All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure

A Note on the correspondence between Qubit Quantum Operations and Special Relativity

We exploit a well-known isomorphism between complex hermitian $2\times 2$ matrices and $\mathbb{R}^4$, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in $\mathbb{E}^{1,3}$, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences.Comment: 6 pages, revtex, v3: revised discussio

Subsystem Pseudo-pure States

A critical step in experimental quantum information processing (QIP) is to implement control of quantum systems protected against decoherence via informational encodings, such as quantum error correcting codes, noiseless subsystems and decoherence free subspaces. These encodings lead to the promise of fault tolerant QIP, but they come at the expense of resource overheads. Part of the challenge in studying control over multiple logical qubits, is that QIP test-beds have not had sufficient resources to analyze encodings beyond the simplest ones. The most relevant resources are the number of available qubits and the cost to initialize and control them. Here we demonstrate an encoding of logical information that permits the control over multiple logical qubits without full initialization, an issue that is particularly challenging in liquid state NMR. The method of subsystem pseudo-pure state will allow the study of decoherence control schemes on up to 6 logical qubits using liquid state NMR implementations.Comment: 9 pages, 1 Figur

Principles of Control for Decoherence-Free Subsystems

Decoherence-Free Subsystems (DFS) are a powerful means of protecting quantum information against noise with known symmetry properties. Although Hamiltonians theoretically exist that can implement a universal set of logic gates on DFS encoded qubits without ever leaving the protected subsystem, the natural Hamiltonians that are available in specific implementations do not necessarily have this property. Here we describe some of the principles that can be used in such cases to operate on encoded qubits without losing the protection offered by the DFS. In particular, we show how dynamical decoupling can be used to control decoherence during the unavoidable excursions outside of the DFS. By means of cumulant expansions, we show how the fidelity of quantum gates implemented by this method on a simple two-physical-qubit DFS depends on the correlation time of the noise responsible for decoherence. We further show by means of numerical simulations how our previously introduced "strongly modulating pulses" for NMR quantum information processing can permit high-fidelity operations on multiple DFS encoded qubits in practice, provided that the rate at which the system can be modulated is fast compared to the correlation time of the noise. The principles thereby illustrated are expected to be broadly applicable to many implementations of quantum information processors based on DFS encoded qubits.Comment: 12 pages, 7 figure

Experimental Implementation of Logical Bell State Encoding

Liquid phase NMR is a general purpose test-bed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherence free subspaces that protect the quantum information from fully correlated dephasing.Comment: 9 Pages, 5 Figure

Quantum Process Tomography of the Quantum Fourier Transform

The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently-developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive - although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors during the quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cummulative effect of small errors in the single qubit gates.Comment: 26 pages, 17 figures, four tables; in press, Journal of Chemical Physic

A Fast, Memory-Efficient Alpha-Tree Algorithm using Flooding and Tree Size Estimation

The alpha-tree represents an image as hierarchical set of alpha-connected components. Computation of alpha-trees suffers from high computational and memory requirements compared with similar component tree algorithms such as max-tree. Here we introduce a novel alpha-tree algorithm using 1) a flooding algorithm for computational efficiency and 2) tree size estimation (TSE) for memory efficiency. In TSE, an exponential decay model was fitted to normalized tree sizes as a function of the normalized root mean squared deviation (NRMSD) of edge-dissimilarity distributions, and the model was used to estimate the optimum memory allocation size for alpha-tree construction. An experiment on 1256 images shows that our algorithm runs 2.27 times faster than Ouzounis and Soille's thanks to the flooding algorithm, and TSE reduced the average memory allocation of the proposed algorithm by 40.4%, eliminating unused allocated memory by 86.0% with a negligible computational cost

A Method for Modeling Decoherence on a Quantum Information Processor

We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an $N^2$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular $\sigma_z\sigma_z$ system-environment couplings which induce coherence (phase) damping, though the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase-damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase-damping, and we use this solution to describe the model's behavior in some limiting cases. In the limit of small stochastic phase kicks the system's coherence decays exponentially at a rate which increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on an nuclear magnetic resonance quantum information processor.Comment: 12 pages, 9 figure

Multivariate calibration approach for quantitative determination of cell-line cross contamination by intact cell mass spectrometry and artificial neural networks

Cross-contamination of eukaryotic cell lines used in biomedical research represents a highly relevant problem. Analysis of repetitive DNA sequences, such as Short Tandem Repeats (STR), or Simple Sequence Repeats (SSR), is a widely accepted, simple, and commercially available technique to authenticate cell lines. However, it provides only qualitative information that depends on the extent of reference databases for interpretation. In this work, we developed and validated a rapid and routinely applicable method for evaluation of cell culture cross-contamination levels based on mass spectrometric fingerprints of intact mammalian cells coupled with artificial neural networks (ANNs). We used human embryonic stem cells (hESCs) contaminated by either mouse embryonic stem cells (mESCs) or mouse embryonic fibroblasts (MEFs) as a model. We determined the contamination level using a mass spectra database of known calibration mixtures that served as training input for an ANN. The ANN was then capable of correct quantification of the level of contamination of hESCs by mESCs or MEFs. We demonstrate that MS analysis, when linked to proper mathematical instruments, is a tangible tool for unraveling and quantifying heterogeneity in cell cultures. The analysis is applicable in routine scenarios for cell authentication and/or cell phenotyping in general

Increased glycation and oxidative damage to apolipoprotein B100 of LDL cholesterol in patients with type 2 diabetes and effect of metformin

OBJECTIVE The aim of this study was to investigate whether apolipoprotein B100 of LDL suffers increased damage by glycation, oxidation, and nitration in patients with type 2 diabetes, including patients receiving metformin therapy. RESEARCH DESIGN AND METHODS For this study, 32 type 2 diabetic patients and 21 healthy control subjects were recruited; 13 diabetic patients were receiving metformin therapy (median dose: 1.50 g/day). LDL was isolated from venous plasma by ultracentrifugation, delipidated, digested, and analyzed for protein glycation, oxidation, and nitration adducts by stable isotopic dilution analysis tandem mass spectrometry. RESULTS Advanced glycation end product (AGE) content of apolipoprotein B100 of LDL from type 2 diabetic patients was higher than from healthy subjects: arginine-derived AGE, 15.8 vs. 5.3 mol% (P < 0.001); and lysine-derived AGE, 2.5 vs. 1.5 mol% (P < 0.05). Oxidative damage, mainly methionine sulfoxide residues, was also increased: 2.5 vs. 1.1 molar equivalents (P < 0.001). 3-Nitrotyrosine content was decreased: 0.04 vs. 0.12 mol% (P < 0.05). In diabetic patients receiving metformin therapy, arginine-derived AGE and methionine sulfoxide were lower than in patients not receiving metformin: 19.3 vs. 8.9 mol% (P < 0.01) and 2.9 vs. 1.9 mol% (P < 0.05), respectively; 3-nitrotyrosine content was higher: 0.10 vs. 0.03 mol% (P < 0.05). Fructosyl-lysine residue content correlated positively with fasting plasma glucose. Arginine-derived AGE residue contents were intercorrelated and also correlated positively with methionine sulfoxide. CONCLUSIONS Patients with type 2 diabetes had increased arginine-derived AGEs and oxidative damage in apolipoprotein B100 of LDL. This was lower in patients receiving metformin therapy, which may contribute to decreased oxidative damage, atherogenicity, and cardiovascular disease