中国科大全球首次实现量子分解算法

日前，中国科大潘建伟教授领导的研究小组，在国际上首次实现了Shot量子分解算法，其研究成果发表在12月19日出版的美国权威物理学期刊《物理评论快报》上，这标志着我国光学量子计算研究达到了国际领先水平。

中国科技大学专家在国际上率先实现量子分解算法

中国科技大学潘建伟教授及其同事杨涛、陆朝阳等，在国际上首次利用光量子计算机实现了休尔量子分解算法，研究成果发表在12月19日出版的美国权威物理学期刊《物理评论快报》上，标志着我国光学量子计算研究达到了国际领先水平。

基于量子分解的航拍图像中值滤波

针对无人机航拍图像在采集或者传输过程中容易产生噪声的问题,提出了一种基于量子图像分解的中值滤波算法。该算法首先将经典图像表示为量子图像,并通过量子理论对量子图像进行分解,得到分解子图,然后利用改进的快速中值滤波算法对分解子图进行去噪,最后将各子图去噪结果进行合成得到最终的去噪图像。实验证明,该方法能够有效去除无人机航拍图像中的椒盐噪声和高斯噪声,所提算法在去噪效果方面与传统中值滤波算法相比,信噪比提高了约17%,与递归中值滤波相比提高了约28%。并且算法的效率得到了一定程度的提高。

基于QR迭代的量子奇异值分解

针对大型矩阵奇异值分解(singular value decomposition,SVD)时使用经典算法时间复杂度较高,以及已有的量子SVD算法要求待分解的矩阵必须具有非稀疏低秩的性质,并且在计算过程中构造任意大小酉矩阵对目前的量子计算机来说实现起来并不容易等问题,提出基于QR迭代的量子SVD。QR迭代使用的是Householder变换,通过量子矩阵乘法运算完成经典矩阵乘法运算过程。实验结果表明,该方法能够得到所求矩阵的奇异值及奇异矩阵,使大型矩阵的SVD具有可行性。

二分法在多线量子逻辑门分解中的应用

将经典的对称二分法应用于多线量子可逆逻辑门的分解中,证明当量子位数n≥5且3≤k≤n-2时,任意多线量子可逆逻辑门(′k-′CNOT门)可以在没有辅助位的情况下由少于[4﹂log2(k-2)」+1-3(2﹂log2(k-2)」+1-k+1)2﹂log2(k-2)」]个′2-′CNOT门(Toffoli门)构成.利用该方法可以使由多线量子可逆逻辑门分解而生成的物理电路门阵列数大幅下降.与Yang等报道的实验结果相比,′2-′CNOT门的数量级由O(2k)减少为O(k2).

随机变量的量子分解和增长图的渐近谱分布

本文给出了一般Bernoulli随机变量X的量子分解,三点路图m步返回路线条数的积分表示以及两类增长图-圈与完全二分图的渐近谱分布.这使得在量子概率框架下研究经典随机变量或经典概率分布成为可能,也在一定程度上展示了图的谱分析中的量子概率技巧.

量子线路中的酉算子分解研究

由量子逻辑门构造的量子线路是实现量子计算的基础。从算子角度来看,量子逻辑门的数学本质是酉算子,研究任意量子门的酉算子分解问题是优化量子线路的关键。本文从Pauli门和Hadamard门这两类基本的逻辑门分析入手,首先拓展了Pauli门、Hadamard门与旋转算子的线路恒等式关系;随后基于具体的线路恒等式关系,对于量子线路中的任意单量子比特门分解结论,提出了更为直观、简便的证明方法。这些工作将有助于后续量子计算的数学本质刻画。

相互作用Fock空间中的离散时间量子Bernoulli噪声

本文提出一种新的离散时间下量子Bernoulli噪声(QBN),并将其引入到相互作用Fock空间中.首先,利用Bernoulli随机变量的量子分解,得到了湮灭、增生、保守算子.然后,构造了相互作用Fock空间中的量子Bernoulli噪声,讨论了它的性质.我们还找到一个算子过程是适应的充要条件.最后,我们重新定义了关于QBN的适应算子过程的积分,并证明了适应算子的鞅性.

Analysis of Molecular Weight Distribution and Antioxidant Activities of Cirrhinus molitorella Skin Collagen Hydrolysates

[Objective] The aim of this work was to identify molecular weight （MW） distribution and antioxidant activity of fish skin col agen hydrolysates. [Method] The MW distribution of hydrolysates was determined using both size exclusion chromatography and matrix-assisted laser desorption ionization time-of-flight mass spec-trometry （MALDI-TOF-MS）. Fish skin were treated by the alkaline protease 2709. [Result] The optional conditions for hyerolysis were time 3 h, temperature 55 ℃, pH 10.0, substrate concentration 80 g/L and E/S 4%. The results of both methods indi-cated that the molecular weight of col agen hydrolysates was from 400 to 1 800 Da, and the peptides’ molecular weight was less than 1 400 Da mostly. The reducing power and antioxidant/radical scavenging activity [1, 1-diphenyl-2-picryl-hydrazyl （DPPH） free radical scavenging activity] were determined. [Conclusion] The results reveal that the fishskin hydrolysate is a potential source of antioxidants.

Realization of Two-Qutrit Quantum Gates with Control Pulses

We investigate the realization of 2-qutrit logic gate in a bipartite 3-level system with qusi-Ising interaction. On the basis of Caftan decomposition of matrices, the unitary matrices of 2-qutrit are factorized into products of a series of realizable matrices. It is equivalent to exerting a certain control field on the system, and the control goal is usually gained by a sequence of control pulses. The general discussion on the realization of 2-qutrit logic gate is made first, and then the realization of the ternary SWAP gate and the ternary √SWAP gate are discussed specifically, and the sequences of control pulses and drift processes implementing these gates are given.

Integrability of N-Component Bariev Model Under Open Boundary Conditions

N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.

Constrained least squares algorithm for channel vector estimation in 2-D RAKE receiver

Based on the fact that the variation of tile direction of arrival (DOA) isslower than that of the channel fading, the steering vector of the desired signal is estimatedfirstly using a subspace decomposition method and then a constrained condition is configured.Traffic signals are further employed to estimate the channel vector based on the constrained leastsquares criterion. We use the iterative least squares with projection (ILSP) algorithm initializedby the pilot to get the estimation. The accuracy of channel estimation and symbol detection can beprogressively increased through the iteration procedure of the ILSP algorithm. Simulation resultsdemonstrate that the proposed algorithm improves the system performance effectively compared withthe conventional 2-D RAKE receiver.

Prime Factorization in the Duality Computer

We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat＇s method in classical computing. All these algorithms may be polynomial in the input size.

Some Theorems About Unitons of Harmonic Maps into U(N)

By using the simplified method of factorization given by Valli, and the correspondence between the harmonic map φ∶S 2→U(N) and U(N) uniton bundle ν(φ) with energy corresponding to the bundles’ second Chern class, which is established by Anand, the energy in a case φ∶S 2→U(N) is investigated in order to estimate the energy of a uniton using the uniton number. It is proved that Uhlenbeck’s factorization is energy decreasing. And a method of estimating the energy of a uniton by the uniton number is given.

Key Exchange Protocol Based on Tensor Decomposition Problem

The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.

Role of Organic Acids in Desorption of Mercury from Contaminated Soils in Eastern Shandong Province,China

Batch experiments were conducted to study the effects of low-molecular-weight organic acids(LMWOAs) on desorption of Hg from two kinds of soils in the eastern Shandong Province,China.Of all LMWOAs,oxalic and citric acids were chosen as the representatives in this experiment because they are most common in soils.Desorption of Hg increases with the increase of extracting time,until the highest desorption amount at 6-8 h,and then declines.It indicates that timeliness is very important when organic acids are used for phytoremediation in contaminated soils.When the concentrations of organic acids increase from 1.0 mmol/L to 10.0 mmol/L,Hg desorption increases significantly regardless of oxalic or citric acid.Compared with oxalic acid,citric acid is more effective to enhance the desorption of Hg,especially from fluvo-aquic soil.With the increase of initial pH value from 3 to 8,Hg desorption decreases directly in the presence of oxalic acid.However,Hg desorption first decreases,then increases,and eventually decreases again in the presence of citric acid due to the variation of competitive ability between chelating of citric acid and adsorption of soil in different pH values.Citric acid showed greater ability to release Hg from soils than oxalic acid.According to the results of the present study,it is found that the bioavailabilities of heavy metal can be improved with selecting suitable types and concentrations of organic acid amendment and reasonable soil condition.

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization （II）： Solution of Equation

In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green＇s function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.

Enhanced visible-light-driven photocatalytic activities of 0D/1D heterojunction carbon quantum dot modified CdS nanowires

Zero‐dimensional carbon dots(0D C‐dots)and one‐dimensional sulfide cadmium nanowires(1D CdS NWs)were prepared by microwave and solvothermal methods,respectively.A series of heterogeneous photocatalysts that consisted of 1D CdS NWs that were modified with 0D C‐dots(C‐dots/CdS NWs)were synthesized using chemical deposition methods.The mass fraction of C‐dots to CdS NWs in these photocatalysts was varied.The photocatalysts were characterized using X‐ray diffraction,scanning electron microscopy,transmission electron microscopy,X‐ray photoelectron spectroscopy,and ultraviolet‐visible spectroscopy.Their photocatalytic performance for the spitting of water and the degradation of rhodamine B(RhB)under visible light irradiation were investigated.The photocatalytic performance of the C‐dots/CdS NWs was enhanced when compared with that of the pure CdS NWs,with the 0.4%C‐dots/CdS NWs exhibiting the highest photocatalytic activity for the splitting of water and the degradation of RhB.The enhanced photocatalytic activity was attributed to a higher carrier density because of the heterojunction between the C‐dots and CdS NWs.This heterojunction improved the electronic transmission capacity and promoted efficient separation of photogenerated electrons and holes.

Entangled States in a Single-Qubit Structure with SQUID Coupled with a Super-conducting Resonator

In this paper, the number-phase quantization scheme of the mesoscopic circuit, which consists of a singlequbit structure with superconducting quantum interference device coupled with a super-conducting resonator, is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-l/2 notation. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can not only be prepared, but also be manipulated by tuning the magnetic flux through the super-conducting loop.

Matrix Tensor Product Approach to the Equivalence of Multipartite States under Local Unitary Transformations

The equivalence of multipartite quantum mixed states under local unitary transformations is studied. A criterion for the equivalence of non-degenerate mixed multipartite quantum states under local unitary transformations is presented.