Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.     

Grover search algorithm in an ion trap systen

Two schemes for the implementation of the two-qubit Grover search algorithm in the ion trap system are proposed. These schemes might be experimentally realizable with presently available techniques. The experimental implementation of the schemes would be an important step toward more complex quantum computation in the ion trap system.     

Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q$q$-statistics  . Starting from the q$q$-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy   preserves a scaling property of this equation. The q$q$-statistical   approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q$q$ is traced. It is found that the q$q$-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length.     

NMR analogue of the generalized Grover＇s algorithm of multiple marked states and its application

The generalized Grover‘s algorithm for the case in which there are multiple marked states is demonstrated on a nuclear magnetic resonance (NMR) quantum computer. The Walsh-Hadamard transform and the phase inversion are all replaced. NMR analogues of Einstein-Podolsky-Rosen states (pseudo-EPR states) are synthesized using the above algorithm.     

NMR analogue of the generalized Grover‘s algorithm of multiple marked states and its application

The generalized Grover's algorithm for the case in which there are multiple marked states is demonstrated on a nuclear magnetic resonance (NMR) quantum computer. The Walsh－Hadamard transform and the phase inversion are all replaced. NMR analogues of Einstein－Podolsky－Rosen states (pseudo-EPR states) are synthesized using the above algorithm.     

Conformational dynamics of $$alpha $$ α -conotoxin PnIB in complex solvent systems

Molecular Diversity - Cone snails are slow-moving animals that secure survival by injecting to their prey a concoction of highly potent and stable neurotoxic peptides called conotoxins. These small...     

From Schrödinger’s equation to the quantum search algorithm

The quantum search algorithm is a technique for searching N possibilities in only O(√N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schrödinger’s equation. This paper also provides a self contained introduction to quantum computing algorithms from a new perspective.     

Geometric Analysis of Grover’s Search Algorithmin the Presence of Perturbation

For an initial uniform superposition over all possible computational basis states, we explore the performance of Grover’s search algorithm geometrically when imposing a perturbation on the Walsh-Hadamard transformation contained in the Grover iteration. We give the geometric picture to visualize the quantum search process in the three-dimensional space and show that Grover’s search algorithm can work well with an appropriately chosen perturbation. Thereby we corroborate Grover’s conclusion that if the perturbation is small, then it will have little impact of an impact on the implementation of this algorithm. We also prove that Grover’s path cannot achieve a geodesic under a perturbation of the Fubini-Study metric.     

Application of Grover’s Quantum Algorithm for SDES Key Searching

Journal of Experimental and Theoretical Physics - The problem of finding the key of Simplified-DES (SDES)—a model of a block cipher DES—by Grover’s quantum algorithm is...     

Linear entropy dynamics of the field in the Jaynes－Cummings model with an intensity-dependent coupling in the dispersive approximation

We present the linear entropy dynamics of the field state in the dispersive cavity in the Jaynes－Cummings model with an intensity-dependent coupling in the dispersive approximation, and investigate the influence of dissipation on entanglement between the field and the atoms. We show that the coherence properties of the field are also affected by the cavity when the nonlinear process of the field interacting with the atoms with an intensity-dependent coupling is involved, and find that the dissipation constant, the intensity of the field and the atomic distribution angle have different influence on the coherence properties of the field.     

Molecular dynamics investigation of the size effect upon the β → α transformation in Zr nanocrystals

The stability of the β phase in cubic zirconium nanoparticles has been calculated as a function of the size r (r varies in the range from 2.5 to 11.5 nm) by the molecular dynamics method with the many-body interatomic interaction potential obtained within the embedded-atom model. It has been demonstrated that the temperature T _k at which the cubic cluster of body-centered cubic zirconium becomes structurally unstable depends nonlinearly on the particle size. The curve T _k (r) exhibits a pronounced maximum in the range r ≈ 4.3−4.7 nm. It has been established that the mechanism of the structural transition from the body-centered cubic phase to the hexagonal close-packed phase depends substantially on the particle size. For particles with sizes in the range from 2.5 to 5.0 nm, there exists a temperature range in which the transition from the body-centered cubic phase to the hexagonal close-packed phase remains incomplete for a long time. In this case, two phases coexist and the initial particle undergoes a strong deformation along the habit plane.     

Pattern Classifications Using Grover’s and Ventura’s Algorithms in a Two-qubits System

Carrying out the classification of patterns in a two-qubit system by separately using Grover’s and Ventura’s algorithms on different possible superposition, it has been shown that the exclusion superposition and the phase-invariance superposition are the most suitable search states obtained from two-pattern start-states and one-pattern start-states, respectively, for the simultaneous classifications of patterns. The higher effectiveness of Grover’s algorithm for large search states has been verified but the higher effectiveness of Ventura’s algorithm for smaller data base has been contradicted in two-qubit systems and it has been demonstrated that the unknown patterns (not present in the concerned data-base) are classified more efficiently than the known ones (present in the data-base) in both the algorithms. It has also been demonstrated that different states of Singh-Rajput MES obtained from the corresponding self-single- pattern start states are the most suitable search states for the classification of patterns |00>,|01 >, |10> and |11> respectively on the second iteration of Grover’s method or the first operation of Ventura’s algorithm.     

Can stochastic resonance and coherence resonance describe CDW dynamics in quasi-one dimensional conductors?

Stochastic resonance (SR) in nonlinear systems is a counterintuitive concept in which a weak periodic signal and noise cooperate and give rise to a maximum in the signal-to-noise ratio at the output of the system when the noise is tuned to a certain value. In the coherence resonance phenomenon (CR), there is no deterministic signal to be enhanced. Intrinsic oscillations are present as transients. Adding an optimum noise turns transients into coherent ones. We discuss the possible application of SR and CR concepts to CDW dynamics in quasi-one dimensional conductors. We show in a preliminary experiment that addition of white noise can modify the behavior of the CDW in the quasi-one dimensional conductor K_0.30MoO₃.     

Selective creation of maximum coherence in multi-level Λ system

We consider the creation of the maximum Raman coherence in the six-level Λ system using optimal control theory. Optimal fields are designed for different initial conditions, resonant, and off-resonant, using the Krotov method including a reference field into the cost functional. Suppression of the population transfer to the intermediate level is achieved via an additional functional constraint which depends on the system dynamics. We demonstrate that the spectrum of the optimised fields has major contribution from the corresponding resonant frequencies independently of the choice of carrier frequency of the initial guess field. We also indicate that the pulse train emerges as a solution of the control problem of coherence optimisation in multi-level quantum systems.     

Simulation of BEPCⅡ′s BPM

Considering the effect of photoelectron, BEPCⅡ′s beam position monitor (BPM) uses antechamber structure. The cut-off frequency of TE mode is maybe lower than the BPM signal processing frequency 500MHz. The power of TE mode will result in beam position measurement error. With monitoring the antechamber's TE mode power amplitude and calculating the transmission of TE mode power to BPM's electrodes, we can calculate the error of position measurement caused by TE mode. We found that the error is beyond the acceptance when the cut-off frequency of TE₁₀ mode is lower than 500MHz. By changing the slot length, the cut-off frequency is higher than 500MHz and the error could be accepted. At last the effect of the wakefield to the beam has been simulated and the longitudinal impedance of wakefield has been calculated.     

Simultaneous classification of Oranges and Apples Using Grover’s and Ventura’ Algorithms in a Two-qubits System

In the present paper, simultaneous classification of Orange and Apple has been carried out using both Grover’s iterative algorithm (Grover 1996) and Ventura’s model (Ventura and Martinez, Inf. Sci. 124, 273–296, 2000) taking different superposition of two- pattern start state containing Orange and Apple both, one- pattern start state containing Apple as search state and another one- pattern start state containing Orange as search state. It has been shown that the exclusion superposition is the most suitable two- pattern search state for simultaneous classification of pattern associated with Apples and Oranges and the superposition of phase-invariance are the best choice as the respective search state based on one –pattern start-states in both Grover’s and Ventura’s methods of classifications of patterns.     

Analysis and implementation of theFMLMS algorithm in AANC

I.IntroductionInthefieldofnoisecontrol,whenthecharacteristicsofthenoisesourcevary,theAANCsystemcanadaptivelyadjustthecontrollerofthecancellingsystemtoachievetheoptimal'complexstrengthofthesecondarysourceandconsequentlyensurethatthenoisecontrolsystemcanworkattheoptimalstatusfrombeginningtoend.So,thetechniqueoftheAANChasbeenappliedtoalmostallofthe3-Dspatialactivenoisecontrol.'ThealgorithmhastakenanimportantroleintheAANC.OneofthemainalgorithmsusedintheAANCistheFiltered-XLMS(FLMS)algori…