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arXiv 2201.05160quant-phcond-mat.supr-con
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拓扑Majorana量子比特系统容错量子门操作的完全描述

Complete description of fault-tolerant quantum gate operations for topological Majorana qubit systems

Adrian Scheppe, Michael Pak

备注：
7 pages, 2 figures
发表信息：
Phys. Rev. A 105 (2022) 012415
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摘要：

在量子计算的主要威胁列表中，量子退相干是最大的威胁之一，因为它会对计算系统内的环境产生损失，而这些损失无法通过纠错方法恢复。这些方法需要假设环境相互作用迫使量子比特态成为量子比特本征态的某种线性组合。实际上，环境导致量子位进入混合状态，其中原始状态不再可恢复。一个有前途的解决方案，这个问题的计算状态的基础上的低躺能量激发拓扑材料。这些状态的存在是由一个全局参数内的哈密顿，防止计算状态耦合本地和散肩保护。在本文中，量子比特是基于非局域的，拓扑马约拉纳费米子（MF），和门操作产生的交换或编织的位置说MF。这种门操作的算法计算是众所周知的，但是，相反的门到编织计算目前还不发达。此外，因为可以从许多不同的可能量子位定义中进行选择，所以从计算到计算的结果门操作看起来不同。这里，为了逻辑流程起见，对两个和四个MF情况的计算进行了概括。这组门是理解和构造六-MF事例的基础。使用这些，通过完全概括可能的量子位定义之间的门和变换的列表来进行系统的完整表征。一个完整的描述这个系统是可取的，并有望为未来的迭代拓扑量子位。

英文摘要：

Among the list of major threats to quantum computation, quantum decoherence poses one of the largest because it generates losses to the environment within a computational system which cannot be recovered via error correction methods. These methods require the assumption that the environmental interaction forces the qubit state into some linear combination of qubit eigenstates. In reality, the environment causes the qubit to enter into a mixed state where the original is no longer recoverable. A promising solution to this problem bases the computational states on the low lying energy excitations within topological materials. The existence of these states is protected by a global parameter within the Hamiltonian which prevents the computational states from coupling locally and decohering. In this paper, the qubit is based on nonlocal, topological Majorana fermions (MF), and the gate operations are generated by swapping or braiding the positions of said MF. The algorithmic calculation for such gate operations is well known, but, the opposite gates-to-braid calculation is currently underdeveloped. Additionally, because one may choose from a number of different possible qubit definitions, the resultant gate operations from calculation to calculation appear different. Here, the calculations for the two- and four-MF cases are recapitulated for the sake of logical flow. This set of gates serves as the foundation for the understanding and construction of the six-MF cases. Using these, a full characterization of the system is made by completely generalizing the list of gates and transformations between possible qubit definitions. A complete description of this system is desirable and will hopefully serve future iterations of topological qubits.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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