Analytic Constructions of General n-Qubit Controlled Gates

In this Letter, we present two analytic expressions that most generally simulate $n$-qubit controlled-$U$ gates with standard one-qubit gates and CNOT gates using exponential and polynomial complexity respectively. Explicit circuits and general expressions of decomposition are derived. The exact numbers of basic operations in these two schemes are given using gate counting technique.Comment: 4 pages 7 figure

Duality and Recycling Computing in Quantum Computers

Quantum computer possesses quantum parallelism and offers great computing power over classical computer \cite{er1,er2}. As is well-know, a moving quantum object passing through a double-slit exhibits particle wave duality. A quantum computer is static and lacks this duality property. The recently proposed duality computer has exploited this particle wave duality property, and it may offer additional computing power \cite{r1}. Simply put it, a duality computer is a moving quantum computer passing through a double-slit. A duality computer offers the capability to perform separate operations on the sub-waves coming out of the different slits, in the so-called duality parallelism. Here we show that an $n$-dubit duality computer can be modeled by an $(n+1)$-qubit quantum computer. In a duality mode, computing operations are not necessarily unitary. A $n$-qubit quantum computer can be used as an $n$-bit reversible classical computer and is energy efficient. Our result further enables a $(n+1)$-qubit quantum computer to run classical algorithms in a $O(2^n)$-bit classical computer. The duality mode provides a natural link between classical computing and quantum computing. Here we also propose a recycling computing mode in which a quantum computer will continue to compute until the result is obtained. These two modes provide new tool for algorithm design. A search algorithm for the unsorted database search problem is designed.Comment: 4 pages and 3 figure

Deleting a marked item from an unsorted database with a single query

In this Letter we present a quantum deletion algorithm that deletes a marked state from an unsorted database of $N$ items with only a single query. This algorithm achieves exponential speedup compared with classical algorithm where O(N) number of query is required. General property of this deleting algorithm is also studied.Comment: 4 pages and 1 figur

The reltation between the electronic structure and thermoelectric transport properties for Zintl compounds M2Zn5As4 (M=K, Rb)

The electronic structure and thermoelectric properties of are studied by the first principles and the semiclassical BoltzTrap theory.Comment: 15page

A new transformation into State Transition Algorithm for finding the global minimum

To promote the global search ability of the original state transition algorithm, a new operator called axesion is suggested, which aims to search along the axes and strengthen single dimensional search. Several benchmark minimization problems are used to illustrate the advantages of the improved algorithm over other random search methods. The results of numerical experiments show that the new transformation can enhance the performance of the state transition algorithm and the new strategy is effective and reliable.Comment: 5 pages, 6 figure

Standardization, Distance, Host Galaxy Extinction of Type Ia Supernova and Hubble Diagram from the Flux Ratio Method

In this paper we generalize the flux ratio method Bailey et al. (2009) to the case of two luminosity indicators and search the optimal luminosity-flux ratio relations on a set of spectra whose phases are around not only the date of bright light but also other time. With these relations, a new method is proposed to constrain the host galaxy extinction of SN Ia and its distance. It is first applied to the low redshift supernovas and then to the high redshift ones. The results of the low redshift supernovas indicate that the flux ratio method can indeed give well constraint on the host galaxy extinction parameter E(B-V), but weaker constraints on R_{V}. The high redshift supernova spectra are processed by the same method as the low redshift ones besides some differences due to their high redshift. Among 16 high redshift supernovas, 15 are fitted very well except 03D1gt. Based on these distances, Hubble diagram is drew and the contents of the Universe are analyzed. It supports an acceleration behavior in the late Universe. Therefore, the flux ratio method can give constraints on the host galaxy extinction and supernova distance independently. We believe, through further studies, it may provide a precise tool to probe the acceleration of the Universe than before.Comment: 33 pages, 9 figures and 6 table

Effects of Imperfect Gate Operations in Shor's Prime Factorization Algorithm

The effects of imperfect gate operations in implementation of Shor's prime factorization algorithm are investigated. The gate imperfections may be classified into three categories: the systematic error, the random error, and the one with combined errors. It is found that Shor's algorithm is robust against the systematic errors but is vulnerable to the random errors. Error threshold is given to the algorithm for a given number $N$ to be factorized.Comment: 5 pages 4 figure

Meaningful Objects Segmentation from SAR Images via A Multi-Scale Non-Local Active Contour Model

The segmentation of synthetic aperture radar (SAR) images is a longstanding yet challenging task, not only because of the presence of speckle, but also due to the variations of surface backscattering properties in the images. Tremendous investigations have been made to eliminate the speckle effects for the segmentation of SAR images, while few work devotes to dealing with the variations of backscattering coefficients in the images. In order to overcome both the two difficulties, this paper presents a novel SAR image segmentation method by exploiting a multi-scale active contour model based on the non-local processing principle. More precisely, we first formulize the SAR segmentation problem with an active contour model by integrating the non-local interactions between pairs of patches inside and outside the segmented regions. Secondly, a multi-scale strategy is proposed to speed up the non-local active contour segmentation procedure and to avoid falling into local minimum for achieving more accurate segmentation results. Experimental results on simulated and real SAR images demonstrate the efficiency and feasibility of the proposed method: it can not only achieve precise segmentations for images with heavy speckles and non-local intensity variations, but also can be used for SAR images from different types of sensors

General Phase Matching Condition for Quantum Searching

We present a general phase matching condition for the quantum search algorithm with arbitrary unitary transformation and arbitrary phase rotations. We show by an explicit expression that the phase matching condition depends both on the unitary transformation U and the initial state. Assuming that the initial amplitude distribution is an arbitrary superposition sin\theta_0 |1> + cos\theta_0 e^{i\delta} |2> with |1> = {1 / sin\beta} \sum_k |\tau_k> and |2> = {1 / cos\beta} \sum_{i \ne \tau}|i> , where |\tau_k> is a marked state and \sin\beta = \sqrt{\sum_k|U_{\tau_k 0}|^2} is determined by the matrix elements of unitary transformation U between |\tau_k> and the |0> state, then the general phase matching condition is tan{\theta / 2} [cos 2\beta + tan\theta_0 cos\delta sin 2\beta]= tan{\phi / 2} [1-tan\theta_0 sin\delta sin 2\beta tan{\theta / 2}], where \theta and \phi are the phase rotation angles for |0> and |\tau_k>, respectively. This generalizes previous conclusions in which the dependence of phase matching condition on $U$ and the initial state has been disguised. We show that several phase conditions previously discussed in the literature are special cases of this general one, which clarifies the question of which condition should be regarded as exact.Comment: 8 pages, no figure

Distributed Continuous-Time and Discrete-Time Optimization With Nonuniform Unbounded Convex Constraint Sets and Nonuniform Stepsizes

This paper is devoted to distributed continuous-time and discrete-time optimization problems with nonuniform convex constraint sets and nonuniform stepsizes for general differentiable convex objective functions. The communication graphs are not required to be strongly connected at any time, the gradients of the local objective functions are not required to be bounded when their independent variables tend to infinity, and the constraint sets are not required to be bounded. For continuous-time multi-agent systems, a distributed continuous algorithm is first introduced where the stepsizes and the convex constraint sets are both nonuniform. It is shown that all agents reach a consensus while minimizing the team objective function even when the constraint sets are unbounded. After that, the obtained results are extended to discrete-time multi-agent systems and then the case where each agent remains in a corresponding convex constraint set is studied. To ensure all agents to remain in a bounded region, a switching mechanism is introduced in the algorithms. It is shown that the distributed optimization problems can be solved, even though the discretization of the algorithms might deviate the convergence of the agents from the minimum of the objective functions. Finally, numerical examples are included to show the obtained theoretical results.Comment: 11 pages, 3figure