[论文解读] Roadmap towards Majorana qubits and nonabelian physics in quantum dot-based minimal Kitaev chains

Athanasios Tsintzis, Rubén Seoane Souto+3 more|arXiv (Cornell University)|Jun 28, 2023

Topological Materials and Phenomena参考文献 111被引用 8

一句话总结

论文提出一种在双量子点 Kitaev 链上使用贫穷的马约拉纳束缚态来研究和演示非阿贝尔物理的路线图， outlining 从马约拉纳质量评估到类似 braiding 的操作的实验。它分析了通过超导区域耦合的真实自旋自由、相互作用的量子点并讨论如何实现基于 PMM 的量子比特、融合和 braiding 协议。

ABSTRACT

The possibility to engineer artificial Kitaev chains in arrays of quantum dots coupled via narrow superconducting regions has emerged as an attractive way to overcome the disorder issues that complicate the realization and detection of topological superconducting phases in other platforms. Although a true topological phase would require long chains, already a two-site chain realized in a double quantum dot can be tuned to points in parameter space where it hosts zero-energy states that seem identical to the Majorana bound states that characterize a topological phase. These states were named "poor man's Majorana bound states" (PMMs) because they lack formal topological protection. In this work, we propose a roadmap for next-generation experiments on PMMs. The roadmap starts with experiments to characterize a single pair of PMMs by measuring the Majorana quality, then moves on to initialization and readout of the parity of a PMM pair, which allows measuring quasiparticle poisoning times. The next step is to couple two PMM systems to form a qubit. We discuss measurements of the coherence time of such a qubit, as well as a test of Majorana fusion rules in the same setup. Finally, we propose and analyse three different types of braiding-like experiments which require more complex device geometries. Our conclusions are supported by calculations based on a realistic model with interacting and spinful quantum dots, as well as by simpler models to gain physical insight. Our calculations show that it is indeed possible to demonstrate nonabelian physics in minimal two-site Kitaev chains despite the lack of a true topological phase. But our findings also reveal that doing so requires some extra care, appropriately modified protocols and awareness of the details of this particular platform.

研究动机与目标

• 为基于量子点的 Kitaev 链中的下一代 PMM 实验提供动机并定义路线图。
• 量化马约拉纳质量及其在现实自旋耦合、相互作用的量子点系统中对非局域和非阿贝尔物理的影响。
• 概述可应用于 PMMs 的初始化、读出、量子比特实现、融合和 braiding 协议。
• 就实现高马约拉纳质量所需的实验控件（CAR 与 ECT 调谐、ABS 能量、自旋轨道耦合）提供指导。
• 评估在最小两站设置中观察非阿贝尔特征所需的实际挑战和协议调整。

提出的方法

• 对通过包含 Andreev 有界态（ABS）区域的超导区域耦合的双量子点（QD）系统进行建模。
• 使用具有 ABS 耦合、并且同时具有弹性反跳（ECT）和横向 Andreev 反射（CAR）的自旋自由、相互作用的 QD 哈密顿量。
• 推导得到无自旋极限以获得直觉，得到一个具有 ECT 和 CAR 幅度以及甜点条件的类 Kitaev 的两站模型。
• 引入马约拉纳质量度量（马约拉纳极化，MP）以量化 PMMs 与真正马约拉纳束缚态的相似程度。
• 发展低能量与有效模型来描述 PMM 的形成，包括一个低能量马约拉纳对及其在外部 QD 上的定位性质。
• 提出并模拟三类 braiding-like 协议族（基于电荷转移、基于测量、基于混合）并分析由于不完美 MP 导致的偏差。

Figure 1: (a) Sketch of a PMM system, with two QDs coupled via a grounded superconductor. We will later consider setups where one or both QDs couple to normal metal leads, charge detectors or additional PMM systems. (b) Energy level diagram showing the orbitals of the individual QDs and the ABS, as

实验结果

研究问题

• RQ1 在只有两站的 QD 基 Kitaev 链中，PMMs 是否可以在没有真正拓扑相的情况下展示非局域和非阿贝尔物理？
• RQ2 为了在 PMMs 中观测到非局域或非阿贝尔现象，需要的马约拉纳质量（MP）是多少，MP 如何在实验中被测量？
• RQ3 如何在现实的 QD–ABS 平台上初始化、读出并实现相干操控 PMM 基比特？
• RQ4 哪些融合和 braiding 协议能够在 PMM 系统中展示非阿贝尔统计，其结果如何取决于 MP？
• RQ5 哪些实验控件（CAR/ECT 平衡、ABS 能量、自旋轨道耦合、磁场）能优化马约拉纳质量并实现类似 braiding 的操作？

主要发现

• 在真实自旋自由、相互作用的量子点耦合到 ABS 的最小两站 Kitaev 链中可以实现 PMMs，但高度 MP 和接近简并性至关重要。
• 马约拉纳质量度量 MP 可以在可达的甜点处计算，并为可行的非局域和非阿贝尔实验提供信息。
• 将两个 PMM 系统耦合可形成量子比特，谱和门操作强烈依赖于 MP 以及系统间耦合。
• 可以通过 PMMs 进行融合式测量，但在与 braiding 测试相同的方式上对 MP 的敏感性较低； braiding 实验需要近似理想的 MP 以获得拓扑类结果。
• 概述三类 braiding-like 实验（基于电荷转移、基于测量、基于混合的 braiding），每类各有优势与挑战。
• 结果由在现实的自旋自由、相互作用模型以及更简单的自旋无模型中的计算支持，以阐明物理并指导实验协议。

Figure 2: (a) Transport setup that allows for measurement of the full differential conductance matrix of a PMM system, such as performed in Ref. [ 57 ] . (b) QD–PMM system embedded in a similar transport setup as in (a). (c) Local differential conductance ( $G=G_{RR}$ ) of the QD–PMM system for a hi