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鉴于“摩尔定律”已经逼近极限, 众多替代传统计算的方法被提出, 其中量子计算是最受关注和研究最广泛的一种. 由于量子体系的不可封闭性, 外界大量不可控的因素会导致量子耗散和退相干, 为了尽可能避免量子叠加态的退相干, 制备具有鲁棒性的量子比特成为了关键环节之一. 马约拉纳零能模是拓扑和超导复合体系中涌现的准粒子, 具有非阿贝尔统计性质, 它的时空编织受到非局域的拓扑性质保护, 因此, 以马约拉纳零能模构造的拓扑量子比特对量子退相干具有天然的鲁棒性. 虽然经过全球范围内各个实验组艰苦卓绝的探求, 目前关于马约拉纳零能模的实验验证仍然扑朔迷离. 本文回顾了量子计算的发展历程和主要的技术手段, 重点介绍了拓扑超导态/体的理论、可观测的实验现象、以及最新的实验研究进展, 并对此做出了分析和评述. 最后对拓扑超导态/体在量子计算领域的应用前景进行了展望.Since the physical limit of Moore's law is being approached, many alternative computing methods have been proposed, among which quantum computing is the most concerned and widely studied. Owing to the non closeability of quantum system, the uncontrollable external factors will lead to quantum dissipation and decoherence. In order to avoid the decoherence of quantum superposition state, the fabrication of robust quantum bits has become one of the key factors. Majorana zero mode (MZM) is a quasi-particle emerging in the topological and superconducting hybrid system. It has non-Abelian statistical properties. Therefore, the topological qubit constructed by MZM has natural robustness to quantum decoherence. Despite the arduous exploration by various experimental groups, the experimental verification of MZM is still lacking. This paper reviews the history and main technical routes of quantum computing, focusing on the theory of topological superconductors, observable experimental phenomena, and the latest experimental progress. Furthermore we discuss and analyze the present status of the topological superconductor research. Finally, we prospect the future experiments and applications of topological superconductors in quantum computing.
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Keywords:
- quantum computing /
- topological superconductor
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图 1 经典比特(左)和量子比特(右)图示. 量子比特可以代表|0
$\rangle $ 态和|1$\rangle $ 态的叠加态Fig. 1. Classic bit (left) and qubit (right). Qubit presents the superposition of |0
$\rangle $ and |1$\rangle $ .
图 5 (a), (b), (c)展示了在x方向为有限边界而y方向为周期性边界时的能级结构, 从(a)到(c)缓慢增加磁场h的大小, 当满足
$ {\psi }_{s}^{2}+ϵ{\left(\mathrm{0, 0}\right)}^{2} < {h}^{2} < {\psi }_{s}^{2}+ϵ{\left(0, \mathrm{\pi }\right)}^{2} $ 时, 即(c), 边界涌现了两个无能隙的边界模, 表明发生了拓扑相变[114]Fig. 5. (a), (b), and (c) The band energy of the lattice Hamiltonian with edges at x direction. The magnetic field increases from Figure (a) to Figure (c). The red thin line indicates a gapless chiral edge mode localized on the one side and green thick line a gapless chiral edge mode on the other side. They appear for
$ {\psi }_{s}^{2}+ϵ{\left(\mathrm{0, 0}\right)}^{2} < {h}^{2} < {\psi }_{s}^{2}+ϵ{\left(0, \mathrm{\pi }\right)}^{2} $ at Figure (c), which indicates the occurrence of topological phase transition[114].
图 11 Fe1+ySexTe1–x上马约拉纳零能模的近量子化电导平台特征 (a) 扫描隧道显微镜示意图[148]; (b) 小图中涡旋的线界面图[148]; (c) 微分电导谱[148]; (d) 三维微分电导谱[148]; (e) 图(c)的彩色图[148]; (f), 图(e)在零偏置是的水平切线[148]; (g) 图(e)在高偏置是的水平切线[148]
Fig. 11. Zero-bias conductance plateau observed on Fe1+ySexTe1–x: (a) Schematic of variable tunnel coupling STM/S method[148]; (b) a line-cut intensity plot along the dashed white arrow in the inset[148]; (c) an overlapping plot of dI/dV spectra[148]; (d) 3D plot of tunnel coupling dependent measurement, dI/dV (E, GN) [148]; (e) color-scale plot of Figure (c) [148]; (f) horizontal line-cut at the zero-bias from Figure (e)[148]; (g) horizaontal line-cuts at high-bias from Figure (e)[148].
图 12 超导抗磁性在Fe1+ySexTe1–x薄片中的分布 (a) 样品光学显微镜照片[150]; (b), (c) 样品的抗磁和磁化强度sSQUID扫描图[150]; (d)—(g) 随温度变化的抗磁sSQUID扫描图[150]; (h) 图(d)中r箭头指向的不同温度抗磁曲线[150]; (i) 根据图(h)做出的彩图[150]; (j) 在图(d)中1和2两点处提取的随温度变化的超流密度[150]
Fig. 12. Distinctive edge features in susceptometry of Fe1+ySexTe1–x flake: (a) Optical image of the sample[150]; (b), (c) the susceptometry and magnetometry images of the sample, respectively[150]; (d)–(g) susceptometry images of the sample at various T[150]; (h) line cuts of the susceptometry images at various T along the vector direction (r) as labeled by the arrow in Figure (d) [150]; (i) interpolated image from the line cuts in Figure (h) [150]; (j) superfluid densities as a function of T extracted from point 1 and 2 in Figure (d)[151]
图 13 Li(Fe, Co)As的电子结构 (a) Li(Fe, Co)As的晶体结构[151]; (b) LiFeAs随ΓM和ΓZ的能带色散[151]; (c), (b) Cut D处的面内能带结构[151]; (d) LiFeAs (001)面的表面谱[151]; (e) 15 K时LiFe1–xCoxAs (x = 3%)的ARPES谱[151]; (f) 10 K时LiFe1–xCoxAs (x = 9%)的ARPES谱[151]
Fig. 13. Electronic structure of Li(Fe, Co)As: (a) Crystal structure of Li(Fe, Co)As[151]; (b) zoomed-in view of the LiFeAs band dispersion along ΓM and ΓZ[151]; (c) in-plane band structure at Cut D in Figure(b) [151]; (d) (001) surface spectrum of LiFeAs[151]; (e) ARPES intensity plot of LiFe1–xCoxAs (x = 3%) at 15 K[151]; (f) ARPES intensity plot of LiFe1–xCoxAs (x = 9%) at 10 K[151].
图 19 分子束外延β-Bi2Pd薄膜的拓扑超导电性和马约拉纳零能模 (a) 扫描隧道显微镜的扫描图[169]; (b) β-Bi2Pd 的微分电导谱[169]; (c) 归一化的零偏置电导峰分布图[169]; (d) 隧穿电导谱[169]; (e) 涡旋核心附近的归一化微分电导谱[169]
Fig. 19. Topological superconductivity and MZM in β-Bi2Pd film grown by MBE: (a) STM topography[169]; (b) Differential conductance dI/dV spectrum[169]; (c) normalized zero-bias conductance map[169]; (d) tunneling conductance dI/dV spectrum[169]; (e) normalized dI/dV spectra measured at location with radial distance r from the vortex center[169].
图 21 Bi2Te3/NbSe2上的零偏置电导峰劈裂 (a) 电导曲线[181]; (b) 通过图(a)做出的彩色图[181]; (c)—(g) 2—6层的电导彩色图[181]; (h) 劈裂点随层数变化曲线[181]
Fig. 21. (a) A series of dI/dV curves[181]; (b) the color image of Figure (a) [181]; (c)–(g) the experimental results for 2-6QL samples, following the similar data process of Figure (b) [181]; (h) summary of the start points of the peak split [181].
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