Fig. 1: LLL projection and flux insertion in the quantum Hall liquid. | Nature Communications

Fig. 1: LLL projection and flux insertion in the quantum Hall liquid.

From: A possible route towards dissipation-protected qubits using a multidimensional dark space and its symmetries

Fig. 1

The LLL projection of a quantum Hall liquid on a torus maps the two-dimensional state into a one-dimensional ring of particles in orbital space. Inserting a flux quanta through one of the two cycles of the torus (depicted in red and blue) corresponds to a unitary operation that acts between the different ground states in the torus. In the one-dimensional representation, these unitary operations correspond to translation of the guiding centers by one orbital (T), or multiplication by a phase (U), depicted by blue and red arrows, respectively.

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