A quantum logic gate for free electrons

Stefan Löffler1, Thomas Schachinger1,2, Peter Hartel3, Peng-Han Lu4,5, Rafal E. Dunin-Borkowski4, Martin Obermair6, Manuel Dries6, Dagmar Gerthsen6, and Peter Schattschneider1,2

1University Service Centre for Transmission Electron Microscopy, TU Wien, Wiedner Hauptstraße 8-10/E057-02, 1040 Wien, Austria
2Institute of Solid State Physics, TU Wien, Wiedner Hauptstraße 8-10/E138-03, 1040 Wien, Austria
3CEOS Corrected Electron Optical Systems GmbH, Englerstraße 28, 69126 Heidelberg, Germany
4Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons (ER-C) and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany
5RWTH Aachen University, Ahornstraße 55, 52074 Aachen, Germany
6Laboratorium für Elektronenmikroskopie (LEM), Karlsruher Institut für Technologie (KIT), Engesserstraße 7, 76131 Karlsruhe, Germany

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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.

This proof-of-principle experiment shows that free electrons in a transmission electron microscope (TEM) can be used as qubits, the building blocks for quantum computers. We demonstrate a quantum logic gate which can transform these qubits from one state to another. With a spatial resolution down to atomic dimensions, the TEM is ideally suited for the study of the fundamentals of quantum manipulation. In addition to the possible applications in quantum computing, this study also paves the way for significantly improving the TEM’s efficiency by transforming the electron beam into an optimal quantum state for a given experiment.

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