任意两个相干态的叠加态的相位分布和Wigner函数(英文)

从相位分布和Wigner函数两个方面研究了任意两个相干态|β〉and |mβeiδ〉的叠加态的量子统计性质.结果表明这种叠加态的非经典特性与β2,振幅系数m,相干态间的位相差δ以及叠加系数间的位相差都有关.当参量选择合适,这种叠加态存在着量子效应.计算了两个相干态等几率混合系综的相位分布和Wigner函数,经过与前者比较,结果表明由于相干项的存在,使得叠加态具有很好的量子力学行为.     

基于相位匹配的量子行走搜索算法及电路实现

量子行走是经典随机行走在量子力学框架下的对应, 理论上可以用来解决一类无序数据库的搜索问题. 因为携带信息的量子态的扩散速度与经典相比有二次方式的增长, 所以量子行走优于经典随机行走, 量子行走的特性值得加以利用. 量子行走作为一种新发现的物理现象的数学描述, 引发了一种新的思维方式, 孕育了一种新的理论计算模型. 最新研究表明, 量子行走本身也是一种通用计算模型, 可被视为设计量子算法的高级工具, 因此受到部分计算机理论科学领域学者的关注和研究. 对于多数问题求解方案的量子算法的设计, 理论上可以只在量子行走模型下进行考虑. 基于Grover算法的相位匹配条件, 本文提出了一个新的基于量子行走的搜索算法. 理论演算表明: 一般情况下本算法的时间复杂度与Grover算法相同, 但是当搜索的目标数目多于总数的1/3时, 本算法搜索成功的概率要大于Grover算法. 本文不但利用Grover算法中相位匹配条件构造了一个新的量子行走搜索算法, 而且在本研究室原有的量子电路设计研究成果的基础上给出了该算法的量子电路表述.     

任意两个相干态的叠加态的相位分布和Wigner函数

从相位分布和Wigner函数两个方面研究了任意两个相干态|β〉 and |mβeiδ〉的叠加态的量子统计性质.结果表明这种叠加态的非经典特性与β2,振幅系数m,相干态间的位相差δ以及叠加系数间的位相差都有关.当参量选择合适,这种叠加态存在着量子效应.计算了两个相干态等几率混合系综的相位分布和Wigner函数,经过与前者比较,结果表明由于相干项的存在,使得叠加态具有很好的量子力学行为.     

含有多目标的量子部分搜索——目标被非平均分配在两块中

Grover搜索是一种量子搜索方法,利用了量子叠加态的性质,通过一些操作的反复作用,而使目标态的几率幅变大,非目标态的几率幅变小,从而以较大的概率找到目标.与经典搜索方法相比,能够较快地从一个数据库中找到目标元.这是一种搜索到目标的全部信息的方法,但是在有些情况下,我们并不需要知道目标的全部信息,而只需要知道目标的部分信息,因而只需要找到含有目标的一部分数据库中的元素,这就是部分搜索.Grover和Radhakrishnan提出了一种部分搜索方法,称为Grover-Radhakrishnan Algorithm of Partial Search(GRK),所考虑的数据库只含有一个目标.在我们的文章中,我们研究了在含有多目标的数据库,且目标被随机分配在两块中时,GRK所需要的查询次数会有怎么样的变化.得到查询次数s和所分块数K、目标数t的关系.并且与平均分配的情况进行比较.     

星图上的散射量子行走搜索算法

量子行走是一种典型的量子计算模型, 近年来开始受到量子计算理论研究者们的广泛关注. 本文首先证明了在星图上硬币量子行走与散射量子行走的酉等价关系, 之后提出了一个在星图上的散射量子行走搜索算法. 该算法的时间复杂度与Grover算法相同, 但是当搜索的目标数目多于总数的1/3时搜索成功概率大于Grover算法.     

抛物线性限制势量子点量子比特及其光学声子效应

在抛物量子点中电子与体纵光学声子强耦合的条件下,应用Peaker变分方法得出了电子的基态和第一激发态的本征能量及基态和第一激发态本征波函数.量子点中这样的二能级体系可作为一个量子比特.当电子处于基态和第一激发态的叠加态时,计算出电子在空间的概率分布作周期性振荡.并且得出了振荡周期随受限长度及耦合强度的变化关系. 关键词： 量子点 量子信息 量子比特     

声子对隧穿量子点分子辐射场系统量子相位的影响

用全量子理论导出隧穿量子点分子-辐射场相互作用系统状态满足的微分方程组, 在相干态辐射场和量子点分子处于隧穿激发态及基态的初始条件下, 应用Pegg-Barnett相位理论计算和分析了辐射场的相位概率分布及相位涨落, 研究了声子-量子点分子作用对辐射场相位的影响, 并与Husimi相位分布做了比较. 结果表明, 温度显著影响光场相位概率分布的时间演化规律, 声子既可以抑制也可以增强辐射场相位扩散和涨落, 取决于量子点分子的初态. Husimi相位分布和Pegg-Barnett相位分布符合度相当高. 关键词： 量子点分子 声子 量子相位 Q函数')" href="#">Q函数     

核磁共振量子计算机与并行量子计算(续完)

3　刘维尔量子计算中的指数加快的搜索算法———Bruschweiler算法3 .1　Bruschweiler算法[4 5]与Grover搜索算法一样 ,Bruschweiler算法也是在无序数据库中寻找目标态 .对于搜寻问题可以总结为 :对于输入态x ,除了当x=z时 ,f(z) =1,其余的 f(x) =0 .z是我们要寻找的目标 .在经典计算机中 ,大概要O(N)步 ;用Grover算法大概要O(N )步 ;用Bruschweiler算法大概仅需要O(n)步 .其中 ,N =2 n.Bruschweiler利用NMR是自旋系综的特点 ,将初始态制备成不同自旋态的线性叠加 ,使初始态处于完全混合态 ,当U变换作用其上时 ,不同的自旋态在做不同…     

抛物线性限制势二能级系统量子点量子比特的温度效应

应用Pekar变分方法,在抛物量子点中电子与体纵光学声子强耦合条件下,得出了电子的基态和第一激发态的本征能量及基态和第一激发态的本征波函数.以量子点中这样的二能级体系作为一个量子比特.当电子处于基态和第一激发态的叠加态时,计算出电子在时空中作周期性振荡的概率分布.并且得出了概率分布随温度及耦合强度的变化关系. 关键词： 量子点 量子比特 温度效应     

压缩真空态中原子与场的量子纠缠和量子discord

在压缩真空库中,研究了原子与场的相互作用下二比特体系的量子discord和量子纠缠的动力学行为.重点分析了原子的初始态系数和压缩真空库的压缩系数对量子纠缠和量子discord的影响.通过数值分析我们得到,随着原子的初始态系数和压缩真空库的压缩系数值的增加,量子纠缠和量子discord都会减小,但量子纠缠比量子discord减小的更快一些.最后研究了在原子的初始态系数和压缩真空库的压缩系数的值相同的情况下,量子discord比量子纠缠存在的时间更长些.     

Grover量子搜索算法及改进

简单地介绍了量子搜索算法中的相位匹配条件、 改进的成功率为100%的量子搜索算法和量子搜索算法中的主要误差等. We briefly introduced some of our recent work related to the phase matching condition in quantum searching algorithms and the improved Grover algorithm. When one replaces the two phase inversions in the Grover algorithm with arbitrary phase rotations, the modified algorithm usually fails in searching the marked state unless a phase matching condition is satisfied between the two phases. The Grover algorithm is not 100% in success rate, an improved Grover algorithm with zero failure rate is given by replacing the phase inversions with angles that depends on the size of the database. Other aspects of the Grover algorithm such as the SO(3) picture of quantum searching, the dominant gate imperfections in the Grover algorithm are also mentioned.     

First experimental demonstration of an exact quantum search algorithm in nuclear magnetic resonance system

The success probability of searching an objective item from an unsorted database using standard Grover's algorithm is usually not exactly 1. It is exactly 1 only when it is used to find the target state from a database with four items. Exact search is always important in theoretical and practical applications. The failure rate of Grover's algorithm becomes big when the database is small, and this hinders the use of the commonly used divide-and-verify strategy. Even for large database, the failure rate becomes considerably large when there are many marked items. This has put a serious limitation on the usability of the Grover's algorithm. An important improved version of the Grover's algorithm, also known as the improved Grover algorithm, solves this problem. The improved Grover algorithm searches arbitrary number of target states from an unsorted database with full success rate. Here, we give the first experimental realization of the improved Grover algorithm, which finds a marked state with certainty, in a nuclear magnetic resonance system. The optimal control theory is used to obtain an optimized control sequence. The experimental results agree well with the theoretical predictions.     

Arbitrary Phase Rotation of the Marked State Cannot Be Used for Grover's Quantum Search Algorithm

A misunderstanding that an arbitrary phase rotation of the marked state together with the inversion about average operation can be used to construct a (less efficient) quantum search algorithm is cleared. The π rotation of the phase of the marked state is not only the choice for efficiency, but also vital in Grover's quantum search algorithm. The results also show that Grover's quantum search algorithm is robust.     

Efficient State Preparation via Ion Trap Quantum Computing and Quantum Searching Algorithm

We present a scheme to-prepare a quantum state in an ion trap with probability approaching to one by means of ion trap quantum computing and Grover's quantum search algorithm acting on trapped ions.     

A Four-Phase Improvement of Grover's Algorithm

When applying Grover's algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. A four-phase improvement of Grover's algorithm is proposed to fix the deficiency, and the unitary and the phase-matching condition are also proposed. With this improved scheme,when the proportion of target is over 1/3, the probability of obtaining correct results is greater than 97.82%with only one iteration using two phases. When the computational complexity is O((?)), the algorithm can succeed with a probability no less than 99.63%.     

Unstructured Adiabatic Quantum Search

In the adiabatic quantum computation model, a computational procedure is described by the continuous time evolution of a time dependent Hamiltonian. We apply this method to the Grover's problem, i.e., searching a marked item in an unstructured database. Classically, the problem can be solved only in a running time of order O(N) (where N is the number of items in the database), whereas in the quantum model a speed up of order has been obtained. We show that in the adiabatic quantum model, by a suitable choice of the time-dependent Hamiltonian, it is possible to do the calculation in constant time, independent of the the number of items in the database. However, in this case the initial time-complexity of is replaced by the complexity of implementing the driving Hamiltonian.     

General Quantum Meet-in-the-Middle Search Algorithm Based on Target Solution of Fixed Weight

Similar to the classical meet-in-the-middle algorithm, the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm. Aiming at the target vector of fixed weight, based on the quantum meet-in-the-middle algorithm, the algorithm for searching all n-product vectors with the same weight is presented, whose complexity is better than the exhaustive search algorithm. And the algorithm can reduce the storage complexity of the quantum meet-in-the-middle search algorithm. Then based on the algorithm and the knapsack vector of the Chor-Rivest public-key crypto of fixed weight d, we present a general quantum meet-in-the-middle search algorithm based on the target solution of fixed weight, whose computational complexity is ∑_j^d=(0(√C_n-k+1^d-j)+O(C_k^jlogC_k^j)) with ∑_i=0^dC_kⁱ memory cost. And the optimal value of k is given. Compared to the quantum meet-in-the-middle search algorithm for knapsack problem and the quantum algorithm for searching a target solution of fixed weight, the computational complexity of the algorithm is lower. And its storage complexity is smaller than the quantum meet-in-the-middle-algorithm.