Quantum picturalism for topological cluster-state computing

Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of computing is a leading candidate for large-scale quantum computing. However, there has been a lack of sufficiently powerful high-level languages to describe computing in this form without resorting to single-qubit operations, which quickly become prohibitively complex as the system size increases. In this paper we apply the category-theoretic work of Abramsky and Coecke to the topological cluster-state model of quantum computing to give a high-level graphical language that enables direct translation between quantum processes and physical patterns of measurement in a computer - a "compiler language". We give the equivalence between the graphical and topological information flows, and show the applicable rewrite algebra for this computing model. We show that this gives us a native graphical language for the design and analysis of topological quantum algorithms, and finish by discussing the possibilities for automating this process on a large scale.Comment: 18 pages, 21 figures. Published in New J. Phys. special issue on topological quantum computin

The Measurement Calculus

Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operations. Among measurement-based quantum computation methods, the recently introduced one-way quantum computer stands out as fundamental. We develop a rigorous mathematical model underlying the one-way quantum computer and present a concrete syntax and operational semantics for programs, which we call patterns, and an algebra of these patterns derived from a denotational semantics. More importantly, we present a calculus for reasoning locally and compositionally about these patterns. We present a rewrite theory and prove a general standardization theorem which allows all patterns to be put in a semantically equivalent standard form. Standardization has far-reaching consequences: a new physical architecture based on performing all the entanglement in the beginning, parallelization by exposing the dependency structure of measurements and expressiveness theorems. Furthermore we formalize several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. This allows us to transfer all the theory we develop for the one-way model to these models. This shows that the framework we have developed has a general impact on measurement-based computation and is not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new version also include formalization of several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. To appear in Journal of AC

Association between substance use and psychosocial characteristics among adolescents of the Seychelles

BACKGROUND: We examined the associations between substance use (cigarette smoking, alcohol drinking, and cannabis use) and psychosocial characteristics at the individual and family levels among adolescents of the Seychelles, a rapidly developing small island state in the African region. METHODS: A school survey was conducted in a representative sample of 1432 students aged 11-17 years from all secondary schools. Data came from a self-administered anonymous questionnaire conducted along a standard methodology (Global School-based Health Survey, GSHS). Risk behaviors and psychosocial characteristics were dichotomized. Association analyses were adjusted for a possible classroom effect. RESULTS: The prevalence of cigarette smoking, alcohol drinking and cannabis use was higher in boys than in girls and increased with age. Age-adjusted and multivariate analyses showed that several individual level characteristics (e.g. suicidal ideation and truancy) and family level characteristics (e.g. poor parental monitoring) were associated with substance use among students. CONCLUSIONS: Our results suggest that health promotion programs should simultaneously address multiple risk behaviors and take into account a wide range of psychosocial characteristics of the students at the individual and family levels

Graph States and the necessity of Euler Decomposition

Coecke and Duncan recently introduced a categorical formalisation of the interaction of complementary quantum observables. In this paper we use their diagrammatic language to study graph states, a computationally interesting class of quantum states. We give a graphical proof of the fixpoint property of graph states. We then introduce a new equation, for the Euler decomposition of the Hadamard gate, and demonstrate that Van den Nest's theorem–locally equivalent graphs represent the same entanglement–is equivalent to this new axiom. Finally we prove that the Euler decomposition equation is not derivable from the existing axioms