Tight Noise Thresholds for Quantum Computation with Perfect Stabilizer Operations

We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove that for all unitary single-qubit gates there exists a tight depolarizing noise threshold that determines whether the gate enables universal quantum computation or if the gate can be simulated by a mixture of Clifford gates. This exact threshold is determined by the Clifford polytope spanned by the 24 single-qubit Clifford gates. The result is in contrast to the situation wherein non-stabilizer qubit states are used; the thresholds in that case are not currently known to be tight.Comment: 4 pages, 2 figure

Tekstbegrip en klantbelang bij financiële producten

De laatste jaren is tekstbegrip van consumenten in de belangstelling gekomen in de wereld van financiële dienstverlening. Onduidelijkheid van productvoorwaarden, folders en brieven zou bijdragen aan wantrouwen in deze sector. Omgekeerd wordt vaak gedacht dat het verbeteren van duidelijkheid van teksten in het belang van de klant is en resulteert in het herstel van vertrouwen. Onderzoek laat echter zien dat het allemaal niet zo eenvoudig is. Tekstbegrip is een moeilijk waar te nemen fenomeen dat opgebouwd lijkt te zijn uit een complexe keten van contextafhankelijke variabelen. Bovendien is het verband tussen tekstbegrip en klantbelang niet evident. In deze bijdrage proberen we de materie te ontrafelen en te ordenen. Een aantal vragen staat daarbij centraal: Wat maakt dat mensen productvoorwaarden, algemene voorwaarden en soortgelijke juridisch relevante teksten wel of niet lezen? Wat is duidelijkheid van tekst en hoe meet je die bij juridische teksten? Is er verband tussen de mate van duidelijkheid van de tekst en consumentengedrag? In deze bijdrage geven we een overzicht van de wetenschappelijke literatuur op dit gebied en evalueren we de uitkomsten daarvan

De prijs van het gelijk

Het verslag van de discussie die is gevoerd tijdens de vergadering van de Nederlandse Vereniging voor Procesrecht van 1 jnui 2007 naar aanleiding van de inleidingen van mr. J.L.R.A. Huydecoper, mr. G.A. van der Veen en mr. F.B. Falkena met als centraal thema de kritische bespreking van het systeem van vergoeding van gerechtelijke en buitengerechtelijke kosten

De reikwijdte van het beslag

Mr. J.H. van Dam-Lely en mr. M.L. Tuil doen verslag van de voorjaarsvergadering van de Nederlandse Vereniging voor Procesrecht op 6 juni 2008 over de ‘reikwijdte van het beslag’. De inleidingen van mr. A.J. van der Meer (beslagverlof en opheffingskortgeding), mr. J.G.A. Linssen (bewijsbeslag) en mr. J.C. van Oven (beslag op verhulde beslagobjecten) worden in het verslag beknopt samengevat; van de discussie wordt uitgebreid verslag gedaan

Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs

We examine the existence and structure of particular sets of mutually unbiased bases (MUBs) in bipartite qudit systems. In contrast to well-known power-of-prime MUB constructions, we restrict ourselves to using maximally entangled stabilizer states as MUB vectors. Consequently, these bipartite entangled stabilizer MUBs (BES MUBs) provide no local information, but are sufficient and minimal for decomposing a wide variety of interesting operators including (mixtures of) Jamiolkowski states, entanglement witnesses and more. The problem of finding such BES MUBs can be mapped, in a natural way, to that of finding maximum cliques in a family of Cayley graphs. Some relationships with known power-of-prime MUB constructions are discussed, and observables for BES MUBs are given explicitly in terms of Pauli operators.Comment: 8 pages, 1 figur

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

Carbon budget of a shallow, lagoonal estuary: Transformations and source-sink dynamics along the river-estuary-ocean continuum

A comprehensive carbon budget was constructed to quantify carbon flows through the freshwater-marine continuum of a temperate, microtidal estuary. We performed coordinated measurements of dissolved inorganic carbon and total organic carbon fluxes to resolve spatial variability between and along the channel and shoals and diel variability across the entire estuary for 2 yr. Net ecosystem metabolism (NEM) was the most significant control on carbon flow within estuary regions. However, metabolic rates were spatially coupled such that counteracting fluxes across the channel-shoal gradient or along the river-ocean gradient resulted in system-wide NEM that was closely in balance (-3.0 +/- 3.3 to 1.1 +/- 4.4 molC m(-2) yr(-1)). Similarly, large diel and seasonal variability in air-water CO2 fluxes were observed during 72 spatial surveys, but these short-term variations generally cancelled out when aggregated to annual budget terms. Although atmospheric exchanges were small (-0.2 +/- 0.1 to 2.0 +/- 0.4 molC m(-2) yr(-1)), they were subject to large errors (+/- 4 molC m(-2) yr(-1)) if diel variability was neglected. Internal mechanisms that maintained balanced carbon flows were strongly impacted by river discharge and were only apparent by separately quantifying channel and shoal fluxes. Notably, metabolic responses of the shoal to river forcing outweighed the responses of the channel, and the net impact was contrary to prior relationships derived from synthesis of lower-resolution carbon budgets. Our budget demonstrates that resolution of carbon fluxes at appropriate scales, including channel-shoal and diel variability, is critical to characterizing ecosystem function and the fate of carbon within the river-ocean continuum

Enhanced Peculiar Velocities in Brane-Induced Gravity

The mounting evidence for anomalously large peculiar velocities in our Universe presents a challenge for the LCDM paradigm. The recent estimates of the large scale bulk flow by Watkins et al. are inconsistent at the nearly 3 sigma level with LCDM predictions. Meanwhile, Lee and Komatsu have recently estimated that the occurrence of high-velocity merging systems such as the Bullet Cluster (1E0657-57) is unlikely at a 6.5-5.8 sigma level, with an estimated probability between 3.3x10^{-11} and 3.6x10^{-9} in LCDM cosmology. We show that these anomalies are alleviated in a broad class of infrared-modifed gravity theories, called brane-induced gravity, in which gravity becomes higher-dimensional at ultra large distances. These theories include additional scalar forces that enhance gravitational attraction and therefore speed up structure formation at late times and on sufficiently large scales. The peculiar velocities are enhanced by 24-34% compared to standard gravity, with the maximal enhancement nearly consistent at the 2 sigma level with bulk flow observations. The occurrence of the Bullet Cluster in these theories is 10^4 times more probable than in LCDM cosmology.Comment: 15 pages, 6 figures. v2: added reference