions of the qubit "pi-over-eight" gate

When visualised as an operation on the Bloch sphere, the qubit "pi-over-eight" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory, typically in situations for which Pauli and Clifford gates are insufficient. Most notably, when it supplements the set of Clifford gates then universal quantum computation can be achieved. The "pi-over-eight" gate is the simplest example of an operation from the third level of the Clifford hierarchy (i.e., it maps Pauli operations to Clifford operations under conjugation). Here we derive explicit expressions for all qudit (d-level, where d is prime) versions of this gate and analyze the resulting group structure that is generated by these diagonal gates. This group structure differs depending on whether the dimensionality of the qudit is two, three or greater than three. We then discuss the geometrical relationship of these gates (and associated states) with respect to Clifford gates and stabilizer states. We present evidence that these gates are maximally robust to depolarizing and phase damping noise, in complete analogy with the qubit case. Motivated by this and other similarities we conjecture that these gates could be useful for the task of qudit magic-state distillation and, by extension, fault-tolerant quantum computing. Very recent, independent work by Campbell, Anwar and Browne confirms the correctness of this intuition, and we build upon their work to characterize noise regimes for which noisy implementations of these gates can (or provably cannot) supplement Clifford gates to enable universal quantum computation.Comment: Version 2 changed to reflect improved distillation routines in arXiv:1205.3104v2. Minor typos fixed. 12 Pages,2 Figures,3 Table

Spherical designs and lattices

In this article we prove that integral lattices with minimum <= 7 (or <= 9) whose set of minimal vectors form spherical 9-designs (or 11-designs respectively) are extremal, even and unimodular. We furthermore show that there does not exist an integral lattice with minimum <=11 which yields a 13-design.Comment: The final publication is available at http://link.springer.com/article/10.1007%2Fs13366-013-0155-

Structure-based knowledge acquisition from electronic lab notebooks for research data provenance documentation

BACKGROUND: Electronic Laboratory Notebooks (ELNs) are used to document experiments and investigations in the wet-lab. Protocols in ELNs contain a detailed description of the conducted steps including the necessary information to understand the procedure and the raised research data as well as to reproduce the research investigation. The purpose of this study is to investigate whether such ELN protocols can be used to create semantic documentation of the provenance of research data by the use of ontologies and linked data methodologies. METHODS: Based on an ELN protocol of a biomedical wet-lab experiment, a retrospective provenance model of the raised research data describing the details of the experiment in a machine-interpretable way is manually engineered. Furthermore, an automated approach for knowledge acquisition from ELN protocols is derived from these results. This structure-based approach exploits the structure in the experiment’s description such as headings, tables, and links, to translate the ELN protocol into a semantic knowledge representation. To satisfy the Findable, Accessible, Interoperable, and Reuseable (FAIR) guiding principles, a ready-to-publish bundle is created that contains the research data together with their semantic documentation. RESULTS: While the manual modelling efforts serve as proof of concept by employing one protocol, the automated structure-based approach demonstrates the potential generalisation with seven ELN protocols. For each of those protocols, a ready-to-publish bundle is created and, by employing the SPARQL query language, it is illustrated that questions about the processes and the obtained research data can be answered. CONCLUSIONS: The semantic documentation of research data obtained from the ELN protocols allows for the representation of the retrospective provenance of research data in a machine-interpretable way. Research Object Crate (RO-Crate) bundles including these models enable researchers to easily share the research data including the corresponding documentation, but also to search and relate the experiment to each other

From Skew-Cyclic Codes to Asymmetric Quantum Codes

We introduce an additive but not $\mathbb{F}_4$-linear map $S$ from $\mathbb{F}_4^{n}$ to $\mathbb{F}_4^{2n}$ and exhibit some of its interesting structural properties. If $C$ is a linear $[n,k,d]_4$-code, then $S(C)$ is an additive $(2n,2^{2k},2d)_4$-code. If $C$ is an additive cyclic code then $S(C)$ is an additive quasi-cyclic code of index $2$. Moreover, if $C$ is a module $\theta$-cyclic code, a recently introduced type of code which will be explained below, then $S(C)$ is equivalent to an additive cyclic code if $n$ is odd and to an additive quasi-cyclic code of index $2$ if $n$ is even. Given any $(n,M,d)_4$-code $C$, the code $S(C)$ is self-orthogonal under the trace Hermitian inner product. Since the mapping $S$ preserves nestedness, it can be used as a tool in constructing additive asymmetric quantum codes.Comment: 16 pages, 3 tables, submitted to Advances in Mathematics of Communication

Persistent effectivity of gas plasma-treated, long time-stored liquid on epithelial cell adhesion capacity and membrane morphology

Research in plasma medicine includes a major interest in understanding gas plasma-cell interactions. The immediate application of gas plasma in vitro inhibits cell attachment, vitality and cell-cell contacts via the liquid. Interestingly, in our novel experiments described here we found that the liquid-mediated plasma effect is long-lasting after storage up to seven days; i. e. the liquid preserves the characteristics once induced by the argon plasma. Therefore, the complete Dulbecco's Modified Eagle cell culture medium was argon plasma-treated (atmospheric pressure, kINPen09) for 60 s, stored for several days (1, 4 and 7 d) at 37°C and added to a confluent mouse hepatocyte epithelial cell (mHepR1) monolayer. Impaired tight junction architecture as well as shortened microvilli on the cell membrane could be observed, which was accompanied by the loss of cell adhesion capacity. Online-monitoring of vital cells revealed a reduced cell respiration. Our first timedependent analysis of plasma-treated medium revealed that temperature, hydrogen peroxide production, pH and oxygen content can be excluded as initiators of cell physiological and morphological changes. The here observed persisting biological effects in plasma-treated liquids could open new medical applications in dentistry and orthopaedics