Ab initio study of optimal control of ammonia molecular vibrational wavepackets: Towards molecular quantum computing

Optimal control theory is applied to a molecular vibrational system in light of its possible application to quantum computing (QC). We present the numerical results of an ammonia molecular vibrational model system with two modes: a bending mode and an asymmetric stretching mode. We demonstrate logic gates fundamental to QC algorithms, namely Hadamard and controlled-NOT gates. Our results show that averages of population transfers at each gate are above 93% high fidelity. A mode that has a double-well structured potential is found to have many transfer pathways, which facilitates obtaining optimal laser pulses.     

Computational investigation and experimental considerations for the classical implementation of a full adder on SO2 by optical pump-probe schemes

Following the scheme recently proposed by Remacle and Levine [Phys. Rev. A 73, 033820 (2006)], we investigate the concrete implementation of a classical full adder on two electronic states (X 1A1 and C 1B2) of the SO2 molecule by optical pump-probe laser pulses using intuitive and counterintuitive (stimulated Raman adiabatic passage) excitation schemes. The resources needed for providing the inputs and reading out are discussed, as well as the conditions for achieving robustness in both the intuitive and counterintuitive pump-dump sequences. The fidelity of the scheme is analyzed with respect to experimental noise and two kinds of perturbations: The coupling to the neighboring rovibrational states and a finite rotational temperature that leads to a mixture for the initial state. It is shown that the logic processing of a full addition cycle can be realistically experimentally implemented on a picosecond time scale while the readout takes a few nanoseconds.     

Quantum optimal control for the full ensemble of randomly oriented molecules having different field-free Hamiltonians

We have presented the optimal control theory formulation to calculate optimal fields that can control the full ensemble of randomly oriented molecules having different field-free Hamiltonians. The theory is applied to the fifty-fifty mixture of randomly oriented (133)CsI and (135)CsI isotopomers and an optimal field is sought to achieve isotope-selective vibrational excitations with high efficiency. Rotational motion is frozen and two total times (T's) of electric field duration, 460,000 and 920,000 a.u. (11.1 and 22.2 ps), are chosen in the present calculation. As a result, the final yields for T = 460,000 and 920,000 a.u. are calculated to be 0.706 and 0.815, respectively. The relatively high final yield obtained for T = 920,000 a.u. strongly suggests that a single laser pulse can control the full ensemble of randomly oriented non-identical molecules. The result is quite encouraging in terms of the application to isotope-separation processes.     

Vibrational molecular quantum computing: basis set independence and theoretical realization of the Deutsch-Jozsa algorithm

The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.     

Quantum optimal control: Hessian analysis of the control landscape

Seeking an effective quantum control entails searching over a landscape defined as the objective as a functional of the control field. This paper considers the problem of driving a state-to-state transition in a finite level quantum system, and analyzes the local topology of the landscape of the final transition probability in terms of the variables specifying the control field. Numerical calculation of the eigenvalues of the Hessian of the transition probability with respect to the control field variables reveals systematic structure in the spectra reflecting the existence of a generic and simple control landscape topology. An illustration shows that the number of nonzero Hessian eigenvalues is determined by the number of quantum states in the system. The Hessian eigenvectors associated with its nonzero eigenvalues are shown to give insight into the cooperative roles of the control variables. The practical consequences of these findings for quantum control are discussed.     

Isotope selective photoionization of NaK by optimal control: theory and experiment

We present a joint theoretical and experimental study of the maximization of the isotopomer ratio (23)Na(39)K(23)Na(41)K using tailored phase-only as well as amplitude and phase modulated femtosecond laser fields obtained in the framework of optimal control theory and closed loop learning (CLL) technique. A good agreement between theoretically and experimentally optimized pulse shapes is achieved which allows to assign the optimized processes directly to the pulse shapes obtained by the experimental isotopomer selective CLL approach. By analyzing the dynamics induced by the optimized pulses we show that the mechanism involving the dephasing of the wave packets between the isotopomers (23)Na (39)K and (23)Na (41)K on the first excited state is responsible for high isotope selective ionization. Amplitude and phase modulated pulses, moreover, allow to establish the connection between the spectral components of the pulse and corresponding occupied vibronic states. It will be also shown that the leading features of the theoretically shaped pulses are independent from the initial conditions. Since the underlying processes can be assigned to the individual features of the shaped pulses, we show that optimal control can be used as a tool for analysis.     

Understanding optimal control results by reducing the complexity

Deciphering control mechanisms from control pulse structures found in closed-loop learning experiments is often complicated due to the complexity of the pulse structure. Simplification of pulse forms is demonstrated by systematically reducing the complexity of the search space, applied on the model-like multi-photon ionization of NaK. Reducing the pulse complexity leads to the exclusion of participating excited states, thereby restricting the involved pathways. The phase function is parameterized by a sinusoidal spectral phase modulation, whose parameters are investigated with respect to the yield and the obtained optimal field. By progressively reducing the number of parameters and thereby the complexity of the phase modulation, control pulses are generated which are more and more reduced to the molecule’s primary dynamical properties. This enables to find optimized control pulses that can be subject to a simple intuitive interpretation.     

Improving solid-state NMR dipolar recoupling by optimal control

We present the first solid-state NMR experiments developed using optimal control theory. Taking heteronuclear dipolar recoupling in magic-angle-spinning NMR as an example, it proves possible to significantly improve the efficiency of the experiments while introducing robustness toward instrumental imperfections such as radio frequency inhomogeneity. The improvements are demonstrated by numerical simulations as well as practical experiments on a 13Calpha,15N-labeled powder of glycine. The experiments demonstrate a gain of 53% in the efficiency for 15N to 13Calpha coherence transfer relative to the typically double-cross-polarization experiments.     

Vibrational spectra of methane clathrate hydrates from molecular dynamics simulation

Molecular dynamics simulations were performed on methane clathrate hydrates at ambient conditions. Thermal expansion results over the temperature range 60-300 K show that the unit cell volume increases with temperature in agreement with experiment. Power spectra were obtained at 273 K from velocity autocorrelation functions for selected atoms, and normal modes were assigned. The spectra were further classified according to individual atom types, allowing the assignment of contributions from methane molecules located in small and large cages within the structure I unit cell. The symmetric C-H stretch of methane in the small cages occurs at a higher frequency than for methane located in the large cages, with a peak separation of 14 cm(-1). Additionally, we determined that the symmetric C-H stretch in methane gas occurs at the same frequency as methane in the large cages. Results of molecular dynamics simulations indicate the use of power spectra obtained from the velocity autocorrelation function is a reliable method to investigate the vibrational behavior of guest molecules in clathrate hydrates.     

Toward a robust and general molecular simulation method for computing solid-liquid coexistence

A rigorous and generally applicable method for computing solid-liquid coexistence is presented. The method overcomes some of the technical difficulties associated with other solid-liquid simulation procedures and can be implemented within either a molecular dynamics or Monte Carlo framework. The method consists of three steps: First, relative Gibbs free energy curves are created for the solid and liquid phases using histogram reweighting. Next, the free energy difference between the solid and liquid phases is evaluated at a single state point by integrating along a pseudosupercritical transformation path that connects the two phases. Using this result, the solid and liquid free energy curves are referenced to a common point, allowing a single coexistence point to be determined. Finally, Gibbs-Duhem integration is used to determine the full coexistence curve. To evaluate its utility, this method is applied to the Lennard-Jones and NaCl systems. Results for solid-liquid coexistence agree with previous calculations for these systems. In addition, it is shown that the NaCl model does not correctly describe solid-liquid coexistence at high pressures. An analysis of the accuracy of the method indicates that the results are most sensitive to the transformation free energy calculation.     

Vibrational spectra of 2-biphenylmethanol. Spectrum simulation and molecular structure

The vibrational spectra of a solid crystalline sample of 2-biphenylmethanol have been measured at room temperature. The IR absorption spectra were recorded in the range 400 cm^–1–3600 cm^–1; Raman spectra were measured in the range 10 cm^–1–1640 cm^–1. The direct mechanical and optoelectronic problems were solved using the fragment method realized as Lev-100 software; the intensity distribution in the IR spectrum of 2-biphenylmethanol was obtained by the same method. The experimental Raman and IR absorption spectra were interpreted by analyzing the calculated data on the frequencies and forms of normal vibrations and their intensities in the IR spectra. IR absorption spectra were simulated for several models of 2-biphenylmethanol conformers that differ in the mutual orientation of fragments. Based on the results of simulation and comparison of the calculated and experimental spectra of conformers we suggested a model for the conformer realized in the solid phase under normal conditions.Original Russian Text Copyright © 2004 by L. M. Babkov, J. Baran, N. A. Davydova, J. I. Kukielskii, and S. V. TrukhachevTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 624–631, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Effective Hamiltonians by optimal control: solid-state NMR double-quantum planar and isotropic dipolar recoupling

We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.     

Observation-assisted optimal control of quantum dynamics

This paper explores the utility of instantaneous and continuous observations in the optimal control of quantum dynamics. Simulations of the processes are performed on several multilevel quantum systems with the goal of population transfer. Optimal control fields are shown to be capable of cooperating or fighting with observations to achieve a good yield, and the nature of the observations may be optimized to more effectively control the quantum dynamics. Quantum observations also can break dynamical symmetries to increase the controllability of a quantum system. The quantum Zeno and anti-Zeno effects induced by observations are the key operating principles in these processes. The results indicate that quantum observations can be effective tools in the control of quantum dynamics.     

Drug search for leishmaniasis: a virtual screening approach by grid computing

The trypanosomatid protozoa Leishmania is endemic in ~100 countries, with infections causing ~2 million new cases of leishmaniasis annually. Disease symptoms can include severe skin and mucosal ulcers, fever, anemia, splenomegaly, and death. Unfortunately, therapeutics approved to treat leishmaniasis are associated with potentially severe side effects, including death. Furthermore, drug-resistant Leishmania parasites have developed in most endemic countries. To address an urgent need for new, safe and inexpensive anti-leishmanial drugs, we utilized the IBM World Community Grid to complete computer-based drug discovery screens (Drug Search for Leishmaniasis) using unique leishmanial proteins and a database of 600,000 drug-like small molecules. Protein structures from different Leishmania species were selected for molecular dynamics (MD) simulations, and a series of conformational “snapshots” were chosen from each MD trajectory to simulate the protein’s flexibility. A Relaxed Complex Scheme methodology was used to screen ~2000 MD conformations against the small molecule database, producing >1 billion protein-ligand structures. For each protein target, a binding spectrum was calculated to identify compounds predicted to bind with highest average affinity to all protein conformations. Significantly, four different Leishmania protein targets were predicted to strongly bind small molecules, with the strongest binding interactions predicted to occur for dihydroorotate dehydrogenase (LmDHODH; PDB:3MJY). A number of predicted tight-binding LmDHODH inhibitors were tested in vitro and potent selective inhibitors of Leishmania panamensis were identified. These promising small molecules are suitable for further development using iterative structure-based optimization and in vitro/in vivo validation assays.     

Vibrational coupled cluster response theory: a general implementation

The calculation of vibrational contributions to molecular properties using vibrational coupled cluster (VCC) response theory is discussed. General expressions are given for expectation values, linear response functions, and transition moments. It is shown how these expressions can be evaluated for arbitrary levels of excitation in the wave function parameterization as well as for arbitrary coupling levels in the potential and property surfaces. The convergence of the method is assessed by benchmark calculations on formaldehyde. Furthermore, excitation energies and infrared intensities are calculated for the fundamental vibrations of furan using VCC limited to up to two-mode and up to three-mode excitations, VCC[2] and VCC[3], as well as VCC with full two-mode and approximate three-mode couplings, VCC[2pt3].     

Vibrational corrections to magneto-optical rotation: a computational study

Vibrational corrections to the Verdet constants of nine molecules (H2, N2, CO, H2O, CH4, benzene, toluene, p-xylene, and o-xylene) were calculated with pure density functional theory (DFT), hybrid DFT, and an approximate coupled-cluster theory. Comparisons are made for the accuracy of the vibrational averages among different methods and with respect to experimental data where available. It is found that vibrational corrections to magneto-optical rotation can be as large as 10% of the equilibrium value. Hybrid DFT with the B3LYP hybrid functional offers reasonable accuracy at a relatively inexpensive computational cost for accurate calculations of vibrationally averaged Verdet constants.     

Vibrational spectral simulation for peptides of mixed secondary structure: method comparisons with the Trpzip model hairpin

Infrared absorption and vibrational circular dichroism (IR and VCD) spectra of model fragments of TrpZip-style beta-hairpin structures are simulated using density functional theory (DFT) methods to estimate the influence of fragment size, end effects, conformational irregularities, peptide side chains, and solvent. Different fragmentation schemes, computing the strands and turn segments separately, were tested by varying the sizes of each and their respective overlaps. For suitably overlapping fragments, atomic property tensors were found to be reliably transferable, as tested by their ability to generate simulated spectra in good agreement with results from ab initio DFT computations for the entire peptide. This fragment approach significantly reduces computational times and opens up a wider range of systems that can be studied with a DFT-based approach as compared to previous methods based on uniform repeating sequences. However, vacuum calculations do not adequately represent the frequency dispersion of solvated molecules, and thus, some alternate strategies for solvation correction are explored for improving the simulation accuracy. Unlike for regular periodic secondary structure, the solvent significantly impacts the spectral shapes of hairpins, due to the different degrees of hydration of individual amide groups, which can be exposed to or shielded from water due to external vs internal hydrogen bonding. This is amplified by the shielding of selected amides from the solvent due to bulky side chains. The peptide plus solvent was structurally modeled with molecular dynamics methods, and then an electrostatic field-based parametrization correction was added to the force field and intensity tensors to compensate for the solvent dipolar field. The effect of the shielding and subsequent reordering of modes has a larger impact on VCD than IR band shapes.     

Adaptive optimal control of fed-batch alcoholic fermentation

An adaptive control scheme is developed for the optimization of a fed-batch ethanol production process. The fermentation process is modeled by an hybrid neural model combining mass balance equations and neural networks, used to represent the kinetic rates. The networks used, the functional link networks (FLN), allow the linear estimation of their parameters; this enables the re-estimation of the parameters at each sampling time, and thus the development of an adaptive optimal control scheme.