No abstract

We study the influence of quantum dot symmetry on the Rabi frequency and phonon-induced spin relaxation rate in a single-electron GaAs spin qubit. We find that anisotropic dependence on the magnetic field direction is independent of the choice of the gating potential. Also, we discover that relative orientation of the quantum dot, with respect to the crystallographic frame, is relevant in systems with C1v, C2v, or Cn (n = 4r) symmetry. To demonstrate the important impact of the gating potential shape on the spin qubit lifetime, we compare the effects of an infinite-wall equilateral triangle, square, and rectangular confinement with the known results for the harmonic potential. In the studied cases, enhanced spin qubit lifetime is revealed, reaching almost six orders of magnitude increase for the equilateral triangle gating.

In this paper, we investigate the impact of gating potential and magnetic field on phonon induced spin relaxation rate and the speed of the electrically driven single-qubit operations inside the InSb nanowire spin qubit. We show that a strong g factor and high magnetic field strength lead to the prevailing influence of electron-phonon scattering due to deformation potential, considered irrelevant for materials with a weak g factor, like GaAs or Si/SiGe. In this regime, we find that spin relaxation between qubit states is significantly suppressed due to the confinement perpendicular to the nanowire axis. We also find that maximization of the number of single-qubit operations that can be performed during the lifetime of the spin qubit requires single or highly asymmetric double quantum dot gating potential.

When discussing the gauge symmetries of any theory, the Henneaux–Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important role in understanding the structure of the full gauge symmetry group of any theory, especially regarding the subgroup of diffeomorphisms. We give a review of the Henneaux–Teitelboim transformations and the resulting gauge group in the general case and then discuss its role in the applications to the class of topological theories called nBF models, relevant for the constructions of higher gauge theories and quantum gravity.