  The topological charge $m$ of vortex electrons spans an infinite-dimensional
Hilbert space. Selecting a two-dimensional subspace spanned by $m=\pm 1$, a
beam electron in a transmission electron microscope (TEM) can be considered as
a quantum bit (qubit) freely propagating in the column. A combination of
electron optical quadrupole lenses can serve as a universal device to
manipulate such qubits at the experimenter's discretion. We set up a TEM probe
forming lens system as a quantum gate and demonstrate its action numerically
and experimentally. High-end TEMs with aberration correctors are a promising
platform for such experiments, opening the way to study quantum logic gates in
the electron microscope.
