Quantum computing measurement and intelligence

One of the grand challenges in the nanoscopic computing era is guarantees of robustness. Robust computing system design is confronted with quantum physical, probabilistic, and even biological phenomena, and guaranteeing high‐reliability is much more difficult than ever before. Scaling devices down to the level of single electron operation will bring forth new challenges due to probabilistic effects and uncertainty in guaranteeing “zero‐one” based computing. Minuscule devices imply billions of devices on a single chip, which may help mitigate the challenge of uncertainty by replication and redundancy. However, such device densities will create a design and validation nightmare with the sheer scale. The questions that confront computer engineers regarding the current status of nanocomputing material and the reliability of systems built from such minuscule devices are difficult to articulate and answer. This article illustrates and discusses two types of quantum algorithms as follows: (1) a simple quantum algorithm and (2) a quantum search algorithm. This article also presents a review of recent advances in quantum computing and intelligence and presents major achievements and obstacles for researchers in the near future. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

The quantum divided basins: A new class of quantum subsystems

The rigorous theory of the quantum divided basins (QDB), the quantum subsystems emerging from the net zero‐flux equation, is considered in this article. This framework, the quantum theory of proper open subsystems, is derived from the extension of the quantum theory of atoms in molecules to encompass the new class of quantum subsystems. It is demonstrated that the regional hypervirial theorem and the associated regional observables as well as the subsystem variational procedure are all expressible for the QDB. The history of QDB is briefly reviewed and the bundles, which were introduced by other researchers, are offered as typical examples whereas new examples of QDB (not yet mentioned in literature) are also presented. Based on some model systems as well as the nitrogen molecule, the regional properties and the morphologies of typical QDB are scrutinized. It is also demonstrated that the QDB may be used to study the fine structure of the electron localization and delocalization. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Synthesizing quantum probability by a single chaotic complex‐valued trajectory

The current trajectory interpretation of quantum mechanics is based on an ensemble viewpoint that the evolution of an ensemble of Bohmian trajectories guided by the same wavefunction Ψ converges asymptotically to the quantum probability . Instead of the Bohm's ensemble‐trajectory interpretation, the present paper gives a single‐trajectory interpretation of quantum mechanics by showing that the distribution of a single chaotic complex‐valued trajectory is enough to synthesize the quantum probability. A chaotic complex‐valued trajectory manifests both space‐filling (ergodic) and ensemble features. The space‐filling feature endows a chaotic trajectory with an invariant statistical distribution, while the ensemble feature enables a complex‐valued trajectory to envelop the motion of an ensemble of real trajectories. The comparison between complex‐valued and real‐valued Bohmian trajectories shows that without the participation of its imaginary part, a single real‐valued trajectory loses the ensemble information contained in the wavefunction Ψ, and this explains the reason why we have to employ an ensemble of real‐valued Bohmian trajectories to recover the quantum probability . © 2015 Wiley Periodicals, Inc.     

Commentaries on quantum similarity (1): Density gradient quantum similarity

Computation of density gradient quantum similarity integrals is analyzed, while comparing such integrals with overlap density quantum similarity measures. Gradient quantum similarity corresponds to another kind of numerical similarity assessment between a pair of molecular frames, which contrarily to the usual up to date quantum similarity definitions are not measures, that is: strictly positive definite integrals. As the density gradient quantum similarity integrals are defined as scalar products of three real functions, they appear to possess a richer structure than the corresponding positive definite density overlap quantum similarity measures, while preserving the overall similarity trends, when the molecular frames are relatively moved in three‐dimensional space. Similarity indices are also studied when simple cases are analyzed in order to perform more comparisons with density overlap quantum similarity. Multiple gradient quantum similarity integrals are also defined. General GTO formulae are given. Numerical results within the atomic shell approximation (ASA) framework are presented as simple examples showing the new performances of the gradient density quantum similarity. Fortran 90 programs illustrating the proposed theoretical development can be downloaded from appropriate websites. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

Quantum computers are reaching one crucial milestone after another. Motivated by their progress in quantum chemistry, we performed an extensive series of simulations of quantum-computer runs that were aimed at inspecting the best-practice aspects of these calculations. In order to compare the performance of different setups, the ground-state energy of the hydrogen molecule was chosen as a benchmark for which the exact solution exists in the literature. Applying the variational quantum eigensolver (VQE) to a qubit Hamiltonian obtained by the Bravyi–Kitaev transformation, we analyzed the impact of various computational technicalities. These included (i) the choice of the optimization methods, (ii) the architecture of the quantum circuits, as well as (iii) the different types of noise when simulating real quantum processors. On these, we eventually performed a series of experimental runs as a complement to our simulations. The simultaneous perturbation stochastic approximation (SPSA) and constrained optimization by linear approximation (COBYLA) optimization methods clearly outperformed the Nelder–Mead and Powell methods. The results obtained when using the Ry variational form were better than those obtained when the RyRz form was used. The choice of an optimum entangling layer was sensitively interlinked with the choice of the optimization method. The circular entangling layer was found to worsen the performance of the COBYLA method, while the full-entangling layer improved it. All four optimization methods sometimes led to an energy that corresponded to an excited state rather than the ground state. We also show that a similarity analysis of measured probabilities can provide a useful insight.     

Some Mathematical and Algorithmic Challenges in the Control of Quantum Dynamics Phenomena

The theory and practice of control over quantum mechanical phenomena is receiving increasing attention, underscored by striking experimental successes. Nevertheless, many questions of fundamental and practical relevance to the field remain unresolved. With the aim of stimulating further development, this paper formulates a number of theoretical questions, divided into three categories. First, questions related to control law design are discussed, with an emphasis on controllability and optimal control theory. This leads to the second category of open problems relevant to closed loop laboratory implementation of quantum control, including learning and feedback methods. The sensitive dependence of control on basic quantum mechanical interactions motivates the third section, which treats coherent dynamical techniques for identifying the system Hamiltonian. An open issue overarching all of these directions is the need to discover general rules for the control of quantum systems. Although the list of issues raised in this paper is extensive, it should be viewed not as a complete menu for exploration, but rather as a springboard to new challenges as the field evolves.     

A benchmark quantum Monte Carlo study of the ground state chromium dimer

We report calculations of the ground state energy and binding curve of the chromium dimer using the variational and diffusion quantum Monte Carlo (VMC and DMC) methods. We examined various single‐determinant and multideterminant wavefunctions multiplied by a Jastrow factor as a trial/guiding wavefunction for VMC/DMC. The molecular orbitals in the single determinants were calculated using restricted or unrestricted Hartree–Fock or density functional theory (DFT) calculations where five commonly used local (SVWN5), semilocal (PW91 and BLYP), and hybrid (B1LYP and B3LYP) functionals were examined. The multideterminant expansions were obtained from the generalized valence bond and (truncated) unrestricted configuration interaction with single and double excitations (UCISD) methods. We also examined a UCISD wavefunction in which UCISD expansions were added to the UB3LYP single‐determinant reference, and their coefficients were optimized at the VMC level. In addition to the wavefunction dependence, the effects of pseudopotentials and backflow transformation were also investigated. The UB3LYP single‐determinant and multideterminant wavefunctions were found to give the variationally best DMC energies within the framework of single‐determinant and multideterminants, respectively, though both the DMC energies were higher than twice the DMC atomic energy. Some of the VMC binding curves show a flat or quite shallow well bottom, which gets recovered deeper by DMC. All the DMC binding curves have a minimum indicating a bound state, but the unrestricted ones overestimate the equilibrium bond length. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

核-壳结构CdSe/ZnS量子点的制备、硫醇修饰及其光学性能

采用高温有机相包覆技术制备了CdSe/ZnS核壳结构量子点材料,考察了包覆量对量子点材料的光学性能的影响,研究了含脂肪链和芳香基的双硫醇分子1,4-苯二甲硫醇和1,8-辛二硫醇对于具有核-壳结构的CdSe/ZnS量子点材料的修饰作用,考察了修饰作用对于量子点的量子效率和荧光强度等光学性能的影响.实验结果表明:随着硫化锌包覆量的增加,量子点的量子效率及其荧光发射强度明显提高;硫醇的修饰能显著增强量子点的发光强度,随着硫醇浓度的增加,其发光性能增强,但是达到一定程度后,光学性能基本不随硫醇浓度的变化而变化.根据固体核磁共振等实验结果推测:硫醇分子可能部分替代了量子点体系中的正三辛基氧膦配体,稳定了量子点体系,对量子点起修饰保护作用,从而提高了量子点的光学性能.     

Improving singlet oxygen generating abilities of phthalocyanines: aluminum tetrasulfonated phthalocyanine in the presence of graphene quantum dots and folic acid

Glutathione-capped graphene quantum dots (GQDs@GSH) were covalently linked to folic acid (FA). Aluminum tetrasulfonated phthalocyanine (ClAlTSPc) was then adsorbed on the GQDs@GSH-FA conjugate to form GQDs@GSH-FA/ClAlTSPc or on GQDs@GSH and pristine GQDs alone to form GQDs@GSH/ClAlTSPc and GQDs/ClAlTSPc, respectively. We report for the first time on the photophysicochemical behavior of the resulting nanoconjugates. The fluorescence quantum yields of pristine GQDs, GQDS@GSH, or GQDs@GSH-FA conjugate were quenched upon non-covalent interaction (π–π) with ClAlTSPc. There was an increase in triplet quantum yields from 0.38 for ClAlTSPc alone to 0.60, 0.75, and 0.73 when ClAlTSPc was linked to pristine GQDs, GQDs@GSH, and GQDs@GSH-FA, respectively. The singlet oxygen quantum yields also increased from 0.37 for ClAlTSPc alone to 0.42 (for ClALTSPc with pristine GQDs), 0.52 (for ClAlTSPc with GQDs@GSH), and 0.54 (for ClAlTSPc with GQDs@GSH-FA). Thus, the present work may lead to a new generation of carbon-based nanomaterial photodynamic therapy agents with overall performance superior to conventional agents in terms of singlet oxygen generation, water dispersibility, and biocompatibility.     

Localization in some discontinuously and randomly driven quantum systems

A charged particle moving in a harmonic, symmetric double well, a square well, or a Morse potential is allowed to interact with a discontinuously reversing spatially homogeneous electric field. Randomly reversing field is seen to cause localization in the quantum system. A critical reversal frequency is seen to exist below which no localization is manifested in the harmonic, double and square well. In the Morse case, there is dissociation if the upper limit of the interval between random kicks exceeds τ_max. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Electronic quantum trajectories in a quantum dot

This article gives a quantum‐trajectory demonstration of the observed electric, magnetic, and thermal effects on a quantum dot with circular or elliptic shape. By applying quantum trajectory method to a quantum dot, we reveal the quantum‐mechanical meanings of the classical concepts of backscattering and commensurability, which were used in the literature to explain the peak locations of the magnetoresistance curve. Under the quantum commensurability condition, electronic quantum trajectories in a circular quantum dot are shown to be stationary like a standing wave, whose presence increases the electrical resistance. A hidden quantum effect called magnetic stagnation is discovered and shown to be the main cause of the observed jumps of the magnetoresistance curve. Quantum trajectories in an elliptic quantum dot are found to be chaotic and an index of chaos called Lyapunov exponent is proposed to measure the irregularity of the various quantum trajectories. It is shown that the response of the Lyapunov exponent to the applied magnetic field captures the main features of the experimental magnetoresistance curve. © 2014 Wiley Periodicals, Inc.     

Pattern recognition in molecular quantum mechanics

It is shown that the classical concept of an open system does not encompass quantal systems but has to be replaced by the non-Boolean notion of an entangled system. Molecular, chemical, or biological phenomena can be considered to be reduced to a fundamental theory like quantum mechanics only if the fundamental and the phenomenological theories are formally and interpretatively connected, and if the classifications used in the empirical sciences are shown to follow from a single set of fundamental dynamical laws. These conditions enforce a non-statistical and ontic interpretation of quantum mechanics, hence a non-Boolean calculus of propositions. In this interpretation the notion of a world state is well-defined, its Schmidt-decomposition defines a background-dependent model state for molecular systems and creates the phenomena we can observe. To any molecular system there is associated in an objective way a nonnegative number which we call the integrity. The integrity measures the inherent fuzziness of the system concept in a holistic theory, and is used to define recognizable molecular patterns.     

Latin American contributions to quantum chemical topology

We survey the contributions from Latin American theoretical chemists to the field of quantum chemical topology (QCT) over nearly the last 30 years with emphasis on the developments and applications of the quantum theory of atoms in molecules (QTAIM). Applications of QCT in the fields of excited states, electron delocalization, chemical bond, aromaticity, conformational analysis, spectroscopic properties, and chemical reactivity are presented. We also consider the coupling of QTAIM with time-dependent density functional theory, the virial theorem in the Kohn-Sham method and the inclusion of electron dynamical correlation in the interacting quantum atoms method using coupled cluster and multi-configurational densities. Additionally, we describe the development of efficient algorithms for the calculation of topological properties derived from the electron density. This review is aimed not only at providing an account of the contributions to QCT in Latin America but also at stimulating guides for further progress in the field.     

Real‐time quantum chemistry

Significant progress in the development of efficient and fast algorithms for quantum chemical calculations has been made in the past two decades. The main focus has always been the desire to be able to treat ever larger molecules or molecular assemblies—especially linear and sublinear scaling techniques are devoted to the accomplishment of this goal. However, as many chemical reactions are rather local, they usually involve only a limited number of atoms so that models of about 200 (or even less) atoms embedded in a suitable environment are sufficient to study their mechanisms. Thus, the system size does not need to be enlarged, but remains constant for reactions of this type that can be described by less than 200 atoms. The question then arises how fast one can obtain the quantum chemical results. This question is not directly answered by linear‐scaling techniques. In fact, ideas such as haptic quantum chemistry (HQC) or interactive quantum chemistry require an immediate provision of quantum chemical information which demands the calculation of data in “real time.” In this perspective, we aim at a definition of real‐time quantum chemistry, explore its realm and eventually discuss applications in the field of HQC. For the latter, we elaborate whether a direct approach is possible by virtue of real‐time quantum chemistry. © 2012 Wiley Periodicals, Inc.     

Carbon Dots for Carbon Dummies: The Quantum and The Molecular Questions Among Some Others

Carbon Dots (CDs) are carbon nanoparticles which were discovered in 2004. Despite two decades of intensive work from the scientific community and a colossal amount of gathered experimental data, no definitive consensus exists to date on several key aspects such as the actual definition of CDs and the origin of their emissive properties. This review proposes a critical evaluation of these fundamental questions. Lay persons will also find here an alternative introduction to the CDs domain, including synthetic strategies, photophysical properties, as well as challenges and outlook of this exciting new area.     

Generation of Molecular Fields, Quantum Similarity Measures and Related Questions

A straightforward discussion on how to generate molecular fields is developed within the postulates of quantum mechanics. The theoretical formalism points towards the generalization and extension of the well-known molecular field forms, associated to density function and electrostatic molecular potential (EMP), including another category of fields associated to quantum molecular similarity measures. The results show that the new formalism can be easily applied to obtain an unlimited number of new information about molecular behavior.