Quantum algorithm for neighborhood preserving embedding

Neighborhood preserving embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point, constructing the weight matrix, and obtaining the transformation matrix. Liang et al. proposed a variational quantum algorithm (VQA) for NPE [Phys. Rev. A 101 032323 (2020)]. The algorithm consists of three quantum sub-algorithms, corresponding to the three steps of NPE, and was expected to have an exponential speedup on the dimensionality n. However, the algorithm has two disadvantages: (i) It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one. (ii) Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA. In this paper, we propose a complete quantum algorithm for NPE, in which we redesign the three sub-algorithms and give a rigorous complexity analysis. It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm, and achieve a significant speedup compared to Liang et al.'s algorithm even without considering the complexity of the VQA.     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

介观电路中量子纠缠的经典对应

从量子力学诞生日起,它的经典对应(或类比)一直是物理学家关心的话题.本文以介观电路量子化的框架中,带有互感的两个介观电容-电感(LC)电路为例,首次讨论了量子纠缠的经典类比(或对应)问题.先用有序算符内的积分理论证明其互感是产生量子纠缠的源头;再推导出求解特征频率的公式,就发现它与一个经典系统的小振动频率的表达式有相似之处,该经典系统组成如下:两个墙壁各连一个相同的弹簧,两个弹簧之间接着一个滑动小车可以在光滑的桌面上运动,小车挂有一根单摆.用分析力学求此系统的小振动频率,发现与上述介观电路的特征频率形式类似,单摆的摆动会造成小车来回振动,摆、小车和弹簧的互相牵制效应反映了小车和摆的"纠缠".     

Negative thermal expansion in NbF_3 and NbOF_2:A comparative theoretical study

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field. Here,the negative thermal expansion of Nb F_3 and Nb OF_2 was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation(QHA). We studied the total charge density, thermal vibration, and lattice dynamic to investigate the thermal expansion mechanism. We found that the presence of O induced the relatively strong covalent bond in Nb OF_2, thus weakening the transverse vibration of F and O in Nb OF_2, compared with the case of Nb F_3.In this study, we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms.The present work not only predicts two NTE compounds, but also provides an insight on thermal expansion control by designing chemical bond type.     

吸收波长和吸收效率可控的超材料吸收器

为了使超材料完美吸收器(metamaterial perfect absorber,MPA)能够同时实现吸收效率和吸收波长的控制,本文提出利用二氧化钒(VO2)和石墨烯作为MPA的材料,通过对MPA的结构设计,在红外波段实现了高吸收,吸收效率最高可达99%.研究发现通过改变VO2的温度和石墨烯的化学势,可同时实现MPA吸收效率和吸收波长的控制,吸收效率调制深度和吸收波长调谐范围分别可达97.08%和3.2μm.通过对MPA在吸收波长处的磁场分布分析可以得出,MPA能够产生高吸收是由于其形成了法布里-帕罗(Fabry-Pérot,FP)干涉腔共振,研究发现MPA的结构参数对FP腔的共振波长具有显著的影响.     

射频等离子制备石墨烯负载Co3O4催化剂及其析氧性能研究

氢能的引入能有效提升配电网的供电可靠性,而电解水制氢是实现低碳转型的关键技术,开发高效的电解水催化剂势在必行。过渡金属氧化物储量大、催化活性高,是具有广阔应用前景的析氧反应催化剂。本文通过射频等离子体处理制备石墨烯上负载Co₃O₄析氧催化剂,XRD、Raman和XPS测试结果显示,二维结构石墨烯的引入加速表面电子迁移,增大了反应面积。等离子体处理促进了纳米粒子在石墨烯上的负载,利用等离子体刻蚀作用在催化剂表面制造出大量碳结构缺陷和氧空位结构,改善了活性位点分布,有效调控Co₃O₄电子结构,提高析氧催化活性。电化学测试表明,本文中合成的Co₃O₄@rGO在电流密度为50 mA·cm^-2时的过电位为410 mV,动力学反应速率较快,表现出优于商业IrO₂的析氧催化活性。     

新型功能碳材料的高压截获

高性能功能材料在诸多领域具有广泛的应用前景,是人们一直关注的研究热点。高压可以有效地改变物质的原子间距和成键方式,是获得新型功能材料的重要途径。在碳材料的高压研究中,许多有趣的功能碳材料,如光学透明碳、高强度弹性碳和超硬非晶碳等,已经通过不同的碳前驱体合成。本文简要介绍了作者近年来在低维碳基纳米复合材料高压研究中取得的进展,基于设计的不同低维碳前驱体,高压下截获了具有超硬特性、新型压致共价聚合及发光增强的碳材料。     

基于抛光基材的热蒸镀铜箔生长高平整单层石墨烯薄膜

在石墨烯的化学气相沉积工艺中,铜箔是决定石墨烯薄膜质量的重要因素。传统铜箔由于制备工艺的限制,存在大量的缺陷,导致石墨烯薄膜的成核密度较高。本工作选用抛光铝板、抛光不锈钢板、微晶玻璃和SiO₂/Si作为基材,用热蒸镀法制备了不同粗糙度的铜箔,并详细讨论了以该系列铜箔生长高平整度石墨烯薄膜的条件及铜箔对石墨烯薄膜品质的影响。实验结果表明,铜箔以(111)取向为主,与基材分离后,表面具有纳米级平整度。在生长石墨烯后,从SiO₂/Si剥离的铜箔成核密度是4种基材中最小的。同时,从SiO₂/Si剥离的铜箔晶体结构变化最不明显,具有良好的结晶性,表面几乎不存在铜晶界缺陷。当压强为3 000 Pa,氢气和甲烷流速分别为300 mL/min和0.5 mL/min时,可以获得约1 mm横向尺寸的石墨烯单晶晶畴。     

Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

Enhanced Power Density of Alcohol Biofuel Cell by Polymer-assisted Crosslinks of 3D Graphene on Carbon Paper as the Bioanode

Herein, we successfully construct the 3D biocompatible graphene through crosslinking 2D graphene nanosheet onto carbon fiber paper with poly(diallyldimethylammonium chloride) (PDDA) as anode of the alcohol biofuel cell. Compared with the bioanode without 3D graphene, the current density and output power of PDDA-graphene-ADH bioanode is increased by 23 % and 41 % at a high concentration of ethanol at pH 8.9, suggesting the stabilization role of graphene in enzyme loading. The study provides us a deep analysis on structures and performances of the bioanode incl. electrochemistry, X-ray photoelectron spectra, and atomic force microscopy images, which is significant to develop the new methods to construct 3D porous electrodes in energy conversion device.