Multiscale Quantum Research Articles

Multi-Scale Quantum Harmonic Oscillator Algorithm With Centroid Motion for Global Numerical Optimization Problems

This paper proposes a new approach for function optimization using a new variant of multi-scale quantum harmonic optimization algorithm (MQHOA). The new approach introduces a centroid motion to improve the convergence efficiency, which is called MQHOA with centroid motion (CM-MQHOA). Instead of replacing the worst particle by the current best individual in the quantum harmonic oscillator process in MQHOA, the weakest player is replaced by a current centroid position in the proposed algorithm. Simple mechanisms are added to maintain the diversity of the population and help achieve the global optima in difficult unimodal and multimodal search spaces. The benefits of the proposed algorithm are improved performance in terms of effectiveness, reliability, accuracy, and efficiency. The approach appears to be able to efficiently deal with several unimodal and multimodal benchmark functions. A variety of standard benchmark functions are used to illustrate the proposed approach. The experimental results are compared with several state-of-the-art optimization algorithms. The comparative results indicate the competitiveness of the proposed algorithm and suggest a viable and attractive addition to the portfolio of computational intelligence techniques.

Analysis of Multiscale Quantum Harmonic Oscillator Algorithm Based on a New Multimode Objective Function

The wavefunction is an important element of the multiscale quantum harmonic oscillator algorithm (MQHOA). To verify the physical model and the multimode optimization performance of the MQHOA for multimode optimization in this paper, we define a multidimensional harmonic-Gaussian potential function. When the wavefunction of the MQHOA for multimode optimization and the probability amplitude of an ammonia molecule are compared, the ground-state wavefunction can reflect the probability distribution of the two-state ammonia molecule. We obtain the extrema of the proposed function using the Hessian matrix and optimize the proposed function with the multimode algorithm. The experiments show that the multimode algorithm can determine the extrema of the proposed function with appropriate parameters. Changes in the proposed function barriers have little effect on the optimization ability of the multimode algorithm. The optimization ability of the multimode algorithm is determined by its own wavefunction.

Multi-Scale Quantum Harmonic Oscillator Algorithm With Truncated Mean Stabilization Strategy for Global Numerical Optimization Problems

A multi-scale quantum harmonic oscillator algorithm (MQHOA) is a quantum population-based algorithm proposed recently. It utilizes the quantum wave function to locate the global optimum of a global numerical optimization problem. As the MQHOA employs the elitism to replace the worst particle in each iteration cycle, it reduces one of the particles in each run, which will cripple the diversity of the population and slow down the convergence speed. Therefore, the particles will be easily trapped into local optima. In this paper, we suggest a new MQHOA with truncated mean stabilization (TS-MQHOA) policy to alleviate the above-mentioned problems. The theoretical and experimental analyses indicate that the truncated mean stabilization strategy helps to diversify the populations and improve the convergence efficiency. The proposed TS-MQHOA is evaluated on a number of dimensionwise unimodal and multimodal CEC benchmark functions, and the computational results are compared with several popular population-based algorithms. The experimental results on complex test problems demonstrate that the proposed TS-MQHOA, in most function evaluations, is able to obtain better convergence toward the global optimum compared with several renowned heuristic algorithms based on swarm intelligence. Meanwhile, the comparative results reveal the competitiveness and superiority of the proposed algorithm, especially on high-dimensional function evaluations.

An optimal secure and verifiable education content searching scheme for cloud-assisted edge computing

Cloud-assisted edge computing transforms service delivery by providing cloud-like services near the radio access network, ensuring low-latency services for mobile devices and alleviating significant pressure on the backbone network. The encryption and storage of multimedia data on untrusted cloud servers have prompted the adoption of searchable encryption for controlled keyword searches on ciphertext. Elevating online learning experiences requires sophisticated data analysis techniques, with Big Data playing a substantial role in efficiently processing extensive learning data and enhancing the value of E-learning platforms. Over time, E-learning management systems evolve into rich repositories of learning materials, enabling subject matter experts to reuse content for creating new online materials. To tackle challenges, we propose an optimal, secure, and verifiable education content searching scheme tailored for cloud-assisted edge computing. We introduce a lightweight encryption scheme for secure data storage and design a multi-scale quantum harmonic oscillator model to enhance content searching effectiveness and ensure accurate retrieval of educational information. Performance evaluation, utilizing benchmark datasets like Kaggle web contented, the CISI test set, and data from MAHE University, consistently validates the efficiency and feasibility of the proposed scheme for E-learning applications.

Benchmarking treewidth as a practical component of tensor network simulations.

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network’s line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.

Coherence in carotenoid-to-chlorophyll energy transfer

The subtle details of the mechanism of energy flow from carotenoids to chlorophylls in biological light-harvesting complexes are still not fully understood, especially in the ultrafast regime. Here we focus on the antenna complex peridinin–chlorophyll a–protein (PCP), known for its remarkable efficiency of excitation energy transfer from carotenoids—peridinins—to chlorophylls. PCP solutions are studied by means of 2D electronic spectroscopy in different experimental conditions. Together with a global kinetic analysis and multiscale quantum chemical calculations, these data allow us to comprehensively address the contribution of the potential pathways of energy flow in PCP. These data support dominant energy transfer from peridinin S2 to chlorophyll Qy state via an ultrafast coherent mechanism. The coherent superposition of the two states is functional to drive population to the final acceptor state, adding an important piece of information in the quest for connections between coherent phenomena and biological functions.

Multi-scale quantum harmonic oscillator algorithm for global numerical optimization

This paper aims to provide a novel metaheuristic algorithm motivated from quantum motion entitled Multi-scale Quantum Harmonic Oscillator Algorithm (MQHOA). The calculation accuracy of MQHOA is adjustable. The physical model and mathematical analysis of the proposed algorithm are detailed and well interpreted in this paper. The structure of MQHOA is very simple, including merely two phases, the quantum harmonic oscillator process (QHO process) and multi-scale process (M process). Experiments are carried out to validate the effectiveness and efficiency of MQHOA by applying it to 30 well defined benchmark functions. We also compare MQHOA with several well-known metaheuristic algorithms, such as genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO) and quantum particle swarm optimization (QPSO). The comparative results indicate the competitive and superior performance of the proposed algorithm in both convergence speed and optimal solution accuracy.

Catalytic mechanism and molecular engineering of quinolone biosynthesis in dioxygenase AsqJ

The recently discovered FeII/α-ketoglutarate-dependent dioxygenase AsqJ from Aspergillus nidulans stereoselectively catalyzes a multistep synthesis of quinolone alkaloids, natural products with significant biomedical applications. To probe molecular mechanisms of this elusive catalytic process, we combine here multi-scale quantum and classical molecular simulations with X-ray crystallography, and in vitro biochemical activity studies. We discover that methylation of the substrate is essential for the activity of AsqJ, establishing molecular strain that fine-tunes π-stacking interactions within the active site. To rationally engineer AsqJ for modified substrates, we amplify dispersive interactions within the active site. We demonstrate that the engineered enzyme has a drastically enhanced catalytic activity for non-methylated surrogates, confirming our computational data and resolved high-resolution X-ray structures at 1.55 Å resolution. Our combined findings provide crucial mechanistic understanding of the function of AsqJ and showcase how combination of computational and experimental data enables to rationally engineer enzymes.

Solution Structure and Ultrafast Vibrational Relaxation of the PtPOP Complex Revealed by ΔSCF-QM/MM Direct Dynamics Simulations

Recent ultrafast experiments have unveiled the time scales of vibrational cooling and decoherence upon photoexcitation of the diplatinum complex [Pt2(P2O5H2)4]4– in solvents. Here, we contribute to the understanding of the structure and dynamics of the lowest lying singlet excited state of the model photocatalyst by performing potential energy surface calculations and Born–Oppenheimer molecular dynamics simulations in the gas phase and in water. Solvent effects were treated using a multiscale quantum mechanics/molecular mechanics approach. Fast sampling was achieved with a modified version of delta self-consistent field implemented in the grid-based projector-augmented wave density functional theory code. The known structural parameters and the PESs of the first singlet and triplet excited states are correctly reproduced. Besides, the simulations deliver clear evidence that pseudorotation of the ligands in the excited state leads to symmetry lowering of the Pt2P8 core. Coherence decay of Pt–Pt stretching ...

Multiscale Quantum Harmonic Oscillator Algorithm for Multimodal Optimization.

This paper presents a variant of multiscale quantum harmonic oscillator algorithm for multimodal optimization named MQHOA-MMO. MQHOA-MMO has only two main iterative processes: quantum harmonic oscillator process and multiscale process. In the two iterations, MQHOA-MMO only does one thing: sampling according to the wave function at different scales. A set of benchmark test functions including some challenging functions are used to test the performance of MQHOA-MMO. Experimental results demonstrate good performance of MQHOA-MMO in solving multimodal function optimization problems. For the 12 test functions, all of the global peaks can be found without being trapped in a local optimum, and MQHOA-MMO converges within 10 iterations.

Terminal Electron–Proton Transfer Dynamics in the Quinone Reduction of Respiratory Complex I

Complex I functions as a redox-driven proton pump in aerobic respiratory chains. By reducing quinone (Q), complex I employs the free energy released in the process to thermodynamically drive proton pumping across its membrane domain. The initial Q reduction step plays a central role in activating the proton pumping machinery. In order to probe the energetics, dynamics, and molecular mechanism for the proton-coupled electron transfer process linked to the Q reduction, we employ here multiscale quantum and classical molecular simulations. We identify that both ubiquinone (UQ) and menaquinone (MQ) can form stacking and hydrogen-bonded interactions with the conserved Q-binding-site residue His-38 and that conformational changes between these binding modes modulate the Q redox potentials and the rate of electron transfer (eT) from the terminal N2 iron–sulfur center. We further observe that, while the transient formation of semiquinone is not proton-coupled, the second eT process couples to a semiconcerted proton uptake from conserved tyrosine (Tyr-87) and histidine (His-38) residues within the active site. Our calculations indicate that both UQ and MQ have low redox potentials around −260 and −230 mV, respectively, in the Q-binding site, respectively, suggesting that release of the Q toward the membrane is coupled to an energy transduction step that could thermodynamically drive proton pumping in complex I.

Multiscale Molecular Dynamics Simulations of Polaritonic Chemistry.

When photoactive molecules interact strongly with confined light modes as found in plasmonic structures or optical cavities, new hybrid light-matter states can form, the so-called polaritons. These polaritons are coherent superpositions (in the quantum mechanical sense) of excitations of the molecules and of the cavity photon or surface plasmon. Recent experimental and theoretical works suggest that access to these polaritons in cavities could provide a totally new and attractive paradigm for controlling chemical reactions that falls in between traditional chemical catalysis and coherent laser control. However, designing cavity parameters to control chemistry requires a theoretical model with which the effect of the light-matter coupling on the molecular dynamics can be predicted accurately. Here we present a multiscale quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulation model for photoactive molecules that are strongly coupled to confined light in optical cavities or surface plasmons. Using this model we have performed simulations with up to 1600 Rhodamine molecules in a cavity. The results of these simulations reveal that the contributions of the molecules to the polariton are time-dependent due to thermal fluctuations that break symmetry. Furthermore, the simulations suggest that in addition to the cavity quality factor, also the Stokes shift and number of molecules control the lifetime of the polariton. Because large numbers of molecules interacting with confined light can now be simulated in atomic detail, we anticipate that our method will lead to a better understanding of the effects of strong coupling on chemical reactivity. Ultimately the method may even be used to systematically design cavities to control photochemistry.

Understanding in-line probing experiments by modeling cleavage of nonreactive RNA nucleotides.

Ribonucleic acid (RNA) is involved in many regulatory and catalytic processes in the cell. The function of any RNA molecule is intimately related with its structure. In-line probing experiments provide valuable structural data sets for a variety of RNAs and are used to characterize conformational changes in riboswitches. However, the structural determinants that lead to differential reactivities in unpaired nucleotides have not been investigated yet. In this work, we used a combination of theoretical approaches, i.e., classical molecular dynamics simulations, multiscale quantum mechanical/molecular mechanical calculations, and enhanced sampling techniques in order to compute and interpret the differential reactivity of individual residues in several RNA motifs, including members of the most important GNRA and UNCG tetraloop families. Simulations on the multinanosecond timescale are required to converge the related free-energy landscapes. The results for uGAAAg and cUUCGg tetraloops and double helices are compared with available data from in-line probing experiments and show that the introduced technique is able to distinguish between nucleotides of the uGAAAg tetraloop based on their structural predispositions toward phosphodiester backbone cleavage. For the cUUCGg tetraloop, more advanced ab initio calculations would be required. This study is the first attempt to computationally classify chemical probing experiments and paves the way for an identification of tertiary structures based on the measured reactivity of nonreactive nucleotides.

Performance degradation of superlattice MOSFETs due to scattering in the contacts

Ideal, completely coherent quantum transport calculations had predicted that superlattice MOSFETs (SL-MOSFET) may offer steep subthreshold swing performance below 60 mV/dec to around 39 mV/dec. However, the high carrier density in the superlattice source suggests that scattering may significantly degrade the ideal device performance. Such effects of electron scattering and decoherence in the contacts of SL-MOSFETs are examined through a multi-scale quantum transport model developed in NEMO5. This model couples the NEGF-based quantum ballistic transport in the channel to a quantum mechanical density of states dominated reservoir, which is thermalized through strong scattering with local quasi-Fermi levels determined by drift-diffusion transport. The simulations show that scattering increases the electron transmission in the nominally forbidden minigap, therefore, degrading the subthreshold swing (S.S.) and the ON/OFF DC current ratio. This degradation varies with both the scattering rate and the length of the scattering dominated regions. Different SL-MOSFET designs are explored to mitigate the effects of such deleterious scattering. Specifically, shortening the spacer region between the superlattice and the channel from 3.5 nm to 0 nm improves the simulated S.S. from 51 mV/dec. to 40 mV/dec.

Exploring the Catalytic Mechanism of Human Glutamine Synthetase by Computer Simulations.

Glutamine synthetase is an important enzyme that catalyzes the ATP-dependent formation of glutamine from glutamate and ammonia. In mammals, it plays a key role in preventing excitotoxicity in the brain and detoxifying ammonia in the liver. In plants and bacteria, it is fundamental for nitrogen metabolism, being critical for the survival of the organism. In this work, we show how the use of classical molecular dynamics simulations and multiscale quantum mechanics/molecular mechanics simulations allowed us to examine the structural properties and dynamics of human glutamine synthetase (HsGS), as well as the reaction mechanisms involved in the catalytic process with atomic level detail. Our results suggest that glutamine formation proceeds through a two-step mechanism that includes a first step in which the γ-glutamyl phosphate intermediate forms, with a 5 kcal/mol free energy barrier and a -8 kcal/mol reaction free energy, and then a second rate-limiting step involving the ammonia nucleophilic attack, with a free energy barrier of 19 kcal/mol and a reaction free energy of almost zero. A detailed analysis of structural features within each step exposed the relevance of the acid-base equilibrium related to protein residues and substrates in the thermodynamics and kinetics of the reactions. These results provide a comprehensive study of HsGS dynamics and establish the groundwork for further analysis regarding changes in HsGS activity, as occur in natural variants and post-translational modifications.

Multiscale Quantum Mechanics/Molecular Mechanics Simulations with Neural Networks.

Molecular dynamics simulation with multiscale quantum mechanics/molecular mechanics (QM/MM) methods is a very powerful tool for understanding the mechanism of chemical and biological processes in solution or enzymes. However, its computational cost can be too high for many biochemical systems because of the large number of ab initio QM calculations. Semiempirical QM/MM simulations have much higher efficiency. Its accuracy can be improved with a correction to reach the ab initio QM/MM level. The computational cost on the ab initio calculation for the correction determines the efficiency. In this paper we developed a neural network method for QM/MM calculation as an extension of the neural-network representation reported by Behler and Parrinello. With this approach, the potential energy of any configuration along the reaction path for a given QM/MM system can be predicted at the ab initio QM/MM level based on the semiempirical QM/MM simulations. We further applied this method to three reactions in water to calculate the free energy changes. The free-energy profile obtained from the semiempirical QM/MM simulation is corrected to the ab initio QM/MM level with the potential energies predicted with the constructed neural network. The results are in excellent accordance with the reference data that are obtained from the ab initio QM/MM molecular dynamics simulation or corrected with direct ab initio QM/MM potential energies. Compared with the correction using direct ab initio QM/MM potential energies, our method shows a speed-up of 1 or 2 orders of magnitude. It demonstrates that the neural network method combined with the semiempirical QM/MM calculation can be an efficient and reliable strategy for chemical reaction simulations.

Structure-electronics relations of discotic liquid crystals from a molecular modelling perspective

ABSTRACTDiscotic liquid crystals (DLCs) have been researched for their potential in electronics applications, such as organic field-effect transistors, organic light-emitting diodes and organic photovoltaics. These molecules generally comprise a rigid planar core surrounded by aliphatic chains, and self-organise into columnar phases. Charge transfer is enabled along these columns, as the spatial overlap of the stacked π orbitals within the columns lead to a quasi-one-dimensional conductivity. An understanding of charge transfer and electronics orbitals in the field of DLCs is valuable for rational design of future DLC molecules in electronics applications. This paper provides a perspective that a range of molecular modelling tools may bring into our understanding on the structure, dynamics and electronics properties of DLCs. Whilst the description of charge transfer of DLCs has been substantially investigated, the understanding on the molecular orbitals had been relatively less explored. We introduce a multiscale molecular mechanics and quantum mechanics approach to understanding the relationship between the bandgap and density of states (DOS) and the structural parameters of a DLC. This investigation is expected to be the starting point for situations where knowledge of DOS for DLCs are of the essence, in applications such as current rectification and thermoelectricity.

On the mass-coupling relation of multi-scale quantum integrable models

We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of the perturbation of a projected product of minimal models. This representation enables us to identify conserved tensor currents on the UV side. These UV operators are then mapped via form factor perturbation theory to operators on the IR side, which are characterized by their form factors. The relation between the UV and IR operators is given in terms of the sought-for mass-coupling relation. By generalizing the $\Theta$ sum rule Ward identity we are able to derive differential equations for the mass-coupling relation, which we solve in terms of hypergeometric functions. We check these results against the data obtained by numerically solving the thermodynamic Bethe Ansatz equations, and find a complete agreement.

Exact Mass-Coupling Relation for the Homogeneous Sine-Gordon Model.

We derive the exact mass-coupling relation of the simplest multiscale quantum integrable model, i.e., the homogeneous sine-Gordon model with two mass scales. The relation is obtained by comparing the perturbed conformal field theory description of the model valid at short distances to the large distance bootstrap description based on the model's integrability. In particular, we find a differential equation for the relation by constructing conserved tensor currents, which satisfy a generalization of the Θ sum rule Ward identity. The mass-coupling relation is written in terms of hypergeometric functions.

Practical Aspects of Multiscale Classical and Quantum Simulations of Enzyme Reactions.

This chapter aims to present some basic multiscale approaches available for enzyme simulations, and to point out practical details and pitfalls that are not often discussed in the literature, but can greatly influence the outcome of any in silico enzyme study. We cover principle methodological steps of multiscale studies of general enzyme reactions. This includes choice of starting structures, boundary conditions, potential energy surfaces, reaction coordinates, simulation methods, as well as the choice of method for the treatment of nuclear quantum effects. Together, these and additional steps are crucial for the success of enzyme-modeling projects and should be considered prior to embarking on multiscale modeling.