Fourier coefficient of parameterized quantum circuits and barren plateau problem

We show the relationship between the Fourier coefficients and the barren plateau problem emerging in parameterized quantum circuits. In particular, the sum of squares of the Fourier coefficients is exponentially restricted concerning the qubits under the barren plateau condition. Throughout theory and numerical experiments, we introduce that this property leads to the vanishing of a probability and an expectation formed by parameterized quantum circuits. The traditional barren plateau problem requires the variance of gradient, whereas our idea does not explicitly need a statistic. Therefore, it is not required to specify the kind of initial probability distribution.Comment: 5 pages, 4 figure

Instability of magnetic skyrmion strings induced by longitudinal spin currents

It is well established that spin-transfer torques exerted by in-plane spin currents give rise to a motion of magnetic skyrmions resulting in a skyrmion Hall effect. In films of finite thickness or in three-dimensional bulk samples the skyrmions extend in the third direction forming a string. We demonstrate that a spin current flowing longitudinally along the skyrmion string instead induces a Goldstone spin wave instability. Our analytical results are confirmed by micromagnetic simulations of both a single string as well as string lattices suggesting that the instability eventually breaks the strings. A longitudinal current is thus able to melt the skyrmion string lattice via a dynamical phase transition. For films of finite thickness or in the presence of disorder a threshold current will be required, and we estimate the latter assuming weak collective pinning.Comment: 10 pages, 7 figure

Instability of Magnetic Skyrmion Strings Induced by Longitudinal Spin Currents

It is well established that spin-transfer torques exerted by in-plane spin currents give rise to a motion of magnetic skyrmions resulting in a skyrmion Hall effect. In films of finite thickness or in three-dimensional bulk samples the skyrmions extend in the third direction forming a string. We demonstrate that a spin current flowing longitudinally along the skyrmion string instead induces a Goldstone spin wave instability. Our analytical results are confirmed by micromagnetic simulations of both a single string as well as string lattices suggesting that the instability eventually breaks the strings. A longitudinal current is thus able to melt the skyrmion string lattice via a dynamical phase transition. For films of finite thickness or in the presence of disorder a threshold current will be required, and we estimate the latter assuming weak collective pinning

Tracing Monopoles and Anti-monopoles in a Magnetic Hedgehog Lattice

The magnetic hedgehog lattice (HL), which was recently discovered in the $B$20-type chiral magnet MnSi$_{1-x}$Ge$_x$, is a topological spin texture with a periodic array of magnetic monopoles and anti-monopoles. Within the continuum approximation, the monopoles and anti-monopoles are predicted to move, collide, and pair annihilate in an applied magnetic field, but it remains unclear how the lattice discretization affects their motions. Here, we study the trajectories of monopoles and anti-monopoles in a lattice system by simulated annealing with field sweep. We show that the monopoles and anti-monopoles move and repel before pair annihilations. We also clarify that their motions are closely related with the field dependence of the scalar spin chirality.Comment: 6 pages, 5 figure