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Results for “variational quantum algorithms”

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PubMed2004

Cooperating or fighting with control noise in the optimal manipulation of quantum dynamics.

This paper investigates the impact of control field noise on the optimal manipulation of quantum dynamics. Simulations are performed on several multilevel quantum systems with the goal of population transfer in the presence of significant control noise. The noise enters as run-to-run variations in the control amplitude and phase with the observation being an ensemble average over many runs as is commonly done in the laboratory. A genetic algorithm with an improved elitism operator is used to find the optimal field that either fights against or cooperates with control field noise. When seeking a high control yield it is possible to find fields that successfully fight with the noise while attaining good quality stable results. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with the noise and thereby drive the dynamics more efficiently. In general, noise reduces the coherence of the dynamics, but the results indicate that population transfer objectives can be met by appropriately either fighting or cooperating with noise, even when it is intense.

Journal Article↗

PubMed2004

Realization of quantum chemistry without wave functions through first-order semidefinite programming.

Determining the energy and properties of an N-electron molecule through a two-electron variational optimization has been a dream for more than half a century. While optimizations, using two-electron reduced density matrices constrained to represent N electrons, have recently been achieved, the computational costs are prohibitive. In this report an efficient algorithm with an order-of-magnitude reduction in floating-point operations and memory usage is presented. Because the optimization occurs on the space of two electrons, this method automatically treats strong, multireference correlation. Application is made to N2 and H6 where the method yields consistent accuracy at all geometries.

Journal Article↗

PubMed2006

Correction of photoresponse nonuniformity for matrix detectors based on prior compensation for their nonlinear behavior.

What we believe to be a novel procedure to correct the nonuniformity that is inherent in all matrix detectors has been developed and experimentally validated. This correction method, unlike other nonuniformity-correction algorithms, consists of two steps that separate two of the usual problems that affect characterization of matrix detectors, i.e., nonlinearity and the relative variation of the pixels' responsivity across the array. The correction of the nonlinear behavior remains valid for any illumination wavelength employed, as long as the nonlinearity is not due to power dependence of the internal quantum efficiency. This method of correction of nonuniformity permits the immediate calculation of the correction factor for any given power level and for any illuminant that has a known spectral content once the nonuniform behavior has been characterized for a sufficient number of wavelengths. This procedure has a significant advantage compared with other traditional calibration-based methods, which require that a full characterization be carried out for each spectral distribution pattern of the incident optical radiation. The experimental application of this novel method has achieved a 20-fold increase in the uniformity of a CCD array for response levels close to saturation.

Journal Article↗

PubMed2005

Optimal choice of dividing surface for the computation of quantum reaction rates.

We consider the calculation of quantum mechanical rate constants for chemical reactions via algorithms that utilize short-time values of the symmetrized flux-flux correlation function. We argue that the dividing surface that makes optimal use of the short-time quantum information is the surface that minimizes the value at the origin of the symmetrized flux-flux correlation function. We also demonstrate that, in the classical limit, this quantum variational criterion produces the same dividing surface as Wigner's variational principle. Finally, we argue that the quantum variational criterion behaves in a nearly optimal fashion with respect to the minimization of the extent of re-crossing flux.

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PubMed2004

Matrix product density operators: simulation of finite-temperature and dissipative systems.

We show how to simulate numerically the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems, and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of matrix product states which is variational.

Journal Article↗

PubMed2006

Computing the density of paths in complex systems.

Trajectories of duration tau joining two points q(0) and q(1) in the configuration space of a classical system satisfy Hamilton's principle: they are stationary points of the classical action. The second variation (fluctuations) of the action around the stationary point signals whether the latter is or not a minimum and delivers the density in trajectory space around the points q(0) and q(1). This concept of density of paths is of great importance in semiclassical quantum theory, where it weights the contribution to the propagator from the single classical trajectories. In this paper, two algorithms based on the concepts of molecular dynamics simulation are introduced for computing the density of paths, also called van Vleck [Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928)] determinant. Examples for realistic systems are presented, together with a suggestion about possible applications in the field of rare events in physics and chemistry.

Journal Article↗

PubMed2005

The reaction path intrinsic reaction coordinate method and the Hamilton-Jacobi theory.

The definition and location of an intrinsic reaction coordinate path is of crucial importance in many areas of theoretical chemistry. Differential equations used to define the path hitherto are complemented in this study with a variational principle of Fermat type, as Fukui [Int. J. Quantum Chem., Quantum Chem. Symp. 15, 633 (1981)] reported in a more general form some time ago. This definition is more suitable for problems where initial and final points are given. The variational definition can naturally be recast into a Hamilton-Jacobi equation. The character of the variational solution is studied via the Weierstrass necessary and sufficient conditions. The characterization of the local minima character of the intrinsic reaction coordinate is proved. Such result leads to a numerical algorithm to find intrinsic reaction coordinate paths based on the successive minimizations of the Weierstrass E-function evaluated on a guess curve connecting the initial and final points of the desired path.

Algorithms↗

PubMed2005

Varying constants.

We review properties of theories for the variation of gravitation and fine structure 'constants'. We highlight some general features of the cosmological models that exist in these theories with reference to recent quasar data that are consistent with time variation in the fine structure constant since a redshift of 3.5. The behaviour of a simple class of varying-alpha cosmologies is outlined in the light of all the observational constraints.

Algorithms↗

PubMed2000

The atom-cavity microscope: single atoms bound in orbit by single photons

The motion of individual cesium atoms trapped inside an optical resonator is revealed with the atom-cavity microscope (ACM). A single atom moving within the resonator generates large variations in the transmission of a weak probe laser, which are recorded in real time. An inversion algorithm then allows individual atom trajectories to be reconstructed from the record of cavity transmission and reveals single atoms bound in orbit by the mechanical forces associated with single photons. In these initial experiments, the ACM yields 2-micrometer spatial resolution in a 10-microsecond time interval. Over the duration of the observation, the sensitivity is near the standard quantum limit for sensing the motion of a cesium atom.

Journal Article↗

PubMed2001

Twist-averaged boundary conditions in continuum quantum Monte Carlo algorithms.

We develop and test Quantum Monte Carlo algorithms that use a"twist" or a phase in the wave function for fermions in periodic boundary conditions. For metallic systems, averaging over the twist results in faster convergence to the thermodynamic limit than periodic boundary conditions for properties involving the kinetic energy and has the same computational complexity. We determine exponents for the rate of convergence to the thermodynamic limit for the components of the energy of coulomb systems. We show results with twist averaged variational Monte Carlo on free particles, the Stoner model and the electron gas using Hartree-Fock, Slater-Jastrow, and three-body and backflow wave function. We also discuss the use of twist averaging in the grand canonical ensemble, and numerical methods to accomplish the twist averaging.

Journal Article↗

PubMed2001

Electron spin resonance and electronic structure of vanadyl-porphyrin in heavy crude oils.

A study of vanadyl-porphyrin by electron spin resonance (ESR) was carried out looking for answers about the role that the central V=O ion plays when these kinds of molecules are present in heavy crude oils. The eigenvalues of the linear combination of atomic orbitals (LCAO) were obtained from the experimental values of g and parameters (ESR). The contributions to the molecular orbitals that describe the various energy levels of vanadyl ion were also obtained for the porphyrin species. The trends of the degree of covalent character of the metal-ligand bonds and the length of the vanadium-oxygen chemical bond are discussed. It is interesting to note that the Fermi contact term, K(eff), is essentially constant for all samples investigated, and it was found to be independent of the calculated electron delocalization (1 - delta(2)) and shows only little variation among the three different samples of oil. The orbital energies derived from our ESR study qualitatively agree with those predicted from MO theory for synthetic vanadyl-porphyrins.

Algorithms↗

PubMed2005

Thermal conductivities of molecular liquids by reverse nonequilibrium molecular dynamics.

The reverse nonequilibrium molecular dynamics method for thermal conductivities is adapted to the investigation of molecular fluids. The method generates a heat flux through the system by suitably exchanging velocities of particles located in different regions. From the resulting temperature gradient, the thermal conductivity is then calculated. Different variants of the algorithm and their combinations with other system parameters are tested: exchange of atomic velocities versus exchange of molecular center-of-mass velocities, different exchange frequencies, molecular models with bond constraints versus models with flexible bonds, united-atom versus all-atom models, and presence versus absence of a thermostat. To help establish the range of applicability, the algorithm is tested on different models of benzene, cyclohexane, water, and n-hexane. We find that the algorithm is robust and that the calculated thermal conductivities are insensitive to variations in its control parameters. The force field, in contrast, has a major influence on the value of the thermal conductivity. While calculated and experimental thermal conductivities fall into the same order of magnitude, in most cases the calculated values are systematically larger. United-atom force fields seem to do better than all-atom force fields, possibly because they remove high-frequency degrees of freedom from the simulation, which, in nature, are quantum-mechanical oscillators in their ground state and do not contribute to heat conduction.

Journal Article↗

PubMed2004

Bipolaron in different configuration of quantum confinement.

The authors used Landau-Pekar variational method to investigate a strong-coupling singlet optical bipolaron in different configuration of quantum confinement. Numerical and analytical results showed that when configuration changes from quantum dot and wire to well, confinement shows different effect on the formation of a bipolaron. In contrast to a bipolaron in a quantum dot or wire, the binding energy of a bipolaron in a quantum well increases with increasing confinement, indicating that confinement favors bipolaron formation in a quantum well.

Algorithms↗

PubMed2003

Stochastic gene expression as a many-body problem.

Gene expression has a stochastic component because of the single-molecule nature of the gene and the small number of copies of individual DNA-binding proteins in the cell. We show how the statistics of such systems can be mapped onto quantum many-body problems. The dynamics of a single gene switch resembles the spin-boson model of a two-site polaron or an electron transfer reaction. Networks of switches can be approximately described as quantum spin systems by using an appropriate variational principle. In this way, the concept of frustration for magnetic systems can be taken over into gene networks. The landscape of stable attractors depends on the degree and style of frustration, much as for neural networks. We show the number of attractors, which may represent cell types, is much smaller for appropriately designed weakly frustrated stochastic networks than for randomly connected networks.

Algorithms↗

PubMed2007

A method for quantitative analysis of spatially variable physiological processes across leaf surfaces.

Many physiological processes are spatially variable across leaf surfaces. While maps of photosynthesis, stomatal conductance, gene expression, water transport, and the production of reactive oxygen species (ROS) for individual leaves are readily obtained, analytical methods for quantifying spatial heterogeneity and combining information gathered from the same leaf but with different instruments are not widely used. We present a novel application of tools from the field of geographical imaging to the multivariate analysis of physiological images. Procedures for registration and resampling, cluster analysis, and classification provide a general framework for the analysis of spatially resolved physiological data. Two experiments were conducted to illustrate the utility of this approach. Quantitative analysis of images of chlorophyll fluorescence and the production of ROS following simultaneous exposure of soybean leaves to atmospheric O3 and soybean mosaic virus revealed that areas of the leaf where the operating quantum efficiency of PSII was depressed also experienced an accumulation of ROS. This correlation suggests a causal relationship between oxidative stress and inhibition of photosynthesis. Overlaying maps of leaf surface temperature and chlorophyll fluorescence following a photoinhibition treatment indicated that areas with low operating quantum efficiency of PSII also experienced reduced stomatal conductance (high temperature). While each of these experiments explored the covariance of two processes by overlaying independent images gathered with different instruments, the same procedures can be used to analyze the covariance of information from multiple images. The application of tools from geographic image analysis to physiological processes occurring over small spatial scales will help reveal the mechanisms generating spatial variation across leaves.

Algorithms↗

PubMed2006

A variational approach to the stochastic aspects of cellular signal transduction.

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kinetics problem is the enormous number of ordinary differential equations involved. In this work, we show how to achieve tremendous reduction in the dimensionality of specific reaction cascade dynamics by solving variationally an equivalent quantum field theoretic formulation of stochastic chemical kinetics. The present formulation avoids cumbersome commutator computations in the derivation of evolution equations, making the physical significance of the variational method more transparent. We propose novel time-dependent basis functions which work well over a wide range of rate parameters. We apply the new basis functions to describe stochastic signaling in several enzymatic cascades and compare the results so obtained with those from alternative solution techniques. The variational Ansatz gives probability distributions that agree well with the exact ones, even when fluctuations are large and discreteness and nonlinearity are important. A numerical implementation of our technique is many orders of magnitude more efficient computationally compared with the traditional Monte Carlo simulation algorithms or the Langevin simulations.

Cells↗

PubMed2006

Variational reduced-density-matrix theory applied to the potential energy surfaces of carbon monoxide in the presence of electric fields.

The variational optimization of the energy with respect to the two-electron reduced-density matrix (2-RDM), constrained by N-representability conditions, can determine the shape of molecular potential energy surfaces with useful accuracy. In this paper, we apply the 2-RDM method with a first-order optimization algorithm [Mazziotti, D. A. Phys. Rev. Lett. 2004, 93, 213001] to investigating the potential energy surfaces of carbon monoxide in the presence and absence of an electric field. Two beneficial characteristics of the 2-RDM method for computing potential energy surfaces include the following: (i) its ability to capture multireference effects without specifying any reference wave function or density matrix and (ii) its guarantee of a global energy minimum in the variational optimization. The 2-RDM method produces electronic ground-state energies with similar accuracy at equilibrium and nonequilibrium geometries in both the presence and the absence of the electric field. Computed dipole moments are similar in accuracy to the values from the computationally expensive configuration interaction with single, double, triple, and quadruple excitations. These surfaces have important applications in quantum molecular control theory.

Carbon Monoxide↗

PubMed2003

Solvent polarity and hydrogen-bonding effects on the nitrogen NMR shieldings of N-nitrosamines and DFT calculations of the shieldings of C-, N-, and O-nitroso systems.

High-precision nitrogen NMR shieldings, bulk susceptibility corrected, are reported for dimethyl-N-nitrosamine (I) and diethyl-N-nitrosamine (II) in a variety of solvents which represent a wide range of solvent properties from the point of view of polarity as well as hydrogen bond donor and acceptor strength. The observed range of solvent-induced nitrogen shielding variations of (I) and (II) is significant for the amino-type nitrogens, up to about 16 ppm, and originates essentially from the deshielding effect of the increasing polarity of solvent. On the other side, the nitroso nitrogen shieldings reveal an even stronger response to solvent effects, within about 20 ppm, but in this case the increasing polarity and hydrogen bond donor strength of solvent produce enhanced shielding. DFT quantum-mechanical calculations using the GIAO/B3PW91/6-311++G** approach and geometry optimizations employing the same basis set and hybrid density functionals show an excellent correlation with the experimental data on C-, N-, and O-nitroso moieties and reproduce not only major changes but also most of the subtle variations in the experimental nitrogen shieldings of the nitroso systems as a whole. A combination of the calculations involving the corresponding N and O-protonated species and the trends observed in the solvent-induced nitrogen shielding variations shows clearly that the prime acceptor site for hydrogen bonding is the nitroso oxygen atom.

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