A Stochastic Liouville Equation Approach for the Effect of Noise in Quantum Computations

We propose a model based on a generalized effective Hamiltonian for studying the effect of noise in quantum computations. The system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. Treating these fluctuations as Gaussian Markov processes with zero mean and delta function correlation times, we derive an exact equation of motion describing the dissipative dynamics for a system of n qubits. We then apply this model to study the effect of noise on the quantum teleportation and a generic quantum controlled-NOT (CNOT) gate. For the quantum CNOT gate, we study the effect of noise on a set of one- and two-qubit quantum gates, and show that the results can be assembled together to investigate the quality of a quantum CNOT gate operation. We compute the averaged gate fidelity and gate purity for the quantum CNOT gate, and investigate phase, bit-flip, and flip-flop errors during the CNOT gate operation. The effects of direct inter-qubit coupling and fluctuations on the control fields are also studied. We discuss the limitations and possible extensions of this model. In sum, we demonstrate a simple model that enables us to investigate the effect of noise in arbitrary quantum circuits under realistic device conditions.Comment: 36 pages, 6 figures; to be submitted to Phys. Rev.

Information decomposition of symbolic sequences

We developed a non-parametric method of Information Decomposition (ID) of a content of any symbolical sequence. The method is based on the calculation of Shannon mutual information between analyzed and artificial symbolical sequences, and allows the revealing of latent periodicity in any symbolical sequence. We show the stability of the ID method in the case of a large number of random letter changes in an analyzed symbolic sequence. We demonstrate the possibilities of the method, analyzing both poems, and DNA and protein sequences. In DNA and protein sequences we show the existence of many DNA and amino acid sequences with different types and lengths of latent periodicity. The possible origin of latent periodicity for different symbolical sequences is discussed.Comment: 18 pages, 8 figure

Nonequilibrium generalization of F\"{o}rster-Dexter theory for excitation energy transfer

F\"{o}rster-Dexter theory for excitation energy transfer is generalized for the account of short time nonequilibrium kinetics due to the nonstationary bath relaxation. The final rate expression is presented as a spectral overlap between the time dependent stimulated emission and the stationary absorption profiles, which allows experimental determination of the time dependent rate. For a harmonic oscillator bath model, an explicit rate expression is derived and model calculations are performed in order to examine the dependence of the nonequilibrium kinetics on the excitation-bath coupling strength and the temperature. Relevance of the present theory with recent experimental findings and possible future theoretical directions are discussed.Comment: published in {\it Chemical Physics} (special issue on Photoprocesses in Multichromophoric Molecular Assemblies

Vibrational analysis of peptides, polypeptides and proteins

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73245/1/j.1399-3011.1984.tb03168.x.pd

Multi-scale sequence correlations increase proteome structural disorder and promiscuity

Numerous experiments demonstrate a high level of promiscuity and structural disorder in organismal proteomes. Here we ask the question what makes a protein promiscuous, i.e., prone to non-specific interactions, and structurally disordered. We predict that multi-scale correlations of amino acid positions within protein sequences statistically enhance the propensity for promiscuous intra- and inter-protein binding. We show that sequence correlations between amino acids of the same type are statistically enhanced in structurally disordered proteins and in hubs of organismal proteomes. We also show that structurally disordered proteins possess a significantly higher degree of sequence order than structurally ordered proteins. We develop an analytical theory for this effect and predict the robustness of our conclusions with respect to the amino acid composition and the form of the microscopic potential between the interacting sequences. Our findings have implications for understanding molecular mechanisms of protein aggregation diseases induced by the extension of sequence repeats

Learning about protein folding via potential functions

Over the last few years we have developed an empirical potential function that solves the protein structure recognition problem : given the sequence for an n -residue globular protein and a collection of plausible protein conformations, including the native conformation for that sequence, identify the correct, native conformation. Having determined this potential on the basis of only some 6500 native/nonnative pairs of structures for 58 proteins, we find it recognizes the native conformation for essentially all compact, soluble, globular proteins having known native conformations in comparisons with 10 4 to 10 6 reasonable alternative conformations apiece. In this sense, the potential encodes nearly all the essential features of globular protein conformational preference. In addition it “knows” about many additional factors in protein folding, such as the stabilization of multimeric proteins, quaternary structure, the role of disulfide bridges and ligands, pro proteins vs. processed proteins, and minimal strand lengths in globular proteins. Comparisons are made with other sorts of protein folding problems, and applications in protein conformational determination and prediction are discussed. © 1994 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38520/1/340200206_ftp.pd

SNOSite: Exploiting Maximal Dependence Decomposition to Identify Cysteine S-Nitrosylation with Substrate Site Specificity

S-nitrosylation, the covalent attachment of a nitric oxide to (NO) the sulfur atom of cysteine, is a selective and reversible protein post-translational modification (PTM) that regulates protein activity, localization, and stability. Despite its implication in the regulation of protein functions and cell signaling, the substrate specificity of cysteine S-nitrosylation remains unknown. Based on a total of 586 experimentally identified S-nitrosylation sites from SNAP/L-cysteine-stimulated mouse endothelial cells, this work presents an informatics investigation on S-nitrosylation sites including structural factors such as the flanking amino acids composition, the accessible surface area (ASA) and physicochemical properties, i.e. positive charge and side chain interaction parameter. Due to the difficulty to obtain the conserved motifs by conventional motif analysis, maximal dependence decomposition (MDD) has been applied to obtain statistically significant conserved motifs. Support vector machine (SVM) is applied to generate predictive model for each MDD-clustered motif. According to five-fold cross-validation, the MDD-clustered SVMs could achieve an accuracy of 0.902, and provides a promising performance in an independent test set. The effectiveness of the model was demonstrated on the correct identification of previously reported S-nitrosylation sites of Bos taurus dimethylarginine dimethylaminohydrolase 1 (DDAH1) and human hemoglobin subunit beta (HBB). Finally, the MDD-clustered model was adopted to construct an effective web-based tool, named SNOSite (http://csb.cse.yzu.edu.tw/SNOSite/), for identifying S-nitrosylation sites on the uncharacterized protein sequences