Higher order topological superconductors as generators of quantum codes
Yizhi You, Daniel Litinski, Felix von Oppen
TL;DR
This paper demonstrates how interactions in higher order topological superconductors can induce topologically ordered phases, including quantum error correcting codes and fracton phases, with potential experimental realizations.
Contribution
It reveals the connection between HOTSC and topologically ordered phases, introducing a framework for realizing quantum codes and fracton matter via interacting HOTSC.
Findings
Interacting HOTSC can realize surface and color codes.
Interactions can induce fracton phases in 3D HOTSC.
Arrays of Majorana wires can experimentally probe these phases.
Abstract
We show that interactions can drive a class of higher order topological superconductors (HOTSC) into symmetry enriched topologically ordered phases exemplified by topological quantum error correcting codes. In two dimensions, interacting HOTSC realize various topologically ordered surface and color codes. In three dimensions, interactions can drive HOTSC protected by subsystem symmetries into recently discovered fracton phases. We explicitly relate fermion parity operators underlying the gapless excitations of the HOTSC to the Wilson algebra of symmetry enriched quantum codes. Arrays of crossed Majorana wires provide an experimental platform for realizing fracton matter and for probing the quantum phase transition between HOTSC and topologically ordered phase.
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