Detailed Quantum Mechanical QSAR Analysis of Certain Aminopyrimidoisoquinolinequinones with Anticancer Activity

A detailed quantum mechanical analysis of electronic disposition of five aminopyrimidoisoquinolinequinones (APIQs) was performed after extraction of this subset of compounds from a larger data set of APIQs via a reported clustering methodology (Elfaki, et al. 2020). Both semi empirical PM3 method and DFT quantum mechanical methods were used to calculate global and local quantum mechanical descriptors (QMDs) to define the electronic environment of these molecules in attempt to rationalize their observed anti-cancer response variability. The biological response is the anticancer activity against human gastric adenocarcenoma (AGS) cell line. The correlation matrix between the calculated global electronic descriptors and biological activity demonstrated that the global dipole moment gives the highest correlation. The local electronic environment was analysed by The Mullikan charges (MC) and Fukui functions for N-5, C-6, C-8 in addition to the N atom of phenylamino side group at C-8. MCs furnished no useful information as each of these atoms had almost identical MC values for all the five compounds with exception of C-6 which gave varied values. Regressing MCs of C-6 against the response traces 60% of the latter variability. As C-6 is an extra annular methyl carbon adjacent to N-5 in isoquinoline residue of APIQ, we reasoned that the chemical reactivities of 4 out of the 5 APIQs might be due to a Chichibabin-type tautomerism implying a possible alkylation aspect in their mechanism of action. The corresponding Fukui functions (f-, f+ and f0) showed a considerable consistency with the patterns of chemical reactivity exhibited by this small set of APIQs.

Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.

Violation of Locality Beyond Bell＇s Theorem for Multiparticle Perfect Correlations

We present the analogous inequalities of Bell's inequality for N-qubit system predicted respectively by realistic theory, quantum mechanics, local theory, local realistic theory, and local quantum theory on the same Belltype joint experiment. It is shown that quantum mechanics can be interpreted by hidden-variable theories while being incompatible to any local theory. A necessary condition for the separability of N-qubit system is derived.

Quantum Solitons and Localized Modes in a One-Dimensional Lattice Chain with Nonlinear Substrate Potential

In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solirons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j = j0.

Measurement-Device-Independent Quantum Key Distribution with Two-Way Local Operations and Classical Communications

Measurement-device-independent quantum key distribution （MDI-QKD） is proven to be immune to all the de- tector side channel attacks. With two symmetric quantum channels, the maximal transmission distance can be doubled when compared with the prepare-and-measure QKD. An interesting question is whether the transmission distance can be extended further. In this work, we consider the contributions of the two-way local operations and classical communications to the key generation rate and transmission distance of the MDI-QKD. Our numerical results show that the secure transmission distances are increased by about 12kin and 8 km when the 1 13 and the 2 B steps are implemented, respectively.

Effect of weak measurement on quantum correlations

We investigate the local quantum uncertainty(LQU)in weak measurement.An expression of weak LQU is explicitly determined.Also,we consider some cases of three special X states,Werner state,circulant two-qubit states,and Heisenberg model via LQU in normal and weak measurements.We find that the LQU in weak measurement is weaker than the case of strong measurement.

Localization of quantum walks on finite graphs

We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.

Transitionless driving on local adiabatic quantum search algorithm

We apply the transitionless driving on the local adiabatic quantum search algorithm to speed up the adiabatic process. By studying quantum dynamics of the adiabatic search algorithm with the equivalent two-level system, we derive the transi- tionless driving Hamiltonian for the local adiabatic quantum search algorithm. We found that when adding a transitionless quantum driving term Ht~ （t） on the local adiabatic quantum search algorithm, the success rate is 1 exactly with arbitrary evolution time by solving the time-dependent Schr6dinger equation in eigen-picture. Moreover, we show the reason for the drastic decrease of the evolution time is that the driving Hamiltonian increases the lowest eigenvalues to a maximum of

Quantum particle swarm optimization for micro-grid system with consideration of consumer satisfaction and benefit of generation side

Considering comprehensive benefit of micro-grid system and consumers,we establish a mathematical model with the goal of the maximum consumer satisfaction and the maximum benefit of power generation side in the view of energy management.An improved multi-objective local mutation adaptive quantum particle swarm optimization(MO-LM-AQPSO)algorithm is adopted to obtain the Pareto frontier of consumer satisfaction and the benefit of power generation side.The optimal solution of the non-dominant solution is selected with introducing the power shortage and power loss to maximize the benefit of power generation side,and its reasonableness is verified by numerical simulation.Then,translational load and time-of-use electricity price incentive mechanism are considered and reasonable peak-valley price ratio is adopted to guide users to actively participate in demand response.The simulation results show that the reasonable incentive mechanism increases the benefit of power generation side and improves the consumer satisfaction.Also the mechanism maximizes the utilization of renewable energy and effectively reduces the operation cost of the battery.

Local quantum Fisher information and quantum correlation in the mixed-spin Heisenberg XXZ chain

We study the local quantum Fisher information(LQFI)in the mixed-spin Heisenberg XXZ chain.Both the maximal and minimal LQFI are studied and the former is essential to determine the accuracy of the quantum parameter estimation,the latter can be well used to characterize the discord-type quantum correlations.We investigate the effects of the temperature and the anisotropy parameter on the maximal LQFI and thus on the accuracy of the parameter estimation.Then we make use of the minimal LQFI to study the discord-type correlations of different site pairs.Different dimensions of the subsystems cause different values of the minimal LQFI which reflects the asymmetry of the discord-type correlation.In addition,the site pairs at different positions of the spin chains have different minimal LQFI,which reveals the influence of the surrounding spins on the bipartite quantum correlation.Our results show that the LQFI obtained through a simple calculation process provides a convenient way to investigate the discord-type correlation in high-dimensional systems.

Solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain

By use of the Hartree approximation and the method of multiple scales, we investigate quantum solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain. It is shown that there exist solitons of two different quantum frequency bands： i.e., magnetic optical solitons and acoustic solitons. At the boundary of the Brillouin zone, these solitons becornc quantum intrinsic localized modes： their quantum eigenfrequencics are below the bottom of the harmonic optical frequency band and above the top of the harmonic acoustic frequency band.

Information and Conditional Probability to Go beyond Hidden Variables

We study the relation between the possibility of describing quantum correlation with hidden variables and the existence of the Bloch sphere. We derive some proposition concerning a quantum expected value under an assumption about the existence of the Bloch sphere in N spin-1/2 systems. However, the hidden variables theory violates the proposition with a magnitude that grows exponentially with the number of particles. Therefore, we have to give up either the existence of the Bloch sphere or the hidden variables theory. We show that the introduction of curved information and the continuity equation of probability are in agreement with classical quantum mechanics. So we give up the hidden variable theory as local theory and we accept the Bloch sphere as global theory connected with the information space.

Beyond Set Theory in Bell Inequality

Feynman pointed out a logic and mathematical paradox in particle physics. The paradox is that we get for the same entity only local dependence and global dependence at the time. This contradiction is coming from the dual nature of the particle viewed as a wave. In the first capacity it has only local dependence;in the second (wave) capacity it has a global dependence. The classical logic has difficulties in resolving this paradox. Changing the classical logic to logic makes the paradox apparent. Particle has the local property or zero dependence with other particles, media has total dependence so it is a global unique entity. Now, in set theory, any element is independent from the other so disjoint set has no elements in common. With this condition we have known that the true/ false logic can be applied and set theory is the principal foundation. Now with conditional probability and dependence by copula the long distance dependence has an effect on any individual entity that now is not isolate but can have different types of dependence or synchronism (constrain) whose effect is to change the probability of any particle. So particle with different degree of dependence can be represented by a new type of set as fuzzy set in which the boundary is not completely defined or where we cannot separate a set in its parts as in the evidence theory. In conclusion the Feynman paradox and Bell violation can be explained at a new level of complexity by many valued logics and new types of set theory.

Nonclassical correlations in two-dimensional graphene lattices

We investigate nonclassical correlations via negativity,local quantum uncertainty(LQU)and local quantum Fisher information(LQFI)for two-dimensional graphene lattices.The explicitly analytical expressions for negativity,LQU and LQFI are given.The close forms of LQU and LQFI confirm the inequality between the quantum Fisher information and skew information,where the LQFI is always greater than or equal to the LQU,and both show very similar behavior with different amplitudes.Moreover,the effects of the different system parameters on the quantified quantum correlation are analyzed.The LQFI reveals more nonclassical correlations than LQU in a two-dimensional graphene lattice system.

Success Rate Versus Finite Run Time in Local Adiabatic Quantum Search Algorithm

In adiabatic quantum algorithm, the success rate is approximately equal to 1 while the run time satisfies the adiabatic condition. But the relation between the short run time and success rate for adiabatic quantum algorithm is poorly understood. In this paper, we study the success rate of local adiabatic quantum search algorithm with an arbitrary finite run time(non-adiabatic evolution). By solving the time-independent Schr¨odinger equation, we obtain differential equations to calculate the success rate. The differential equations show that the success rate is closely related to the adiabatic parameter s(t). Utilize the differential equations, we give the function of success rate versus run time in local adiabatic search numerically. The result indirectly verifies that T ～ O(N^(1/2)) is optimal in local adiabatic search.