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

The maximally entangled symmetric state in terms of the geometric measure

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and reference

The Expectation Monad in Quantum Foundations

The expectation monad is introduced abstractly via two composable adjunctions, but concretely captures measures. It turns out to sit in between known monads: on the one hand the distribution and ultrafilter monad, and on the other hand the continuation monad. This expectation monad is used in two probabilistic analogues of fundamental results of Manes and Gelfand for the ultrafilter monad: algebras of the expectation monad are convex compact Hausdorff spaces, and are dually equivalent to so-called Banach effect algebras. These structures capture states and effects in quantum foundations, and also the duality between them. Moreover, the approach leads to a new re-formulation of Gleason's theorem, expressing that effects on a Hilbert space are free effect modules on projections, obtained via tensoring with the unit interval.Comment: In Proceedings QPL 2011, arXiv:1210.029

Bacterial diversity and community composition from seasurface to subseafloor

© The International Society for Microbial Ecology, 2015. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in ISME Journal 10 (2016): 979–989, doi:10.1038/ismej.2015.175.We investigated compositional relationships between bacterial communities in the water column and those in deep-sea sediment at three environmentally distinct Pacific sites (two in the Equatorial Pacific and one in the North Pacific Gyre). Through pyrosequencing of the v4–v6 hypervariable regions of the 16S ribosomal RNA gene, we characterized 450 104 pyrotags representing 29 814 operational taxonomic units (OTUs, 97% similarity). Hierarchical clustering and non-metric multidimensional scaling partition the samples into four broad groups, regardless of geographic location: a photic-zone community, a subphotic community, a shallow sedimentary community and a subseafloor sedimentary community (greater than or equal to1.5 meters below seafloor). Abundance-weighted community compositions of water-column samples exhibit a similar trend with depth at all sites, with successive epipelagic, mesopelagic, bathypelagic and abyssopelagic communities. Taxonomic richness is generally highest in the water-column O2 minimum zone and lowest in the subseafloor sediment. OTUs represented by abundant tags in the subseafloor sediment are often present but represented by few tags in the water column, and represented by moderately abundant tags in the shallow sediment. In contrast, OTUs represented by abundant tags in the water are generally absent from the subseafloor sediment. These results are consistent with (i) dispersal of marine sedimentary bacteria via the ocean, and (ii) selection of the subseafloor sedimentary community from within the community present in shallow sediment.This study was funded by the Biological Oceanography Program of the US National Science Foundation (grant OCE-0752336) and by the NSF-funded Center for Dark Energy Biosphere Investigations (grant NSF-OCE-0939564)

Virtual Machine Support for Many-Core Architectures: Decoupling Abstract from Concrete Concurrency Models

The upcoming many-core architectures require software developers to exploit concurrency to utilize available computational power. Today's high-level language virtual machines (VMs), which are a cornerstone of software development, do not provide sufficient abstraction for concurrency concepts. We analyze concrete and abstract concurrency models and identify the challenges they impose for VMs. To provide sufficient concurrency support in VMs, we propose to integrate concurrency operations into VM instruction sets. Since there will always be VMs optimized for special purposes, our goal is to develop a methodology to design instruction sets with concurrency support. Therefore, we also propose a list of trade-offs that have to be investigated to advise the design of such instruction sets. As a first experiment, we implemented one instruction set extension for shared memory and one for non-shared memory concurrency. From our experimental results, we derived a list of requirements for a full-grown experimental environment for further research

Exploring new drilling prospects in the southwest Pacific

A major International Ocean Discovery Program (IODP) workshop covering scientific ocean drilling in the southwest Pacific Ocean was held in Sydney, Australia, in late 2012. The workshop covered all fields of geoscience, and drilling targets in the area from the Equator to Antarctica. High-quality contributions and a positive and cooperative atmosphere ensured its success. The four science themes of the new IODP science plan were addressed. An additional resource-oriented theme considered possible co-investment opportunities involving IODP vessels. As a result of the workshop, existing proposals were revised and new ones written for the April 2013 deadline. Many of the proposals are broad and multidisciplinary in nature, hence broadening the scientific knowledge that can be produced by using the IODP infrastructure. This report briefly outlines the workshop and the related drilling plans

Search for supersymmetry in hadronic final states with missing transverse energy using the variables αT and b-quark multiplicity in pp collisions at [Formula: see text].

An inclusive search for supersymmetric processes that produce final states with jets and missing transverse energy is performed in pp collisions at a centre-of-mass energy of 8 TeV. The data sample corresponds to an integrated luminosity of 11.7 fb-1 collected by the CMS experiment at the LHC. In this search, a dimensionless kinematic variable, αT, is used to discriminate between events with genuine and misreconstructed missing transverse energy. The search is based on an examination of the number of reconstructed jets per event, the scalar sum of transverse energies of these jets, and the number of these jets identified as originating from bottom quarks. No significant excess of events over the standard model expectation is found. Exclusion limits are set in the parameter space of simplified models, with a special emphasis on both compressed-spectrum scenarios and direct or gluino-induced production of third-generation squarks. For the case of gluino-mediated squark production, gluino masses up to 950-1125 GeV are excluded depending on the assumed model. For the direct pair-production of squarks, masses up to 450 GeV are excluded for a single light first- or second-generation squark, increasing to 600 GeV for bottom squarks

Stacking faults and superstructures in a layered brownmillerite

Stacking faults in Ca4Fe2Mn0.5Ti0.5O9 have been examined using X-ray diffraction and high-resolution transmission electron microscopy. Electron diffraction revealed two superstructures with ordered stacking sequences