Generalised quantum weakest preconditions

Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.Comment: 7 pages, no figures, added references, changed conten

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Learning in Community: The Song and Dance Women of the Fiery Cottage

This paper looks at how learning is opened up when it occurs in a loving and living space. Working together in a small cottage in a university campus has brought unexpected rewards to the theoretical learning of each of the inhabitants. The history of the women who have passed through this place resonates in the conversations. The place itself provides the conditions for sewing the frayed fabric of creative learning. In the hollow of this lies the shared meaning making that seeps across boundaries. There is a sense of the hidden, subversive unnamed and uncontested which gathers us into the living experience of learning. Here we celebrate the [in]competent, maverick and illegitimate. And here the questions are revealed as seeds for challenging theories of knowledge. We ask, if learning is fundamental to life then what happens when we celebrate the living? We are not attempting to arrive at definitive answers but to open up a conversation with multiple voices

Cortinarius subgenus Leprocybe in Europe: expanded Sanger and Next Generation Sequencing unveil unexpected diversity in the Mediterranean

Molecular phylogenies in the past decade have demonstrated that the described diversity of Cortinarius is still underestimated, especially outside continental and boreal ecoregions where the genus has been historically investigated. We tackled this issue by revisiting the so far unresolved subgenus Leprocybe, and focused on the largely unexplored Mediterranean hotspot of biodiversity. The sequencing and phylogenetic analysis of 161 vouchered collections from Austria, Cyprus, France, Germany, Italy and Spain, including 16 types, allowed for the delineation of 11 species in this lineage, three of them recognised as new to science and formally introduced as C. jimenezianus, C. selinolens and C. viridans spp. nov., respectively. Interestingly, the newly described species exhibit a strict Mediterranean distribution, and one of them is putatively endemic to the island of Cyprus, highlighting the remarkable potential of this neglected ecoregion to uncover further undescribed diversity of Cortinarius in the future. The present work also unveils 23 synonymies in this subgenus, as well as previously undetected crypticism within C. venetus. Next Generation Sequencing carried out on three old and contaminated holotypes, successfully decrypts their phylogenetic identity, including that of C. leproleptopus, finally settling the long-standing controversy over the taxonomic status of this species. A brief overview of each species in the subgenus is lastly provided and a key is proposed to facilitate the identification of presently known European taxa of Leprocybe in the field