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1 2 Experimental and theoretical challenges for the trapped electron quantum computerWe discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studies and the analysis of all important elements, relevant for the experimental stage. On the theoretical side, we discuss different methods to couple electron qubits. We estimate the relevant qubit coherence times and draw implications for the experimental setting. A critical assessment of quantum information processing with trapped electrons is concluding the article.

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In this paper we analyze the localization of W (n), the fiber of the double suspension map S 2n−1 → Ω 2 S 2n+1 , with respect to E(2). If four cells at the bottom of DpM 2np−1 , the pth extended power spectrum of the Moore spectrum, are collapsed to a point, then one obtains a spectrum C. Let QM 2np−1 → QC be the James-Hopf map followed by the collapse map. Then we show that the secondary suspension map BW (n) → QM 2np−1 has a lifting to the fiber of QM 2np−1 → QC and this lifting is shown to be a v 2-periodic equivalence, hence an E(2)-equivalence.