Showing papers by "Choy Heng Lai published in 2008"

Nonadditive quantum error-correcting code.

Abstract: We report the first nonadditive quantum error-correcting code, namely, a ((9, 12, 3)) code which is a 12-dimensional subspace within a 9-qubit Hilbert space, that outperforms the optimal stabilizer code of the same length by encoding more levels while correcting arbitrary single-qubit errors. Taking advantage of the graph states, we construct explicitly a complete encoding-decoding circuit for the proposed nonadditive error-correcting code.

Transition to global synchronization in clustered networks.

Abstract: Received 7 October 2007; revised manuscript received 20 February 2008; published 15 April 2008A clustered network is characterized by a number of distinct sparsely linked subnetworks clusters , eachwith dense internal connections. Such networks are relevant to biological, social, and certain technologicalnetworked systems. For a clustered network the occurrence of global synchronization, in which nodes fromdifferent clusters are synchronized, is of interest. We consider Kuramoto-type dynamics and obtain an analyticformula relating the critical coupling strength required for global synchronization to the probabilities of intra-cluster and intercluster connections, and provide numerical verification. Our work also provides direct supportfor a previous spectral-analysis-based result concerning the role of random intercluster links in enhancing thesynchronizability of a clustered network.DOI: 10.1103/PhysRevE.77.046211 PACS number s : 05.45.Xt, 89.75.Hc

Optimal resource allocation for efficient transport on complex networks

Abstract: The problem of efficient transport on a complex network is studied in this paper. We find that there exists an optimal way to allocate resources for information processing on each node to achieve the best transport capacity of the network, or the largest input information rate which does not cause jamming in network traffic, provided that the network structure and routing strategy are given. More interestingly, this achievable network capacity limit is closely related to the topological structure of the network, and is actually inversely proportional to the average distance of the network, measured according to the same routing rule.

Detecting groups of similar components in complex networks

Abstract: We study how to detect groups in a complex network each of which consists of component nodes sharing a similar connection pattern. Based on the mixture models and the exploratory analysis set up by Newman and Leicht (2007 Proc. Natl. Acad. Sci. USA 104 9564), we develop an algorithm that is applicable to a network with any degree distribution. The partition of a network suggested by this algorithm also applies to its complementary network. In general, groups of similar components are not necessarily identical with the communities in a community network; thus partitioning a network into groups of similar components provides additional information of the network structure. The proposed algorithm can also be used for community detection when the groups and the communities overlap. By introducing a tunable parameter that controls the involved effects of the heterogeneity, we can also investigate conveniently how the group structure can be coupled with the heterogeneity characteristics. In particular, an interesting example shows a group partition can evolve into a community partition in some situations when the involved heterogeneity effects are tuned. The extension of this algorithm to weighted networks is discussed as well.

Onset of synchronization in complex gradient networks

Abstract: Recently, it has been found that the synchronizability of a scale-free network can be enhanced by introducing some proper gradient in the coupling. This result has been obtained by using eigenvalue-spectrum analysis under the assumption of identical node dynamics. Here we obtain an analytic formula for the onset of synchronization by incorporating the Kuramoto model on gradient scale-free networks. Our result provides quantitative support for the enhancement of synchronization in such networks, further justifying their ubiquity in natural and in technological systems.

Stability of the steady state of delay-coupled chaotic maps on complex networks.

Abstract: We study the stability of the steady state of coupled chaotic maps with randomly distributed time delays evolving on a random network. An analysis method is developed based on the peculiar mathematical structure of the Jacobian of the steady state due to time-delayed coupling, which enables us to relate the stability of the steady state to the locations of the roots of a set of lower-order bound equations. For delta -distributed time delays (or fixed time delay), we find that the stability of the steady state is determined by the maximum modulus of the roots of a set of algebraic equations, where the only nontrivial coefficient in each equation is one of the eigenvalues of the normalized adjacency matrix of the underlying network. For general distributed time delays, we find a necessary condition for the stable steady state based on the maximum modulus of the roots of a bound equation. When the number of links is large, the nontrivial coefficients of the bound equation are just the probabilities of different time delays. Our study thus establishes the relationship between the stability of the steady state and the probability distribution of time delays, and provides a better way to investigate the influence of the distributed time delays in coupling on the global behavior of the systems.

Model-based detector and extraction of weak signal frequencies from chaotic data.

Abstract: Detecting a weak signal from chaotic time series is of general interest in science and engineering. In this work we introduce and investigate a signal detection algorithm for which chaos theory, nonlinear dynamical reconstruction techniques, neural networks, and time-frequency analysis are put together in a synergistic manner. By applying the scheme to numerical simulation and different experimental measurement data sets (Henon map, chaotic circuit, and NH3 laser data sets), we demonstrate that weak signals hidden beneath the noise floor can be detected by using a model-based detector. Particularly, the signal frequencies can be extracted accurately in the time-frequency space. By comparing the model-based method with the standard denoising wavelet technique as well as supervised principal components analysis detector, we further show that the nonlinear dynamics and neural network-based approach performs better in extracting frequencies of weak signals hidden in chaotic time series.

Multiple effects of gradient coupling on network synchronization.

Abstract: Recent studies have shown that the synchronizability of complex networks can be significantly improved by gradient or asymmetric couplings, and increase of the gradient strength could enhance the network synchronizability monotonically. Here we argue and demonstrate that, for a typical complex network, there could be an optimal gradient where the maximum network synchronizability is achieved. That is, large gradient may deteriorate synchronization. We attribute the suppressing effect of gradient coupling to the phenomenon of network breaking and show that, comparing with sparse homogeneous networks, dense heterogeneous networks suffer less from network breaking and, consequently, benefit more from large gradient in improving synchronization. The findings are supported by indirect simulations of eigenvalue analysis and direct simulations of coupled nonidentical oscillators.

Synchronizability of network ensembles with prescribed statistical properties.

Abstract: It has been shown that synchronizability of a network is determined by the local structure rather than the global properties. With the same global properties, networks may have very different synchronizability. In this paper, we numerically studied, through the spectral properties, the synchronizability of ensembles of networks with prescribed statistical properties. Given a degree sequence, it is found that the eigenvalues and eigenratios characterizing network synchronizability have well-defined distributions, and statistically, the networks with extremely poor synchronizability are rare. Moreover, we compared the synchronizability of three network ensembles that have the same nodes and average degree. Our work reveals that the synchronizability of a network can be significantly affected by the local pattern of connections, and the homogeneity of degree can greatly enhance network synchronizability for networks of a random nature.

Effect of the shape of periodic forces and second periodic forces on horseshoe chaos in Duffing oscillator

Abstract: The effect of the shape of six different periodic forces and second periodic forces on the onset of horseshoe chaos are studied both analytically and numerically in a Duffing oscillator The external periodic forces considered are sine wave, square wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectified sine wave, and modulus of sine wave An analytical threshold condition for the onset of horseshoe chaos is obtained in the Duffing oscillator driven by various periodic forces using the Melnikov method Melnikov threshold curve is drawn in a parameter space For all the forces except modulus of sine wave, the onset of cross-well asymptotic chaos is observed just above the Melnikov threshold curve for onset of horseshoe chaos For the modulus of sine wave long time transient motion followed by a periodic attractor is realized The possibility of controlling of horseshoe and asymptotic chaos in the Duffing oscillator by an addition of second periodic force is then analyzed Parametric regimes where suppression of horseshoe chaos occurs are predicted Analytical prediction is demonstrated through direct numerical simulations Starting from asymptotic chaos we show the recovery of periodic motion for a range of values of amplitude and phase of the second periodic force Interestingly, suppression of chaos is found in the parametric regimes where the Melnikov function does not change sign

Transition to amplitude death in scale-free networks

Abstract: Transition to amplitude death in scale-free networks of nonlinear oscillators is investigated. As the coupling strength increases, the network will undergo three stages in approaching to the state of complete amplitude death. The first stage is featured by a \emph{"stair-like"} distribution of the node amplitude, and the transition is accomplished by a \emph{hierarchical death} of the amplitude stairs. The second and third stages are characterized by, respectively, a continuing elimination of the synchronous clusters and a fast death of the non-synchronized nodes.

Universal quantum computation with trapped ions in thermal motion by adiabatic passage

Abstract: We propose a universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.

Trapped Ion Quantum Computation by Adiabatic Passage

Abstract: We propose a new universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.

Detecting groups of similar components in complex networks

Abstract: We study how to detect groups in a complex network each of which consists of component nodes sharing a similar connection pattern. Based on the mixture models and the exploratory analysis set up by Newman and Leicht (Newman and Leicht 2007 {\it Proc. Natl. Acad. Sci. USA} {\bf 104} 9564), we develop an algorithm that is applicable to a network with any degree distribution. The partition of a network suggested by this algorithm also applies to its complementary network. In general, groups of similar components are not necessarily identical with the communities in a community network; thus partitioning a network into groups of similar components provides additional information of the network structure. The proposed algorithm can also be used for community detection when the groups and the communities overlap. By introducing a tunable parameter that controls the involved effects of the heterogeneity, we can also investigate conveniently how the group structure can be coupled with the heterogeneity characteristics. In particular, an interesting example shows a group partition can evolve into a community partition in some situations when the involved heterogeneity effects are tuned. The extension of this algorithm to weighted networks is discussed as well.