Anharmonic properties of the vibrational quantum computer

We developed an efficient approach to study the coherent control of vibrational state-to-state transitions. The approximations employed in our model are valid in the regime of the low vibrational excitation specific to the vibrational quantum computer. Using this approach we explored how the vibrational properties of a two-qubit system affect the accuracy of subpicosecond quantum gates. The optimal control theory and numerical propagation of laser-driven vibrational wave packets were employed. The focus was on understanding the effect of the three anharmonicity parameters of the system. In the three-dimensional anharmonicity parameter space we identified several spots of high fidelity separated by low fidelity planar regions. The seemingly complicated picture is explained in terms of interferences between different state-to-state transitions. Very general analytic relationships between the anharmonicity parameters and the frequencies are derived to describe the observed features. Geometrically, these expressions represent planes in the three-dimensional anharmonicity parameter space. Results of this work should help to choose a suitable candidate molecule for the practical implementation of the vibrational two-qubit system.     

Quantum computing based on vibrational eigenstates: pulse area theorem analysis

In a recent paper [D. Babikov, J. Chem. Phys. 121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laser-pulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard two-level model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates.     

Regularity of low-lying quantum eigenstates in a classically mixing system

Low-lying quantum energy eigenstates of the classically mixing stadium system are shown to be highly regular and to be well described by an adiabatic separable Hamiltonian. The results clearly demonstrate quantum regularity in an energy regime of extreme classical chaos.     

Implementing quantum gates on oriented optical isomers

Optical enantiomers are proposed to encode molecular two-qubit information processing. Using sequences of pairs of nonresonant optimally polarized pulses, different schemes to implement quantum gates, and to prepare entangled states, are described. We discuss the role of the entanglement phase and the robustness of the pulse sequences which depend on the area theorem. Finally, possible scenarios to generalize the schemes to n-qubit systems are suggested.     

Ordering of fluoro-mesogens: a statistical approach based on quantum mechanics and computer simulation

Computational analysis of the molecular ordering of nematic p -phenylene-4-methoxy benzoyl 4-trifluoromethylbenzoate (FLUORO1) and smectic 4-propyloxyphenyl 4-(4-trifluoromethylbenzoyloxy) benzoate (FLUORO2) mesogens has been carried out with respect to translatory and orientational motions. The net atomic charge and atomic dipole components at each atomic centre of the molecule have been evaluated using the CNDO/2 method. Rayleigh-Schrodinger perturbation theory, along with the multicentred-multipole expansion method, has been employed to evaluate long range intermolecular interactions while a '6-exp' potential function has been assumed for short range interactions. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at the phase transition temperature using the Maxwell-Boltzmann formula. The flexibility of various configurations has been studied in terms of the variation of probability due to small departures from the most probable configuration. The results obtained enable the determination of the peculiarities of the molecular ordering, as well as the construction of models of the structures of FLUORO1 and FLUORO2 in different modes of interaction. The mesophase nature has been correlated with the parameters introduced in this paper.     

Best molecular multiple quantum bit for the diatomic molecular quantum computer using potassium nitride and calcium nitride through vibrational progression

In this article, based on the former accurate and precise ab initio calculation results for potassium nitride (KN) and calcium nitride (CaN), I revisit the possibilities and potentials of KN and CaN as the best candidate for molecular multiple quantum bit (MMQB) for the diatomic molecular quantum computer (DMQC), and would like to propose the two molecules as CPUs of the DMQC. Lowest lying four electronic states of CaN are energetically located within 1800 cm^?1. These four states form the good molecular electronic two quantum bits through the dipole and weak spin–orbit interactions. ³Π state of KN is calculated to lie above ground ³Σ^? state by 177 cm^?1. KN is a promising candidate for an electronic one quantum bit. When vibrational progression is considered to be accompanied by the electronic transition, CaN and KN are good candidates for larger MMQBs up to a thousand even in the single molecule because the concrete quantum state bearing the quantum bit is each molecular ro‐vibronic state, that is, the specific rotational state on each vibronic level. When CaN and KN work in assemblies as quantum bit, those assemblies become larger MMQBs, the number of which might reach the Avogadro number because the molecular spectra appearing in the molecular spectroscopy are the results from the observation by the photon‐exchange among intramolecular quantum states made up of 10¹⁵ to the Avogadro (6.02 × 10²³ mol^?1) number of molecules interacting with radiation. Even without the vibrational progression, in the case of the lowest two quantum bit of KN, which is a stable vibronic two quantum bit, a thousand of KN molecules provide a thousand of MMQBs. That is the same situation as that for CaN. Using KN and CaN as MMQBs (playing the triple roles of CPU, RAMs (memory), and storages) ultra‐fast “in core” quantum computation can be done. An application of the full‐CI quantum chemistry calculation results for the demonstration of the DMQC is discussed. I strongly hope that the MMQB will “oscillate” and that the DMQC will be realized in the near future for the welfare of human being and the further development of modern material civilization. © 2014 Wiley Periodicals, Inc.     

Exploring sequential quantum adiabatic switching across supersymmetric partners for finding the eigenstates of a system

We demonstrate that one can exhaustively determine the n‐bound eigenstates of a Hamiltonian H by constructing a sequence of supersymmetric (SUSY) partner Hamiltonians and invoking a time‐dependent quantum adiabatic switching algorithm for passage from the ground state of one to the other. The ground states of the initial pair H⁽⁰⁾ and H⁽¹⁾ are constructed by solving the Riccati equation for the superpotential ?⁽⁰⁾ for H⁽⁰⁾ and adiabatically switching from the ground state Ψ of H⁽⁰⁾ to the ground state Ψ of H⁽¹⁾. The charge operator Q is then used to recover the first excited state Ψ of H⁽⁰⁾. The procedure is repeated for the ground states of SUSY pairs H^{(n + 1)} and H^{(n + 2)}, and appropriate charge operators lead to the excited states Ψ of H⁽⁰⁾ with , thereby exhausting the full eigenspectrum of H⁽⁰⁾. The workability of the proposed method is shown with several well‐known examples. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Hydrogen adsorbed in a metal organic framework-5: coupled translation-rotation eigenstates from quantum five-dimensional calculations

We report rigorous quantum five-dimensional (5D) calculations of the coupled translation-rotation (T-R) eigenstates of a H(2) molecule adsorbed in metal organic framework-5 (MOF-5), a prototypical nanoporous material, which was treated as rigid. The anisotropic interactions between H(2) and MOF-5 were represented by the analytical 5D intermolecular potential energy surface (PES) used previously in the simulations of the thermodynamics of hydrogen sorption in this system [Belof et al., J. Phys. Chem. C 113, 9316 (2009)]. The global and local minima on this 5D PES correspond to all of the known binding sites of H(2) in MOF-5, three of which, α-, β-, and γ-sites are located on the inorganic cluster node of the framework, while two of them, the δ- and ε-sites, are on the phenylene link. In addition, 2D rotational PESs were calculated ab initio for each of these binding sites, keeping the center of mass of H(2) fixed at the respective equilibrium geometries; purely rotational energy levels of H(2) on these 2D PESs were computed by means of quantum 2D calculations. On the 5D PES, the three adjacent γ-sites lie just 1.1 meV above the minimum-energy α-site, and are separated from it by a very low barrier. These features allow extensive wave function delocalization of even the lowest translationally excited T-R eigenstates over the α- and γ-sites, presenting significant challenges for both the quantum bound-state calculations and the analysis of the results. Detailed comparison is made with the available experimental data.     

Coherent vibrational quantum beats as a probe of Langmuir-Blodgett monolayers

We combine frequency- and femtosecond time-domain measurements of vibrational coherences for spectroscopic characterization of surface monolayer films, utilizing 3-wave mixing as the surface-selective technique. Frequency-domain spectra in the CH-stretch region are obtained by infrared + visible sum frequency generation (SFG). Time-domain coherences are measured using SFG free induction decay (SFG-FID), where a 75 fs IR pulse excites several vibrational modes and a delayed 40 fs visible pulse probes the oscillating surface polarization. A unified framework based on optical Bloch equations is used to simultaneously analyze the time- and frequency-domain data. We compare molecular organization of monolayers in different two-dimensional phases. Highly ordered films transferred at high surface pressure are dominated by two transitions in the frequency domain, CH3 symmetric stretch (2875 cm(-1)) and CH3-Fermi resonance with bend overtone (2935 cm(-1)), and a coherent quantum beat in the time-domain at the difference frequency (approximately 540 fs period). At lower surface pressure, relative amplitudes change and additional transitions emerge (CH3 asymmetric stretch and CH2 modes), indicating changes in molecular orientation and onset of disorder. Information redundancy in the combined frequency- and time-domain data allows more accurate determination of the spectral parameters than purely frequency- or time-domain techniques.     

Refinement trajectory and determination of eigenstates by a wavelet based adaptive method

The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates is traced in terms of the resolution. An adaptive method is developed for identifying the fine structure localization regions, where further refinement of the wave function is necessary.     

Colorimetric logic gates based on aptamer-crosslinked hydrogels

We have developed a novel molecular logic gate system based on the incorporation of aptamer-crosslinked hydrogels. Modified gold nanoparticles are used as the output signal, which is visible to the naked eye. This system is designed for AND and OR operations using two chemicals as stimulus inputs.     

Converged vibrational energy levels and quantum mechanical vibrational partition function of ethane

The vibrational partition function of ethane is calculated in the temperature range of 200-600 K using well-converged energy levels that were calculated by vibrational configuration interaction, and the results are compared to the harmonic oscillator partition function. This provides the first test of the harmonic oscillator approximation for a molecule with more than five atoms. The absolute free energies computed by the harmonic oscillator approximation are in error by 0.59-0.62 kcal/mol over the 200-600 K temperature range.     

Laser control of vibrational excitation in carboxyhemoglobin: a quantum wave packet study

A coherent control algorithm is applied to obtain complex-shaped infrared laser pulses for the selective vibrational excitation of carbon monoxide at the active site of carbonmonoxyhemoglobin, modeled by the six-coordinated iron-porphyrin-imidazole-CO complex. The influence of the distal histidine is taken into account by an additional imidazole molecule. Density-functional theory is employed to calculate a multidimensional ground-state potential energy surface, and the vibrational dynamics as well as the laser interaction is described by quantum wave-packet calculations. At each instant in time, the optimal electric field is calculated and used for the subsequent quantum dynamics. The results presented show that the control scheme is applicable to complex systems and that it yields laser pulses with complex time-frequency structures, which, nevertheless, have a clear physical interpretation.     

Environment effects on the CO vibrational shifts in erbium complexes: a quantum chemical study

The stability of lanthanide complexes and the efficiency of the energy transfer process, which makes these molecules interesting materials for technological applications, are correlated to the chemical environment surrounding the metal ion. In particular the efficiency depends on the relative position of the antenna (the ligand moiety that acts as photon absorption center) and the lanthanide ion (the emitting center), while the stability of the complex is correlated to the strength of the coordination between the rare earth and the ligands. For these reasons, knowledge of the structural properties of the complex is an interesting task to achieve. Since a large number of ligand structures hold the carboxylate group (COO(-)), which is used as an anchor for binding the antennae to the lanthanide ion, in this work we will show how the vibrational shifts of this group, induced by the interactions between the carboxylate moiety and the metal center of the lanthanide complex, can be used for obtaining in a simple way information on the structure of the chemical environment surrounding the lanthanide ion.     

Photonic Boolean logic gates based on DNA aptamers

We designed a pair of DNA-based logic gates that sense single-stranded DNAs and aptamer ligands to produce fluorescence outputs according to Boolean logic functions AND and OR.     

Molecular logic gates based on 2-tyrylquinoline derivatives

Various logical operations can be performed by molecular logic gates (MLG) based on 2-styrylquinoline derivatives using irradiation with light and protonation as input signals and absorbance (optical density) as output signal. The MLG operation type (“INH”, “OR”, “AND”) depends on the observation wavelength.     

Molecular ordering of a cyano compound at a displacive transition temperature: a statistical analysis based on quantum mechanics and computer simulations

A statistical analysis has been carried out to determine the configurational preference of a pair of 4-cyanophenyl 4-n-pentylbenzoate (CPPB) molecules with respect to translatory and orientational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. Configurational energy has been computed using the Rayleigh—Schodinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at the phase transition temperature using the Maxwell—Boltzmann formula. An attempt has been made to identify the most probable configuration at the phase transition temperature. Further, the flexibility of various configurations has been studied in terms of variation of probability due to small departures from the most probable configuration. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements of the molecular pair have been considered. The results are discussed in the light of experimental as well as theoretical observations. The nature of the mesophase has been correlated with the parameter introduced in this paper.