Collaborative Research: Non-Ideal Majorana Fermions: A Practical Approach to Topological Quantum Computation

量子计算的主要障碍是影响量子计算机基本单元--即所谓的量子比特--的“噪声”，这是它们与环境弱而非零耦合的结果。由于这种耦合本质上是局部的，克服噪声问题的一个有前途的方法是使用拓扑量子现象来编码信息--拓扑量子现象是指某些类型的量子系统不受局部扰动影响的稳健的全局特性。一个很有前途的实现强拓扑量子比特的平台是基于一种特殊的量子准粒子，称为Majorana费米子或Majorana零模(MZM)。PIS和其他研究小组最近的理论研究表明，实验可能已经发现了MZM的非理想版本，即所谓的准Majorana模式。在这个项目中，PI将研究拓扑保护的基本方面，以及与最大化量子比特寿命和最小化具有非理想Majorana费米子的量子器件中的噪声比率相关的实际设计问题。由于该领域正在进行的大多数研究都集中在理想的Majorana费米子上，而这在实践中可能很难实现，因此本研究对于使用可能已经可用的非理想的Majorana费米子来设计第一代拓扑量子比特将是至关重要的。该项目将通过加深我们对凝聚态系统中拓扑量子物质的理解，并研究基于实验可用设备的拓扑量子计算的可行性，为国家利益服务，并促进NSF的科学进步使命。该项目将为克莱姆森大学的本科生和研究生提供极好的教育和培训机会，包括经济困难的学生和代表不足的少数族裔，这些学生占学生总数的很大比例。该项目由量子信息科学计划(物理部)和已建立的激励竞争研究计划(EPSCoR)共同资助。半导体-超导体(SM-SC)纳米线异质结中的Majorana零模(MZM)目前正被研究为未来量子计算机中拓扑量子位的可能构建块。PI等人的理论研究表明，实验研究的SM-Sc异质结的大部分参数空间实际上被所谓的准Majorana零模占据，这些模彼此之间的长度尺度远低于纳米线长度。由于拓扑量子计算(TQC)中的容错原理严重依赖于使用由纳米线长度分隔的拓扑MZM对量子信息进行非局部编码，这种情况给TQC的可行性带来了一个主要问题，因为准Majorana不能为容错量子比特操作提供足够的拓扑保护。尽管如此，准马约拉纳很可能会出现在第一代基于马约拉纳的量子比特设备中，要么是故意的，要么是偶然的。这个项目填补了由于几乎没有研究拓扑量子比特设计和编织和纠错方案的关键空白，当组成构件是准Majoranas而不是理想的拓扑MZM时。PI将执行以下智能目标的分析和数值研究：(1)基于可控准Majorana零模的SM-SC量子比特器件的设计和建模；(2)理解和表征控制准Majorana量子比特寿命的关键物理过程；以及(3)准Majorana零模纯测量TQC方案中的误差分析。首要目标是调查准Majorana零模(而不是理想的MZM)容错TQC的可行性，并更好地了解基于Majorana拓扑量子的工程实践方面。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The main obstacle to quantum computation is the “noise” affecting the basic units of a quantum computer – the so-called qubits – as a result of their weak, but nonzero coupling to the environment. Since this coupling is essentially local, a promising approach to overcoming the noise problem is to encode the information using topological quantum phenomena – robust global properties characterizing certain types of quantum systems that are immune to local perturbations. A promising platform for realizing robust topological qubits is based on a special kind of quantum quasiparticle called a Majorana fermion or Majorana zero mode (MZM). Recent theoretical studies by the PIs and other groups indicate that experiments may have already uncovered non-ideal versions of MZMs, the so-called quasi-Majorana modes. In this project the PIs will examine fundamental aspects of topological protection and practical design questions related to maximizing qubit lifetime and minimizing noise rates in quantum devices with non-ideal Majorana fermions. With most of the ongoing research in the field focusing on ideal Majorana fermions, which in practice may be hard to realize, the present studies will be critical to engineering the first generation of topological qubits using what may be already available, namely, non-ideal Majorana fermions. The project will serve the national interest and promote the NSF mission of progress of science by deepening our understanding of topological quantum matter in condensed matter systems and investigating the feasibility of topological quantum computation based on experimentally available devices. The project will provide excellent education and training opportunities to undergraduate and graduate students at Clemson University, including economically disadvantaged students and underrepresented minorities who constitute a significant percentage of the student population. This project is jointly funded by the Quantum Information Science Program (Physics Division), and the Established Program to Stimulate Competitive Research (EPSCoR). Majorana zero modes (MZMs) in semiconductor-superconductor (SM-SC) nanowire heterostructures are currently being investigated as possible building blocks for topological qubits in a future quantum computer. Theoretical studies by the PIs and others have shown that much of the parameter space of the experimentally investigated SM-SC heterostructures is in fact occupied by so-called quasi-Majorana zero modes, which are separated from each other by a length scale well below the nanowire length. Since the principle of fault tolerance in topological quantum computation (TQC) depends critically on the non-local encoding of quantum information using topological MZMs separated by the length of the nanowire, this situation presents a major problem for the feasibility of TQC, as quasi-Majoranas do not enjoy sufficient topological protection for fault-tolerant qubit operations. Nonetheless, quasi-Majoranas are likely to be present in the first generation of Majorana-based qubit devices either by design, or by accident. This project fills the critical void created by the near absence of studies of topological qubit designs and schemes for braiding and error correction when the constituent building blocks are quasi-Majoranas, rather than ideal topological MZMs. The PIs will perform analytical and numerical research with the following intellectual goals: (1) Designing and modeling SM-SC qubit devices based on controllable quasi-Majorana zero modes, (2) Understanding and characterizing the key physical processes that control the quasi-Majorana qubit lifetimes, and (3) Error analysis in measurement-only TQC schemes with quasi-Majorana zero modes. The overarching goal is to investigate the feasibility of fault tolerant TQC with quasi-Majorana zero modes (rather than ideal MZMs) and to better understand practical aspects of engineering Majorana-based topological qubits.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.