  We propose to use the topological charge instead of the spin variable to span
a two-dimensional Hilbert space for beam electrons in a transmission electron
microscope (TEM). In this basis, an electron can be considered as a qbit freely
floating in vacuum. We show how a combination of magnetic quadrupoles with a
magnetic drift tube can serve as a universal device to manipulate such qbits at
the experimenter's discretion. High-end TEMs with aberration correctors, high
beam coherence and utmost stability are a promising platform for such
experiments, allowing the construction of quantum logic gates for single beam
electrons in a microscope.
