Accuracy of gates in a quantum computer based on vibrational eigenstates

A model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical time-propagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.     

Decoherence effects on superpositions of chiral states in a chiral molecule

The superposition of chiral states of chiral molecules, as delocalized quantum states of a many-particle system, can be used for the experimental investigations of decoherence theory. In this regard, a great challenge is the precise quantification of the robustness of these superpositions against environmental effects. The methods so far proposed need the detailed specification of the internal states of the molecule, usually requiring heavy numerical calculations. Here, by using the linearized quantum Boltzmann equation and by borrowing ideas employed for analyzing other quantum systems, we present a general and simple approach, of wide applicability, which can be used to compute the dominant contribution to the decoherence rate for the superpositions of chiral states of chiral molecules, due to environmental scattering.     

Estimation of concrete compressive strength by a fuzzy logic model

Concrete mix design is a process of proportioning the ingredients in right proportions. The aim of this study is to design a fuzzy logic model for determination of the compressive strength of a concrete. The datasets which have been loaded into a fuzzy logic model contain 1,030 concrete mixtures. Input fields of the fuzzy expert system are weight percent of cement, water, blast furnace slag, fly ash, super plasticizer, fine aggregate, coarse aggregate, and age of the concrete. Output field is concrete compressive strength. Finally, 897 rules used for this fuzzy logic modeling.     

Characterization of quantum algorithms by quantum process tomography using quadrupolar spins in solid-state nuclear magnetic resonance

NMR quantum computing with qubit systems represented by nuclear spins (I=12) in small molecules in liquids has led to the most successful experimental quantum information processors so far. We use the quadrupolar spin-32 sodium nuclei of a NaNO3 single crystal as a virtual two-qubit system. The large quadrupolar coupling in comparison with the environmental interactions and the usage of strongly modulating pulses allow us to manipulate the system fast enough and at the same time keeping the decoherence reasonably slow. The experimental challenge is to characterize the "calculation" behavior of the quantum processor by process tomography which is here adapted to the quadrupolar spin system. The results of a selection of quantum gates and algorithms are presented as well as a detailed analysis of experimental results.     

Quantum algorithm for obtaining the energy spectrum of molecular systems

Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schr?dinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.     

Classical aspects emerging from local control of energy and particle transfer in molecules

The question in how far classical mechanics can be used to describe coherent control processes in molecules is addressed within the framework of local control theory. Therefore, quantum and classical calculations are compared for a model proton transfer process and also for the multi-photon infrared dissociation of the HOD molecule. It is shown that control fields can be derived classically as long as wave packet dispersion is not too large. This hints at further applications which might be helpful to devise control fields for complex molecular systems being present in biological processes.     

Identification of critical genes in microarray experiments by a Neuro-Fuzzy approach

Gene expression profiling by microarray technology is usually difficult to interpret into a simpler pattern. One approach to resolve the complexity of gene expression profiles is the application of artificial neural networks (ANNs). A potential difficulty in this strategy, however, is that the non-linear nature of ANN makes it essentially a 'black-box' computation process. Addition of a fuzzy logic approach is useful because it can complement ANN by explicitly specifying membership function during computation. We employed a hybrid approach of neural network and fuzzy logic to further analyze a published microarray study of gene responses to eight bacteria in human macrophages. The original analysis by hierarchical clustering found common gene responses to all bacteria but did not address individual responses. Our method allowed exploration of the gene response of the host to individual bacterium. We implemented a two-layer, feed-forward neural network containing the principle of 'competitive learning' (i.e. 'winner-take-all'). The weights of the trained neural network were fed into a fuzzy logic inference system. A new measurement, called the impact rating (IR) was also introduced to explore the degree of importance of each gene. To assess the reliability of the IR value, a bootstrap re-sampling method was applied to the dataset and a confidence level for each IR was obtained. Our approach has successfully uncovered the unique features of host response to individual bacterium. Further, application of gene ontology (GO) annotation to the genes of high IR values in each response has suggested new biological pathways for individual host-pathogen interactions.     

Magneto-optical interactions in single-molecule magnets: Low-temperature photon-induced demagnetization

We show that the irradiation of SMM molecules at optical wavelengths can drive an increase or a decrease of the magnetic moment of a SMM, even though the energy of the photons does not correspond to a precise electronic or spin transition, the light pulse triggering a phonon-assisted spin transition. The process is sensitive to the power of the incident light. This result most probably explains why it has been so far impossible to observe the opening of the hysteresis loop on thin films of SMM with the XMCD technique. The consequences of these observations are manifold: they bring a means of controlling molecular magnets, open prospects in the field of quantum computing, and may enable the realization of coherent microwave sources through stimulated superradiance.     

Establishing a New Link between Fuzzy Logic,Neuroscience, and Quantum Mechanics through Bayesian Probability: Perspectives in Artificial Intelligence and Unconventional Computing

Human interaction with the world is dominated by uncertainty. Probability theory is a valuable tool to face such uncertainty. According to the Bayesian definition, probabilities are personal beliefs. Experimental evidence supports the notion that human behavior is highly consistent with Bayesian probabilistic inference in both the sensory and motor and cognitive domain. All the higher-level psychophysical functions of our brain are believed to take the activities of interconnected and distributed networks of neurons in the neocortex as their physiological substrate. Neurons in the neocortex are organized in cortical columns that behave as fuzzy sets. Fuzzy sets theory has embraced uncertainty modeling when membership functions have been reinterpreted as possibility distributions. The terms of Bayes’ formula are conceivable as fuzzy sets and Bayes’ inference becomes a fuzzy inference. According to the QBism, quantum probabilities are also Bayesian. They are logical constructs rather than physical realities. It derives that the Born rule is nothing but a kind of Quantum Law of Total Probability. Wavefunctions and measurement operators are viewed epistemically. Both of them are similar to fuzzy sets. The new link that is established between fuzzy logic, neuroscience, and quantum mechanics through Bayesian probability could spark new ideas for the development of artificial intelligence and unconventional computing.     

Inverse quantum chemistry: Concepts and strategies for rational compound design

The rational design of molecules and materials is becoming more and more important. With the advent of powerful computer systems and sophisticated algorithms, quantum chemistry plays a decisive role in the design process. While traditional quantum chemical approaches predict the properties of a predefined molecular structure, the goal of inverse quantum chemistry is to find a structure featuring one or more desired properties. Herein, we review inverse quantum chemical approaches proposed so far and discuss their advantages as well as their weaknesses. © 2014 Wiley Periodicals, Inc.     

Multifunction moonlighting and intrinsically disordered proteins: Information catalysis, non-rigid molecule symmetries and the ‘logic gate’ spectrum

Intrinsically disordered proteins (IDP) appear far more likely to engage in functional moonlighting than well-structured proteins. The recent use of nonrigid molecule theory to address IDP structure and dynamics produces this result directly: mirror image subgroup or subgroupoid tiling matching of the molecular fuzzy lock-and-key can be much richer for IDP's since the number of possible group or groupoid symmetries can grow exponentially with molecule length, while tiling matching for 3D structured proteins is relatively limited. An ‘information catalysis’ model suggests how this mechanism can produce a vast spectrum of biological logic gates having subtle properties far beyond familiar AND, OR, XOR, etc. behaviors. Inferring the general from the particular, the analysis adds weight to arguments that a fundamental defining characteristic of the living state is the operation of chemical or other cognitive processes at virtually every scale and level of organization.     

Entanglement of polar molecules in pendular states

In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.     

Photoquenching: The dependence of the primary quantum yield of a monophotonic laser-induced photochemical process on the intensity and duration of the exciting pulse

Excited state absorption in large molecules leads to a decrease of the primary quantum yield of a photochemical or a photophysical process. Since then the quantum yield decreases with increasing light intensity this effect is called photoquenching.Kinetic analysis of the excitation in a general level scheme of a large molecule yields expressions for the quentum yield of a laser-induced photochemical process. Calculation of the quantum yield for various combinations of molecular parameters and laser pulse characteristics shows quenching of the photochemical process due to excited state absorption, at laser intensities for which bleaching effects and other nonlinear processes are negligeable. The applicability of the steady state approximation in analyzing laser-induced processes is discussed. Experiments are reported, which confirm the calculated intensity-dependent quantum yield function. Previous measurements of intensity-induced quenching can now be discussed quantitatively. Care should be taken in interpreting laser-induced photochemical yields, especially at mode locked laser intensities; correct values can only be obtained by extrapolation to zero laser intensity     

Toward a fuzzy atom view within the context of the quantum theory of atoms in molecules: quasi-atoms

The notion of quasi-atoms is introduced within the context of the quantum theory of atoms in molecules. Being a subset of the quantum divided basins that were introduced previously, quasi-atoms are the quantum subsystems that are practically indistinguishable from the topological atoms; thus, revealing the continuous evolution of quantum divided basins into topological atoms. This indistinguishability is rooted in the limited accuracy of chemical observations; they are not sensitive to discriminate a topological atom from its associated quasi-atoms. In this regard, it is disclosed that the set of quantum atoms is in a wide-range including members other than topological atoms; the quasi-atoms are concrete examples. Finally, the idea of the fuzzy set of atoms that is foreign to the disjoint partitioning schemes for which the orthodox QTAIM is a classic example is extended employing the set of quasi-atoms.     

Ab initio quality properties for macromolecules using the ADMA approach

We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate-size "parent molecules" that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree-Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.     

Representation of molecular structure using quantum topology with inductive logic programming in structure–activity relationships

The requirement of aligning each individual molecule in a data set severely limits the type of molecules which can be analysed with traditional structure activity relationship (SAR) methods. A method which solves this problem by using relations between objects is inductive logic programming (ILP). Another advantage of this methodology is its ability to include background knowledge as 1st-order logic. However, previous molecular ILP representations have not been effective in describing the electronic structure of molecules. We present a more unified and comprehensive representation based on Richard Bader's quantum topological atoms in molecules (AIM) theory where critical points in the electron density are connected through a network. AIM theory provides a wealth of chemical information about individual atoms and their bond connections enabling a more flexible and chemically relevant representation. To obtain even more relevant rules with higher coverage, we apply manual postprocessing and interpretation of ILP rules. We have tested the usefulness of the new representation in SAR modelling on classifying compounds of low/high mutagenicity and on a set of factor Xa inhibitors of high and low affinity.     

Amphoteric doping of carbon nanotubes by encapsulation of organic molecules: electronic properties and quantum conductance

In order to investigate and optimize the electronic transport processes in carbon nanotubes doped with organic molecules, we have performed large-scale quantum electronic structure calculations coupled with a Green's function formulation for determining the quantum conductance. Our approach is based on an original scheme where quantum chemistry calculations on finite systems are recast to infinite, non-periodic (i.e., open) systems, therefore mimicking actual working devices. Results from these calculations clearly suggest that the electronic structure of a carbon nanotube can be easily manipulated by encapsulating appropriate organic molecules. Charge transfer processes induced by encapsulated organic molecules lead to efficient n- and p-type doping of the carbon nanotube. Even though a molecule can induce p and n doping, it is shown to have a minor effect on the transport properties of the nanotube as compared to a pristine tube. This type of doping therefore preserves the intrinsic properties of the pristine tube as a ballistic conductor. In addition, the efficient process of charge transfer between the organic molecules and the nanotube is shown to substantially reduce the susceptibility of the pi electrons of the nanotube to modification by oxygen while maintaining stable doping (i.e., no dedoping) at room temperature.     

Alternative treatment of rotational quantum systems

The method of the Hill determinant proves to be useful in treating purely rotating quantum systems. The rotational Stark effect in symmetric-top molecules and the internal rotation in molecules are discussed as illustrative examples. The procedure can be used either to obtain the energy eigenvalues for a given model potential or to built it from experimental data.     

Coherent effects in energy transport in model dendritic structures investigated by ultrafast fluorescence anisotropy spectroscopy

Measurements of ultrafast fluorescence anisotropy decay in model branched dendritic molecules of different symmetry are reported. These molecules contain the fundamental branching center units of larger dendrimer macromolecules with either three (C(3))- or four (T(d), tetrahedral)-fold symmetry. The anisotropy for a tetrahedral system is found to decay on a subpicosecond time scale (880 fs). This decay can be qualitatively explained by F?rster-type incoherent energy migration between chromophores. Alternatively, for a nitrogen-centered trimer system, the fluorescence anisotropy decay time (35 fs) is found to be much shorter than that of the tetramers, and the decay cannot be attributed to an incoherent hopping mechanism. In this case, a coherent interchromophore energy transport mechanism should be considered. The mechanism of the ultrafast energy migration process in the branched systems is interpreted by use of a phenomenological quantum mechanical model, which examines the two extreme cases of incoherent and coherent interactions.     

Quantum tunneling of magnetization and related phenomena in molecular materials

Molecules comprising a large number of coupled paramagnetic centers are attracting much interest because they may show properties which are intermediate between those of simple paramagnets and classical bulk magnets and provide unambiguous evidence of quantum size effects in magnets. To date, two cluster families, usually referred to as Mn12 and Fe8, have been used to test theories. However, it is reasonable to predict that other classes of molecules will be discovered which have similar or superior properties. To do this it is necessary that synthetic chemists have a good understanding of the correlation between the structure and properties of the molecules, for this it is necessary that concepts such as quantum tunneling, quantum coherence, quantum oscillations are understood. The goal of this article is to review the fundamental concepts needed to understand quantum size effects in molecular magnets and to critically report what has been done in the field to date.