Recently, there has been substantial interest in realizations of skyrmions, in particular in quasi-2D systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultra-dense magnetic memories. Here, we use the most general form of the quasi-2D free energy with DzyaloshinskiiMoriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with four-fold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyro-dynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. We find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.

We present a Lie-algebraic classification and detailed construction of the dynamical invariants, also known as Lewis-Riesenfeld invariants, of the four-level systems including two-qubit systems which are most relevant and sufficiently general for quantum control and computation. These invariants not only solve the time-dependent Schrödinger equation of four-level systems exactly but also enable the control, and hence quantum computation based on which, of four-level systems fast and beyond adiabatic regimes.

We theoretically analyze the errors in one-and two-qubit gates in SiMOS and Si/SiGe spin qubit experiments, and present a pulse sequence which can suppress the errors in exchange coupling due to charge noise using ideal local rotations. In practice, the overall fidelity of the pulse sequence will be limited only by the quality of the single-qubit gates available: the C-phase infidelity comes out to be ≈ 2.5× the infidelity of the single-qubit operations. Based on experimental data, we model the errors and show that C-phase gate infidelities can be suppressed by two orders in magnitude.Our pulse sequence is simple and we expect an experimental implementation would be relatively straightforward. We also evaluate the performance of this gate against 1/f noise. Assuming a soft ultraviolet cutoff, we show that the pulse sequence designed for quasistatic noise still performs well when the cutoff occurs below ∼ 1MHz with experimentally achievable one-qubit Rabi frequencies, suppressing the infidelity by an order of magnitude compared to the existing direct adiabatic protocol. We also analyze the effects of nonadiabaticity during finite rise periods, and find that adiabaticity is not a limitation for the current values of exchange coupling. arXiv:1806.01262v2 [cond-mat.mes-hall]

We study the dynamical control of a magnetic skyrmion bubble by using counter-propagating surface acoustic waves (SAWs) in a ferromagnet. First, we determine the bubble mass and derive the force due to SAWs acting on a magnetic bubble using Thiele's method. The force that pushes the bubble is proportional to the strain gradient for the major strain component. We then study the dynamical pinning and motion of magnetic bubbles by SAWs in a nanowire. In a disk geometry, we propose a SAWs-driven skyrmion bubble oscillator with two resonant frequencies.

We show that elongated magnetic skyrmions can host Majorana bound states in a proximitycoupled two-dimensional electron gas sandwiched between a chiral magnet and an s-wave superconductor. Our proposal requires stable skyrmions with unit topological charge, which can be realized in a wide range of multilayer magnets, and allows quantum information transfer by using standard methods in spintronics via skyrmion motion. We also show how braiding operations can be realized in our proposal.