Revisiting the hopes for scalable quantum computation

Abstract

The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based on a number of assumptions, which are supposed to be satisfied exactly, like axioms, e.g. zero undesired interactions between qubits, etc. However in the physical world no continuous quantity can be exactly zero, it can only be more or less small. Thus the "error per qubit per gate" threshold must be complemented by the required precision with which each assumption should be fulfilled. This issue was never addressed. In the absence of this crucial information, the prospects of scalable quantum computing remain uncertain.Comment: 4 pages, title modifie

Influences of a topological defect on the spin Hall effect

“…SHE was predicted in first by [2,3]. This effect, which occurs as a result of the spin-orbit coupling (SOC) between electrons and impurities, is called extrinsic [4].…”

The effect of inertia on the Dirac electron, the spin Hall current and the momentum space Berry curvature

“…As spin current is nonconserved quantity, the control and generation of spin current is a challenging task. Since, the theoretical prediction of the spin Hall effect (SHE) [4], the application of spintronics has seen considerable advancement. This effect is observed experimentally in semiconductors and metals [5].…”

Current-driven domain wall motion along high perpendicular anisotropy multilayers: The role of the Rashba field, the spin Hall effect, and the Dzyaloshinskii-Moriya interaction

“…These SOTs could, at least, be originated by two phenomena: the Rashba effect due to the large SOC and structure inversion asymmetry at the two different heavy-metal/ferromagnet and ferromagnet/oxide interfaces [10][11][12][13][14] and/or the spin Hall current generated from the heavy metal layer and injected in the thin ferromagnet. [15][16][17][18][19][20][21] On the other hand, a thin ferromagnetic layer in contact with a heavy-metal with strong SOC is expected to experience an interfacial anisotropic exchange due to the Dzyaloshinskii-Moriya interaction (DMI). [22][23][24][25][26][27][28][29] The DMI is a chiral spin-orbit interaction originating from relativistic effects that occur due to the lack of inversion symmetry of the atomic structure, and it can result in topologically rich magnetization patterns such as spiral, skyrmions 25,27,28 or chiral domain walls.…”