On Quantum Algorithms for Noncommutative Hidden Subgroups

Quantum algorithms for factoring and discrete logarithm have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the possibility of extending this general viewpoint to finding hidden subgroups of noncommutative groups. We present a quantum algorithm for the special case of dihedral groups which determines the hidden subgroup in a linear number of calls to the input function. We also explore the difficulties of developing an algorithm to process the data to explicitly calculate a generating set for the subgroup. A general framework for the noncommutative hidden subgroup problem is discussed and we indicate future research directions.Comment: 13 pages, no figures, LaTeX2

A Quantum Observable for the Graph Isomorphism Problem

Suppose we are given two graphs on $n$ vertices. We define an observable in the Hilbert space \Co[(S_n \wr S_2)^m] which returns the answer ``yes'' with certainty if the graphs are isomorphic and ``no'' with probability at least $1-n!/2^m$ if the graphs are not isomorphic. We do not know if this observable is efficiently implementable.Comment: 5 pages, no figure

The quantum query complexity of the hidden subgroup problem is polynomial

We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm. However our quantum algorithm requires exponential time, as in the classical case. Our algorithm utilizes a new technique for constructing error-free algorithms for non-decision problems on quantum computers.Comment: To appear in Information Processing Letters (IPL

Ontological co-belonging in Peter Sloterdijk's spherological philosophy of mediation

(Winner of the 2017 Paragraph annual essay prize competition, on the theme of ‘Belongings’) This article examines the ontology and politics of Peter Sloterdijk's Spheres trilogy, focusing in particular upon the notion of microspherical enclosure explicated in the first volume of this series. Noting Sloterdijk's unusual alignment of his philosophy with media theory, three main contentions are put forward. Firstly, that Sloterdijk's reconfiguration of Heidegger's fundamental ontology represents a largely unacknowledged renunciation of the primacy of Being-towards-death in the authentic existence of Dasein, foregrounding instead an originary co-belonging between mother and child. Secondly, that Sloterdijk borrows from media theory a concern regarding the facticity of all communication, grounding philosophical discourse in the determinate locality of its origin, but does so while exalting a pre-natal communicative immediacy that would seem to disparage the everydayness of Dasein. Finally, that Sloterdijk's oft-justified scepticism regarding globalization often retreats into an anti-cosmopolitanism that, in its nostalgia for the comfort, security and immediacy of the matrixial co-belonging (and the various attempts by humans to replicate this enclosure), evinces a covert but potentially noxious politics of exclusion

Assessment of cleaning to control lead dust in homes of children with moderate lead poisoning: treatment of lead-exposed children trial

In this article we describe the assessment and control of lead dust exposure in the Treatment of Lead-exposed Children (TLC) Trial, a clinical trial of the effects of oral chelation on developmental end points in urban children with moderately elevated blood lead levels. To reduce potential lead exposure from settled dust or deteriorated paint during the drug treatment phase of the trial, the homes of 765 (98%) of the randomized children (both active and placebo drug treatment groups) were professionally cleaned. Lead dust measurements were made in a sample of 213 homes before and after cleaning. Geometric mean dust lead loadings before cleaning were 43, 29, 308, and 707 micro g/ft2 in the kitchen floor, playroom floor, playroom windowsill, and playroom window well samples respectively. Following cleaning, floor dust lead loadings were reduced on average 32% for paired floor samples (p < 0.0001), 66% for windowsills (p < 0.0001), and 93% for window wells (p < 0.0001). Cleaning was most effective for 146 homes with precleaning dust lead levels above the recommended clearance levels, with average reductions of 44%, 74%, and 93% for floors (p < 0.0001), windowsills (p < 0.0001), and window wells (p < 0.0001), respectively. Despite these substantial reductions in dust lead loadings, a single professional cleaning did not reduce the lead loadings of all dust samples to levels below current federal standards for lead in residential dust. Attainment of dust levels below current standards will require more intensive cleaning and lead hazard reduction strategies