Nonlocality as a Benchmark for Universal Quantum Computation in Ising Anyon Topological Quantum Computers

An obstacle affecting any proposal for a topological quantum computer based on Ising anyons is that quasiparticle braiding can only implement a finite (non-universal) set of quantum operations. The computational power of this restricted set of operations (often called stabilizer operations) has been studied in quantum information theory, and it is known that no quantum-computational advantage can be obtained without the help of an additional non-stabilizer operation. Similarly, a bipartite two-qubit system based on Ising anyons cannot exhibit non-locality (in the sense of violating a Bell inequality) when only topologically protected stabilizer operations are performed. To produce correlations that cannot be described by a local hidden variable model again requires the use of a non-stabilizer operation. Using geometric techniques, we relate the sets of operations that enable universal quantum computing (UQC) with those that enable violation of a Bell inequality. Motivated by the fact that non-stabilizer operations are expected to be highly imperfect, our aim is to provide a benchmark for identifying UQC-enabling operations that is both experimentally practical and conceptually simple. We show that any (noisy) single-qubit non-stabilizer operation that, together with perfect stabilizer operations, enables violation of the simplest two-qubit Bell inequality can also be used to enable UQC. This benchmarking requires finding the expectation values of two distinct Pauli measurements on each qubit of a bipartite system.Comment: 12 pages, 2 figure

Multipower variation for Brownian semistationary processes

In this paper we study the asymptotic behaviour of power and multipower variations of processes $Y$:$$Y_t=\int_{-\in fty}^tg(t-s)\sigma_sW(\mathrm{d}s)+Z_t,$$ where $g:(0,\infty)\rightarrow\mathbb{R}$ is deterministic, $\sigma >0$ is a random process, $W$ is the stochastic Wiener measure and $Z$ is a stochastic process in the nature of a drift term. Processes of this type serve, in particular, to model data of velocity increments of a fluid in a turbulence regime with spot intermittency $\sigma$. The purpose of this paper is to determine the probabilistic limit behaviour of the (multi)power variations of $Y$ as a basis for studying properties of the intermittency process $\sigma$. Notably the processes $Y$ are in general not of the semimartingale kind and the established theory of multipower variation for semimartingales does not suffice for deriving the limit properties. As a key tool for the results, a general central limit theorem for triangular Gaussian schemes is formulated and proved. Examples and an application to the realised variance ratio are given.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ316 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function

For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate affecting the non-stabilizer resource is sufficiently high, then these states and operations can become simulable in the sense of the Gottesman-Knill theorem, reducing the overall power of the circuit to no better than classical. In this paper we find the depolarizing noise rate at which this happens, and consequently the most robust non-stabilizer states and non-Clifford gates. In doing so, we make use of the discrete Wigner function and derive facets of the so-called qudit Clifford polytope i.e. the inequalities defining the convex hull of all qudit Clifford gates. Our results for robust states are provably optimal. For robust gates we find a critical noise rate that, as dimension increases, rapidly approaches the the theoretical optimum of 100%. Some connections with the question of qudit magic state distillation are discussed.Comment: 14 pages, 1 table; Minor changes vs. version

Biofortification of UK food crops with selenium

Se is an essential element for animals. In man low dietary Se intakes are associated with health disorders including oxidative stress-related conditions, reduced fertility and immune functions and an increased risk of cancers. Although the reference nutrient intakes for adult females and males in the UK are 60 and 75 μg Se/d respectively, dietary Se intakes in the UK have declined from >60 μg Se/d in the 1970s to 35 μg Se/d in the 1990s, with a concomitant decline in human Se status. This decline in Se intake and status has been attributed primarily to the replacement of milling wheat having high levels of grain Se and grown on high-Se soils in North America with UK-sourced wheat having low levels of grain Se and grown on low-Se soils. An immediate solution to low dietary Se intake and status is to enrich UK-grown food crops using Se fertilisers (agronomic biofortification). Such a strategy has been adopted with success in Finland. It may also be possible to enrich food crops in the longer term by selecting or breeding crop varieties with enhanced Se-accumulation characteristics (genetic biofortification). The present paper will review the potential for biofortification of UK food crops with Se

Transport through an impurity tunnel coupled to a Si/SiGe quantum dot

Achieving controllable coupling of dopants in silicon is crucial for operating donor-based qubit devices, but it is difficult because of the small size of donor-bound electron wavefunctions. Here we report the characterization of a quantum dot coupled to a localized electronic state, and we present evidence of controllable coupling between the quantum dot and the localized state. A set of measurements of transport through this device enable the determination of the most likely location of the localized state, consistent with an electronically active impurity in the quantum well near the edge of the quantum dot. The experiments we report are consistent with a gate-voltage controllable tunnel coupling, which is an important building block for hybrid donor and gate-defined quantum dot devices.Comment: 5 pages, 3 figure

Surface area measurements of marine basalts: Implications for the subseafloor microbial biomass

These first measurements of specific surface area (SSA) of bulk samples of subsurface marine basalts were undertaken to determine the potential area available for microbial colonization. SSA ranged from 0.3 to 52 m2/g of basalt with the lowest value coming from pillow basalt and the highest value from breccia. The average for massive and pillow basalts combined was 2.3 m2/g. The total specific surface area of the extrusive volcanic rocks of the ocean crust is estimated to be 1024 m2. This surface area could provide attachment for up to 1034 cells if cell density is the same as that of experimentally colonized basalt surfaces. Independent measures and calculations of biomass in basalts suggest that cell densities on surfaces are only 10−4 times those in laboratory experiments and, therefore, the surface area of basalt does not limit microbial biomass in the igneous ocean crust. Citation: Nielsen, M. E., and M. R. Fisk (2010), Surface area measurements of marine basalts: Implications for the subseafloor microbial biomass

Evidence for Efimov quantum states in an ultracold gas of cesium atoms

Systems of three interacting particles are notorious for their complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics. However, the observation of Efimov quantum states has remained an elusive goal. Here we report the observation of an Efimov resonance in an ultracold gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied. We also detect a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems. While Feshbach resonances have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter to the world of few-body quantum phenomena.Comment: 18 pages, 3 figure

Incidence of WISE -selected obscured AGNs in major mergers and interactions from the SDSS

We use the Wide-field Infrared Survey Explorer (WISE) and the Sloan Digital Sky Survey (SDSS) to confirm a connection between dust-obscured active galactic nuclei (AGNs) and galaxy merging. Using a new, volume-limited (z ≤ 0.08) catalogue of visually selected major mergers and galaxy–galaxy interactions from the SDSS, with stellar masses above 2 × 1010 M⊙, we find that major mergers (interactions) are 5–17 (3–5) times more likely to have red [3.4] − [4.6] colours associated with dust-obscured or ‘dusty’ AGNs, compared to non-merging galaxies with similar masses. Using published fibre spectral diagnostics, we map the [3.4] − [4.6] versus [4.6] − [12] colours of different emission-line galaxies and find that one-quarter of Seyferts have colours indicative of a dusty AGN. We find that AGNs are five times more likely to be obscured when hosted by a merging galaxy, half of AGNs hosted by a merger are dusty, and we find no enhanced frequency of optical AGNs in merging over non-merging galaxies. We conclude that undetected AGNs missed at shorter wavelengths are at the heart of the ongoing AGN-merger connection debate. The vast majority of mergers hosting dusty AGNs are star forming and located at the centres of Mhalo < 1013 M⊙ groups. Assuming plausibly short-duration dusty-AGN phases, we speculate that a large fraction of gas-rich mergers experience a brief obscured AGN phase, in agreement with the strong connection between central star formation and black hole growth seen in merger simulations