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

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

How to obtain lattices from (f,σ,δ)-codes via a generalization of Construction A

We show how cyclic (f,σ,δ)-codes over finite rings canonically induce a Z-lattice in RN by using certain quotients of orders in nonassociative division algebras defined using the skew polynomial f. This construction generalizes the one using certain σ-constacyclic codes by Ducoat and Oggier, which used quotients of orders in non-commutative associative division algebras defined by f, and can be viewed as a generalization of the classical Construction A for lattices from linear codes. It has the potential to be applied to coset coding, in particular to wire-tap coding. Previous results by Ducoat and Oggier are obtained as special cases

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

A bacteriophage detection tool for viability assessment of Salmonella cells

Available online 7 September 2013Salmonellosis, one of the most common food and water-borne diseases, has a major global health and economic impact. Salmonella cells present high infection rates, persistence over inauspicious conditions and the potential to preserve virulence in dormant states when cells are viable but non-culturable (VBNC). These facts are challenging for current detection methods. Culture methods lack the capacity to detect VBNC cells, while biomolecular methods (e.g. DNA- or protein-based) hardly distinguish between dead innocuous cells and their viable lethal counterparts. This work presents and validates a novel bacteriophage (phage)-based microbial detection tool to detect and assess Salmonella viability. Salmonella Enteritidis cells in a VBNC physiological state were evaluated by cell culture, flow-cytometry and epifluorescence microscopy, and further assayed with a biosensor platform. Free PVP-SE1 phages in solution showed the ability to recognize VBNC cells, with no lysis induction, in contrast to the minor recognition of heat-killed cells. This ability was confirmed for immobilized phages on gold surfaces, where the phage detection signal follows the same trend of the concentration of viable plus VBNC cells in the sample. The phage probe was then tested in a magnetoresistive biosensor platform allowing the quantitative detection and discrimination of viable and VBNC cells from dead cells, with high sensitivity. Signals arising from 3 to 4 cells per sensor were recorded. In comparison to a polyclonal antibody that does not distinguish viable from dead cells, the phage selectivity in cell recognition minimizes false-negative and false-positive results often associated with most detection methods

Phenotypic Variation and Bistable Switching in Bacteria

Microbial research generally focuses on clonal populations. However, bacterial cells with identical genotypes frequently display different phenotypes under identical conditions. This microbial cell individuality is receiving increasing attention in the literature because of its impact on cellular differentiation, survival under selective conditions, and the interaction of pathogens with their hosts. It is becoming clear that stochasticity in gene expression in conjunction with the architecture of the gene network that underlies the cellular processes can generate phenotypic variation. An important regulatory mechanism is the so-called positive feedback, in which a system reinforces its own response, for instance by stimulating the production of an activator. Bistability is an interesting and relevant phenomenon, in which two distinct subpopulations of cells showing discrete levels of gene expression coexist in a single culture. In this chapter, we address techniques and approaches used to establish phenotypic variation, and relate three well-characterized examples of bistability to the molecular mechanisms that govern these processes, with a focus on positive feedback.