Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco et al. [Phys. Rev. Lett. 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Intra-molecular hydrogen bonding with organic fluorine in the solution state: Deriving evidence by a two dimensional NMR experiment

The direct evidence for the existence of intra-molecular C-F center dot center dot center dot H-N hydrogen bond in organofluorine molecules, in the liquid state, is derived using NMR spectroscopy by the detection of long range interactions among fluorine, nitrogen and hydrogen atoms. The present study reports the determination of the relative signs and magnitudes of through space and through bond couplings to draw unambiguous evidence on the existence of weak molecular interactions involving organic fluorine. It is a simple, easy to implement, N-15 natural abundant two dimensional heteronuclear N-15-H-1 double quantum-single quantum correlation experiment. The existence of intra-molecular hydrogen bond is conclusively established in the investigated molecules. (C) 2011 Elsevier B.V. All rights reserved.

Combining adiabatic and Hartmann-Hahn cross-polarization for sensitivity enhancement in solid state separated local field 2D-NMR experiments of partially ordered systems

In this Letter, we examine magnetization in double- and zero-quantum reservoirs of an ensemble of spin-1/2 nuclei and describe their role in determining the sensitivity of a class of separated local field NMR experiments based on Hartmann-Hahn cross-polarization. We observe that for the liquid crystal system studied, a large dilute spin-polarization, obtained initially by the use of adiabatic cross-polarization, can enhance the sensitivity of the above experiment. The signal enhancement factors, however, are found to vary and depend on the local dynamics. The experimental results have been utilized to obtain the local order-parameters of the system. (C) 2012 Elsevier B. V. All rights reserved.

Probing acid-amide intermolecular hydrogen bonding by NMR spectroscopy and DFT calculations

Benzene carboxylic acids and Benzamide act as their self-complement in molecular recognition to form inter-molecular hydrogen bonded dimers between amide and carboxylic acid groups, which have been investigated by H-1, C-13 and N-15 NMR spectroscopy. Extensive NMR studies using diffusion ordered spectroscopy (DOSY), variable temperature 1D, 2D NMR, established the formation of heterodimers of benzamide with benzoic acid, salicylic acid and phenyl acetic acid in deuterated chloroform solution. Association constants for the complex formation in the solution state have been determined. The results are ascertained by X-ray diffraction in the solid state. Intermolecular interactions in solution and in solid state were found to be similar. The structural parameters obtained by X-ray diffraction studies are compared with those obtained by DFT calculations. (C) 2012 Elsevier B.V. All rights reserved.

ENTANGLEMENT IN A 3-SPIN HEISENBERG-XY CHAIN WITH NEAREST-NEIGHBOR INTERACTIONS, SIMULATED IN AN NMR QUANTUM SIMULATOR

The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. Phys. Rev. A 72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.

Evolution of quantum discord and its stability in two-qubit NMR systems

We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.

Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm-a global-optimization method inspired by nature's evolutionary process-for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses. © 2012 American Physical Society.

Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm-a global-optimization method inspired by nature's evolutionary process-for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses.

High resolution methyl selective C-13-NMR of proteins in solution and solid state

New C-13-detected NMR experiments have been devised for molecules in solution and solid state, which provide chemical shift correlations of methyl groups with high resolution, selectivity and sensitivity. The experiments achieve selective methyl detection by exploiting the one bond J-coupling between the C-13-methyl nucleus and its directly attached C-13 spin in a molecule. In proteins such correlations edit the C-13-resonances of different methyl containing residues into distinct spectral regions yielding a high resolution spectrum. This has a range of applications as exemplified for different systems such as large proteins, intrinsically disordered polypeptides and proteins with a paramagnetic centre.

GFT projection NMR for efficient H-1/C-13 sugar spin system identification in nucleic acids

A newly implemented G-matrix Fourier transform (GFT) (4,3)D HC(C)CH experiment is presented in conjunction with (4,3)D HCCH to efficiently identify H-1/C-13 sugar spin systems in C-13 labeled nucleic acids. This experiment enables rapid collection of highly resolved relay 4D HC(C)CH spectral information, that is, shift correlations of C-13-H-1 groups separated by two carbon bonds. For RNA, (4,3)D HC(C)CH takes advantage of the comparably favorable 1'- and 3'-CH signal dispersion for complete spin system identification including 5'-CH. The (4,3)D HC(C)CH/HCCH based strategy is exemplified for the 30-nucleotide 3'-untranslated region of the pre-mRNA of human U1A protein.

Crowding, molecular volume and plasticity: An assessment involving crystallography, NMR and simulations

The discrepancy between the X-ray and NMR structures of Mycobacterium tuberculosis peptidyl-tRNA hydrolase in relation to the functionally important plasticity of the molecule led to molecular dynamics simulations. The X-ray and the NMR studies along with the simulations indicated an inverse correlation between crowding and molecular volume. A detailed comparison of proteins for which X-ray and the NMR structures appears to confirm this correlation. In consonance with the reported results of the investigations in cellular compartments and aqueous solution, the comparison indicates that the crowding results in compaction of the molecule as well as change in its shape, which could specifically involve regions of the molecule important in function. Crowding could thus influence the action of proteins through modulation of the functionally important plasticity of the molecule. Selvaraj M, Ahmad R, Varshney U and Vijayan M 2012 Crowding, molecular volume and plasticity: An assessment involving crystallography, NMR and simulations. J. Biosci. 37 953-963] DOI 10.1007/s12038-012-9276-5

NMR Analysis of Cross Strand Aromatic Interactions in an 8 Residue Hairpin and a 14 Residue Three Stranded beta-Sheet Peptide

Cross strand aromatic interactions between a facing pair of phenylalanine residues in antiparallel beta-sheet structures have been probed using two structurally defined model peptides. The octapeptide Boc-(LFVPPLFV)-P-D-P-L-OMe (peptide 1) favors the beta-hairpin conformation nucleated by the type II' beta-turn formed by the (D)Pro-(L)Pro segment, placing Phe2 and Phe7 side chains in proximity. Two centrally positioned (D)Pro-(L)Pro segments facilitate the three stranded beta-sheet formation in the 14 residue peptide Boc-LFV(D)P(L)PLFVA(D)P(L)PLFV-OMe (peptide 2) in which the Phe2/Phe7 orientations are similar to that in the octapeptide. The anticipated folded conformations of peptides 1 and 2 are established by the delineation of intramolecularly hydrogen bonded NH groups and by the observation of specific cross strand NOEs. The observation of ring current shifted aromatic protons is a diagnostic of close approach of the Phe2 and Phe7 side chains. Specific assignment of aromatic proton resonances using HSQC and HSQC-TOCSY methods allow an analysis of interproton NOEs between the spatially proximate aromatic rings. This approach facilitates specific assignments in systems containing multiple aromatic rings in spectra at natural abundance. Evidence is presented for a dynamic process which invokes a correlated conformational change about the C-alpha-C-beta(chi(1)) bond for the pair of interacting Phe residues. NMR results suggest that aromatic ring orientations observed in crystals are maintained in solution. Anomalous temperature dependence of ring current induced proton chemical shifts suggests that solvophobic effects may facilitate aromatic ring clustering in apolar solvents.

Chiral discrimination and the measurement of enantiomeric excess from a severely overcrowded NMR spectrum

NMR spectroscopic chiral visualization, unambiguous assignment of peaks pertaining to R and S enantiomers and the subsequent measurement of enantiomeric composition demands a highly resolved spectrum. The method fails when the spectrum is severely overcrowded or highly complex, thereby hampering the determination of enantiomeric excess. In order to circumvent such problems we propose the utility of pure shift spectrum obtained by resolving the chemical shift and coupling information in two orthogonal dimensions. The skew projected spectrum yields singlet's at the respective chemical shift positions, permitting the unravelling of the superimposed spectral transitions for each enantiomer and measurement of enantiomeric composition. (C) 2012 Elsevier B. V. All rights reserved.

NMR studies of preimplantation embryo metabolism in human assisted reproductive techniques: a new biomarker for assessment of embryo implantation potential

There has been growing interest in understanding energy metabolism in human embryos generated using assisted reproductive techniques (ART) for improving the overall success rate of the method. Using NMR spectroscopy as a noninvasive tool, we studied human embryo metabolism to identify specific biomarkers to assess the quality of embryos for their implantation potential. The study was based on estimation of pyruvate, lactate and alanine levels in the growth medium, ISM1, used in the culture of embryos. An NMR study involving 127 embryos from 48 couples revealed that embryos transferred on Day 3 (after 72 h in vitro culture) with successful implantation (pregnancy) exhibited significantly (p < 10(-5)) lower pyruvate/alanine ratios compared to those that failed to implant. Lactate levels in media were similar for all embryos. This implies that in addition to lactate production, successfully implanted embryos use pyruvate to produce alanine and other cellular functions. While pyruvate and alanine individually have been used as biomarkers, the present study highlights the potential of combining them to provide a single parameter that correlates strongly with implantation potential. Copyright (C) 2012 John Wiley & Sons, Ltd.

Engagement of CF3 Group in N-H center dot center dot center dot F-C Hydrogen Bond in the Solution State: NMR Spectroscopy and MD Simulation Studies

Unambiguous evidence for the engagement of CF3 group in N-H center dot center dot center dot F-C hydrogen bond in a low polarity solvent, the first observation of its kind, is reported. The presence of such weak molecular interactions in the solution state is convincingly established by one and two-dimensional H-1, F-19, and natural abundant N-15 NMR spectroscopic studies. The strong and direct evidence is derived by the observation of through-space couplings, such as, (1h)J(FH), (1h)J(FN), and (2h)J(FF), where the spin polarization is transmitted through hydrogen bond. In an interesting example of a molecule containing two CF3 groups getting simultaneously involved in hydrogen bond, where hydrogen bond mediated couplings are not reflected in the NMR spectrum, F-19-F-19 NOESY experiment yielded confirmatory evidence. Significant deviations in the strengths of (1)J(NH), variable temperature, and the solvent induced perturbations yielded additional support. The NMR results are corroborated by both DFT calculations and MD simulations, where the quantitative information on different ways of involvement of fluorine in two and three centered hydrogen bonds, their percentage of occurrences, and geometries have been obtained. The hydrogen bond interaction energies have also been calculated.