Random Walk Quantum Clustering Algorithm Based on Space

In the random quantum walk, which is a quantum simulation of the classical walk, data points interacted when selecting the appropriate walk strategy by taking advantage of quantum-entanglement features; thus, the results obtained when the quantum walk is used are different from those when the classical walk is adopted. A new quantum walk clustering algorithm based on space is proposed by applying the quantum walk to clustering analysis. In this algorithm, data points are viewed as walking participants, and similar data points are clustered using the walk function in the pay-off matrix according to a certain rule. The walk process is simplified by implementing a space-combining rule. The proposed algorithm is validated by a simulation test and is proved superior to existing clustering algorithms, namely, Kmeans, PCA + Kmeans, and LDA-Km. The effects of some of the parameters in the proposed algorithm on its performance are also analyzed and discussed. Specific suggestions are provided.     

On the Relationship Between Continuous- and Discrete-Time Quantum Walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete- time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.     

Study of a carbon dioxide ring laser gyroscope

We have experimentally investigated a basic ring laser gyroscope (RLG) with carbon dioxide gain, and studied the prospects of developing a practical CO₂ RLG. Rotation sensing was demonstrated on a number of transitions in the 9.4 m and 10.4 m vibration-rotation bands. Gyro response is discussed with regard to lock-in, bias, homogeneous broadening effects, and high power operation. We show that such a system may offer important advantages over standard helium-neon RLGs, including reduced quantum limit and backscattering. The prospects and possible approaches for developing a practical high power CO₂ RLG are discussed, and a method of eliminating cross-saturation at high pressure is proposed and analyzed.     

Irreversibility of a quantum walk induced by controllable decoherence employing random unitary operations

Quantum walk is different from random walk in reversibility and interference. Observation of the reduced re- versibility in a realistic quantum walk is of scientific interest in understanding the unique quantum behavior. We propose an idea to experimentally investigate the decoherence-induced irreversibility of quantum walks with trapped ions in phase space via the average fidelity decay. By introducing two controllable decoherence sources, i.e., the phase damping channel (i.e., dephasing) and the high temperature amplitude reservoir (i.e., dissipation), in the intervals between the steps of quantum walk, we find that the high temperature amplitude reservoir shows more detrimental effects than the phase damping channel on quantum walks. Our study also shows that the average fidelity decay works better than the position variance for characterizing the transition from quantum walks to random walk. Experimental feasibility to monitor the irreversibility is justified using currently available techniques.     

Non-Markovian decoherent quantum walks

Quantum walks act in obviously different ways from their classical counterparts, but decoherence will lessen and close this gap between them. To understand this process, it is necessary to investigate the evolution of quantum walks under different decoherence situations. In this article, we study a non-Markovian decoherent quantum walk on a line. In a short time regime, the behavior of the walk deviates from both ideal quantum walks and classical random walks. The position variance as a measure of the quantum walk collapses and revives for a short time, and tends to have a linear relation with time. That is, the walker's behavior shows a diffusive spread over a long time limit, which is caused by non-Markovian dephasing affecting the quantum correlations between the quantum walker and his coin. We also study both quantum discord and measurement-induced disturbance as measures of the quantum correlations, and observe both collapse and revival in the short time regime, and the tendency to be zero in the long time limit. Therefore, quantum walks with non-Markovian decoherence tend to have diffusive spreading behavior over long time limits, while in the short time regime they oscillate between ballistic and diffusive spreading behavior, and the quantum correlation collapses and revives due to the memory effect.     

Quantum to classical transition for random walks

We look at two possible routes to classical behavior for the discrete quantum random walk on the integers: decoherence in the quantum "coin" which drives the walk, or the use of higher-dimensional (or multiple) coins to dilute the effects of interference. We use the position variance as an indicator of classical behavior and find analytical expressions for this in the long-time limit; we see that the multicoin walk retains the "quantum" quadratic growth of the variance except in the limit of a new coin for every step, while the walk with decoherence exhibits "classical" linear growth of the variance even for weak decoherence.     

Limit Theorems for Open Quantum Random Walks

We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of Schrödinger-Heisenberg representation in quantum mechanics. By this, we can compute the distribution of the open quantum random walks concretely for many examples and thereby we can also obtain the limit distributions of them. In particular, it is possible to get rid of the initial state when we consider the evolution of the walk, it appears only in the last step of the computation.     

激光陀螺捷联惯性导航系统误差分析及仿真计算

激光陀螺随机游走现象的存在，严重影响了捷联惯性导航系统的导航性能。本文用数学分析的方法推导出激光陀螺随机游走造成的系统导航误差标准偏差的解析表达式，以便定量地研究激光陀螺随机游走对系统精度的影响，并提出改进措施。同时按照给定的飞行轨迹和随机游走系数，进行了系统数学仿真计算，对仿真计算结果进行了分析。     

Continuous-time quantum walks on star graphs

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K₂ graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.     

Classical random walk with memory versus quantum walk on a one-dimensional infinite chain

Quantum walk is a very useful tool for building quantum algorithms due to the faster spreading of probability distributions as compared to a classical random walk. Comparing the spreading of the probability distributions of a quantum walk with that of a mnemonic classical random walk on a one-dimensional infinite chain, we find that the classical random walk could have a faster spreading than that of the quantum walk conditioned on a finite number of walking steps. Quantum walk surpasses classical random walk with memory in spreading speed when the number of steps is large enough. However, in such a situation, quantum walk would seriously suffer from decoherence. Therefore, classical walk with memory may have some advantages in practical applications.     

Two models of quantum random walk

We present an overview of two models of quantum random walk. In the first model, the discrete quantum random walk, we present the explicit solution for the recurring amplitude of the quantum random walk on a one-dimensional lattice. We also introduce a new method of solving the problem of random walk in the most general case and use it to derive the hitting amplitude for quantum random walk on the hypercube. The second is a special model based on a local interaction between neighboring spin-1/2 particles on a one-dimensional lattice. We present explicit results for the relevant quantities and obtain an upper bound on the speed of convergence to limiting probability distribution.     

Fundamental limitations of sensitivity of whispering gallery mode gyroscopes

We analyze theoretically both the fundamental and the technical quantum limitations of the sensitivity of a passive resonant optical gyroscope based on a high finesse monolithic optical microcavity. We show that the quantum back action associated with the resonantly enhanced optical cross- and self-phase modulation results in the standard quantum limit of the angle random walk of the gyroscope, which reaches approximately 0.2 deg/hr^1/2 for a millimeter scale CaF₂ whispering gallery mode resonator based device.     

Quantum walk under coherence non-generating channels

We investigate the probability distribution of the quantum walk under coherence non-generating channels. We definea model called generalized classical walk with memory. Under certain conditions, generalized classical random walk withmemory can degrade into classical random walk and classical random walk with memory. Based on its various spreadingspeed, the model may be a useful tool for building algorithms. Furthermore, the model may be useful for measuring thequantumness of quantum walk. The probability distributions of quantum walks are generalized classical random walkswith memory under a class of coherence non-generating channels. Therefore, we can simulate classical random walkand classical random walk with memory by coherence non-generating channels. Also, we find that for another class ofcoherence non-generating channels, the probability distributions are influenced by the coherence in the initial state of thecoin. Nevertheless, the influence degrades as the number of steps increases. Our results could be helpful to explore therelationship between coherence and quantum walk.     

“冷沉积”的Ag-BaO薄膜在超短脉冲激光作用下的光电发射

研究了冷沉积制备条件下获得的Ag-BaO薄膜在超短激光脉冲串作用下的光电发射．得到Ag-BaO薄膜的阈值光强为10W/cm²，光量子效率达10^-4数量级．光电流密度与入射光强的关系主要表现为一段曲率随光强增大而逐步减小的曲线．其光量子效率是一个可变值，它的变化规律同入射光强及薄膜本身的性能有关 关键词：     

体温计模型的临界行为

提出一个可用离散朗之万方程描述的体温计模型.该体温计的特点是其温度示数只能随外界温度的升高而上升,当外界温度降低时,其示数却不能下降.根据体温计示数这种只升不降的特点,定义了“停顿”事件.用随机行走的理论解析地推导了停顿时间分布函数数值模拟和解析结果都显示这种分布函数呈幂律形式D(s)∝s^-ξ,揭示出在这一过程中所表现出的临界性. 关键词：     

Theory of intensity noise in semiconductor laser emission

The intensity fluctuations expected in the output of cw semiconductor lasers are studied analytically using linearized multimode rate equations. Spontaneous emission causes intrinsic fluctuations of the laser wave. A power-independent contribution to the intensity fluctuations may occur due to inversion-induced modulation noise. The correlation of the low-frequency noise of different laser modes is investigated. The results are in agreement with experimental data reported in the literature.     

Random Time-Dependent Quantum Walks

We consider the discrete time unitary dynamics given by a quantum walk on the lattice \mathbb Z^d{\mathbb {Z}^d} performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable in \mathbb Z^d{\mathbb {Z}^d} when the sequence of unitary updates is given by an i.i.d. sequence of random matrices. When averaged over the randomness, this distribution is shown to display a drift proportional to the time and its centered counterpart is shown to display a diffusive behavior with a diffusion matrix we compute. A moderate deviation principle is also proven to hold for the averaged distribution and the limit of the suitably rescaled corresponding characteristic function is shown to satisfy a diffusion equation. A generalization to unitary updates distributed according to a Markov process is also provided.     

Two Quantum Coins Sharing a Walker

For classical random walks, changing or not changing coins makes a trivial influence on the random-walk behaviors. In this paper, we investigate the quantum walk where a walker’s movement is controlled by two initially independent coins alternately partially or fully after each step. We observe that there exist complicated inter-coin correlations in the quantum walk. Specifically, we study the correlations of two coins by tracing out the walker, and analyze classical, general, and quantum correlations between two coins in terms of classical mutual information, quantum mutual information, and measurement-induced disturbance. Our analysis shows different quantum features from that in classical random walks.

     

Temperature dependence of luminescence intensity under Bose condensation of interwell excitons

Photoluminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructure) containing large-scale random potential fluctuations in the planes of heteroboundaries is studied. The properties of excitons, in which a photoexcited electron and a hole are spatially separated in neighboring quantum wells, were investigated upon variation of the power density of off-resonance laser excitation and temperature (1.5–4.2 K), both under lateral (in the heteroboundary plane) confinement of the excitation region to a few micrometers and without such a limitation (directly from the region of laser-induced photoexcitation focused to a spot not exceeding 30 μ. Under low pumping (with a power smaller than a microwatt), interwell excitons are strongly localized due to small-scale random potential fluctuations and the corresponding photoluminescence line is nonhomogeneously broadened to 2.5–3.0 meV. With increasing pumping power, the narrow line of delocalized excitons with a width of approximately 1 meV emerges in a threshold manner (the intensity of this line increases superlinearly near the threshold with increasing pumping). For a fixed pumping, the intensity of this line decreases linearly upon heating until it completely vanishes from the spectrum. The observed effect is attributed to Bose condensation in a quasi-two-dimensional system of interwell excitons. Within the proposed model, we show that the linear mode in the behavior of the luminescence intensity until its disappearance in the continuum of the photoluminescence spectrum upon a change in temperature is observed only for the condensed part of interwell excitons. At the same time, the luminescence of the above-the-condensate part of excitons is almost insensitive to temperature variations in the temperature range studied.     

Mechanism of refrigeration cycle on laser cooling of solids

A simple model is developed to study the laser cooling of solids.The condition of laser cooling of a solid is developed.By using some parameters of the Yb 3＋ ion,which is most widely used in laser cooling,we then calculate the cooling power and the cooling efficiency.In order to make a more precise analysis, the effect of fluorescent reabsorption,which is unavoidable in the cooling process,is discussed using the random walk model.Taking Tm 3＋ ion as an example,we derive the average number of absorption events and determine the change in quantum efficiency due to reabsorption.Finally,we obtain the red-shift of the fluorescent wavelength and the requirement of sample dimension.