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的“噪声”——所谓的量子位——由于它们与环境的弱耦合，但非零耦合。由于这种耦合本质上是局部的，克服噪声问题的一种有希望的方法是使用拓扑量子现象对信息进行编码——拓扑量子现象具有鲁棒的全局特性，表征某些类型的量子系统不受局部扰动的影响。实现鲁棒拓扑量子比特的一个很有前途的平台是基于一种特殊的量子准粒子，称为马约拉纳费米子或马约拉纳零模式（MZM）。pi和其他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，即所谓的准马约拉纳模式。在这个项目中，pi将研究拓扑保护的基本方面和与最大化量子比特寿命和最小化非理想马约拉纳费米子量子器件噪声率相关的实际设计问题。由于该领域的大多数正在进行的研究都集中在理想的马约拉纳费米子上，这在实践中可能很难实现，因此目前的研究对于使用可能已经可用的，即非理想的马约拉纳费米子来设计第一代拓扑量子位至关重要。该项目将深化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，从而服务于国家利益，促进国家科学基金会的科学进步使命。该项目将为克莱姆森大学的本科生和研究生提供优秀的教育和培训机会，包括经济上处于不利地位的学生和占学生人数很大比例的未被充分代表的少数民族。该项目由量子信息科学计划（物理部）和促进竞争研究的既定计划（EPSCoR）共同资助。半导体-超导体（SM-SC）纳米线异质结构中的马约拉纳零模式（MZMs）目前正被研究作为未来量子计算机中拓扑量子比特的可能构建块。pi和其他人的理论研究表明，实验研究的SM-SC异质结构的大部分参数空间实际上被所谓的准马约拉纳零模式所占据，它们彼此之间的距离远远小于纳米线的长度。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，这种情况对TQC的可行性提出了一个主要问题，因为准majoranas不能为容错量子比特操作提供足够的拓扑保护。尽管如此，基于马约拉纳的第一代量子比特设备中很可能存在准马约拉纳，要么是设计的，要么是偶然的。该项目填补了由于拓扑量子比特设计和编织和纠错方案的研究几乎缺失所造成的关键空白，当组成构件是准马约拉纳时，而不是理想的拓扑mzm。pi将进行以下智能目标的分析和数值研究：(1)设计和建模基于可控准马约拉纳零模式的SM-SC量子比特器件，(2)理解和表征控制准马约拉纳量子比特寿命的关键物理过程，以及(3)具有准马约拉纳零模式的仅测量TQC方案的误差分析。总体目标是研究准马约拉纳零模式（而不是理想的MZMs）容错TQC的可行性，并更好地理解工程中基于马约拉纳的拓扑量子位的实际方面。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.