Long-range coupling of spin qubits in superconductor-semiconductor hybrid structures

该项目的目的是从理论上研究使用超导片或导线作为耦合器的前景，这种耦合器允许在长达几微米的距离上可控地诱导自旋量子比特之间的交换耦合。这种耦合对于使自旋比特成为可伸缩的体系结构至关重要。耦合通过具有确定自旋的准粒子通过超导体的虚交换进行。我们将研究磁性和非磁性无序、自旋轨道相互作用和非平衡准粒子的作用，以及它们如何影响栅极保真度，当栅极通过超导体进行远程耦合时。特别是，我们将详细研究在执行门的过程中如何产生准粒子，这将使我们能够找到门可以操作的速度限制。我们还将详细模拟量子点和超导体电子库之间的隧道耦合，因为它是决定我们希望实现的耦合强度的最重要的数字。所采用的方法是解析和数值方法的结合：例如，对于清洁超导体，我们将求解Bogoliubov-de Gennes方程。对无序系统的研究采用了适用于比费米波长长得多的平均自由程的半经典格林函数技术，并辅以在较小平均自由程范围内使用递归格林函数的数值方法。非平衡问题将用自旋量子比特密度矩阵的主方程来研究，使我们能够同时考虑相干交换耦合和不同的退相干机制。

The aim of the project is to theoretically investigate the prospects of using superconducting sheets or wires as couplers that allows for controllably inducing exchange coupling between spin qubits over a distance of up to several microns. Such a coupling is crucial to make spin gubits a scalable architecture. The coupling proceeds via a virtual exchange of a quasiparticle with definite spin through the superconductor. We will investigate the role of magnetic and non-magnetic disorder, spin-orbit interaction, and non-equilibrium quasiparticles and how they influence the gate fidelities, when the gates are mediated by the long-range coupling through the superconductor. In particular, we will study in detail how quasiparticles are generated in the process of performing the gates, which will enable us to find limits on the speed at which the gates can be operated. We will also model the tunnel coupling between the quantum dot and the electron reservoir of the superconductor in detail, as it is the single most-important number determining the strength of the coupling we can hope to achieve. The methods employed are a combination of analytical as well as numerical approaches: e.g. for the clean superconductors, we will solve the Bogoliubov-de Gennes equation. The study of the disordered system is performed by employing semiclassical Green's functions techniques valid for mean free paths much longer than the Fermi wave-length, supplemented by numerical approaches using recursive Green's function in the regime of smaller mean free path. The non-equilibrium problems will be investigated with master equations for the density matrix of the spin qubit that enable us to take both the coherent exchange coupling as well as the different decoherence mechanisms into account.