Error generation and propagation in Majorana-based topological qubits
Error generation and propagation in Majorana-based topological qubits
复制标题
DOI：
10.1103/physrevb.100.134307
复制
发表时间：
2019-05
影响因子：
3.7
通讯作者：
Aaron Conlon;D. Pellegrino;J. K. Slingerland;Shane Dooley;G. Kells
中科院分区：
文献类型：
--
作者：
Aaron Conlon;D. Pellegrino;J. K. Slingerland;Shane Dooley;G. Kells
我们研究了由非拓扑结隔开的两根$p$波超导导线组成的拓扑存储器的动力学演化，重点讨论了由于非绝热引起的初级误差(即量子比特损失)和次级误差(比特和相位反转)。在量子比特丢失的问题上，我们考察了系统对周期性边界驱动和有意穿梭Majorana束缚态的响应。在前一个场景中，我们展示了量子比特损失率与导线边缘的局域态密度是如何强烈相关的，这一事实可以使具有较大能隙的系统更容易受到高频噪声的影响。在第二种情况下，我们证实了先前关于超绝热和临界速度的预测，但没有看到任何证据表明边缘边界的协调运动减少了量子比特损失。我们对二次比特翻转错误的分析表明，两条线中都必须发生非绝热，并且为了打开这个错误通道，必须存在线间隧道效应。我们还演示了如何通过打乱两根导线的中心区域来最大限度地减少这种过程。最后，我们确定了相位翻转误差的错误通道，这可能是由于体激发态的能量不匹配而发生的。在这里讨论的非相互作用系统中，由于量子比特子空间中有限大小的分裂，这个误差系统地与预期的相位旋转相反。
We investigate dynamical evolution of a topological memory that consists of two $p$-wave superconducting wires separated by a non-topological junction, focusing on the primary errors (i.e., qubit-loss) and secondary errors (bit and phase-flip) that arise due to non-adiabaticity. On the question of qubit-loss we examine the system's response to both periodic boundary driving and deliberate shuttling of the Majorana bound states. In the former scenario we show how the frequency dependent rate of qubit-loss is strongly correlated with the local density of states at the edge of wire, a fact that can make systems with a larger gap more susceptible to high frequency noise. In the second scenario we confirm previous predictions concerning super-adiabaticity and critical velocity, but see no evidence that the coordinated movement of edge boundaries reduces qubit-loss. Our analysis on secondary bit flip errors shows that it is necessary that non-adiabaticity occurs in both wires and that inter-wire tunnelling be present for this error channel to be open. We also demonstrate how such processes can be minimised by disordering central regions of both wires. Finally we identify an error channel for phase flip errors, which can occur due to mismatches in the energies of states with bulk excitations. In the non-interacting system considered here this error systematically opposes the expected phase rotation due to finite size splitting in the qubit subspace.