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

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

Model-Based and Model-Free Control Predicts Alcohol Consumption Developmental Trajectory in Young Adults: A 3-Year Prospective Study.

BACKGROUND: A shift from goal-directed toward habitual control has been associated with alcohol dependence. Whether such a shift predisposes to risky drinking is not yet clear. We investigated how goal-directed and habitual control at age 18 predict alcohol use trajectories over the course of 3 years. METHODS: Goal-directed and habitual control, as informed by model-based (MB) and model-free (MF) learning, were assessed with a two-step sequential decision-making task during functional magnetic resonance imaging in 146 healthy 18-year-old men. Three-year alcohol use developmental trajectories were based on either a consumption score from the self-reported Alcohol Use Disorders Identification Test (assessed every 6 months) or an interview-based binge drinking score (grams of alcohol/occasion; assessed every year). We applied a latent growth curve model to examine how MB and MF control predicted the drinking trajectory. RESULTS: Drinking behavior was best characterized by a linear trajectory. MB behavioral control was negatively associated with the development of the binge drinking score; MF reward prediction error blood oxygen level-dependent signals in the ventromedial prefrontal cortex and the ventral striatum predicted a higher starting point and steeper increase of the Alcohol Use Disorders Identification Test consumption score over time, respectively. CONCLUSIONS: We found that MB behavioral control was associated with the binge drinking trajectory, while the MF reward prediction error signal was closely linked to the consumption score development. These findings support the idea that unbalanced MB and MF control might be an important individual vulnerability in predisposing to risky drinking behavior

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

Small integral membrane protein 10 like 1 downregulation enhances differentiation of adipose progenitor cells

Small integral membrane protein 10 like 1 (SMIM10L1) was identified by RNA sequencing as the most significantly downregulated gene in Phosphatase and Tensin Homologue (PTEN) knockdown adipose progenitor cells (APCs). PTEN is a tumor suppressor that antagonizes the growth promoting Phosphoinositide 3-kinase (PI3K)/AKT/mechanistic Target of Rapamycin (mTOR) cascade. Diseases caused by germline pathogenic variants in PTEN are summarized as PTEN Hamartoma Tumor Syndrome (PHTS). This overgrowth syndrome is associated with lipoma formation, especially in pediatric patients. The mechanisms underlying this adipose tissue dysfunction remain elusive. We observed that SMIM10L1 downregulation in APCs led to an enhanced adipocyte differentiation in two- and three-dimensional cell culture and increased expression of adipogenesis markers. Furthermore, SMIM10L1 knockdown cells showed a decreased expression of PTEN, pointing to a mutual crosstalk between PTEN and SMIM10L1. In line with these observations, SMIM10L1 knockdown cells showed increased activation of PI3K/AKT/mTOR signaling and concomitantly increased expression of the adipogenic transcription factor SREBP1. We computationally predicted an α-helical structure and membrane association of SMIM10L1. These results support a specific role for SMIM10L1 in regulating adipogenesis, potentially by increasing PI3K/AKT/mTOR signaling, which might be conducive to lipoma formation in pediatric patients with PHTS