Approaching the Ground State of a Quantum Spin Glass using a Zero-Temperature Quantum Monte Carlo

Here we discuss the annealing behavior of an infinite-range $\pm J$ Ising spin glass in presence of a transverse field using a zero-temperature quantum Monte Carlo. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particularly, when the transverse field is low, much more efficiently.Comment: 8 pages, 6 fig

Quantum Annealing in a Kinetically Constrained System

Classical and quantum annealing is discussed for a kinetically constrained chain of $N$ non-interacting asymmetric double wells, represented by Ising spins in a longitudinal field $h$. It is shown that in certain cases, where the kinetic constraints may arise from infinitely high but vanishingly narrow barriers appearing in the relaxation path of the system, quantum annealing exploiting the quantum-mechanical penetration of sufficiently narrow barriers may be far more efficient than its thermal counterpart. We have used a semiclassical picture of scattering dynamics to do our simulation for the quantum system.Comment: 5 pages, 3 figure

Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point

We study an infinite range ferromagnetic Ising model in the presence of a transverse magnetic field which exhibits a quantum paramagnetic-ferromagnetic phase transition at a critical value of the transverse field. In the thermodynamic limit, the low-temperature properties of this model are dominated by the behavior of a single large classical spin governed by an anisotropic Hamiltonian. Using this property, we study the quench and AC dynamics of the model both numerically and analytically, and develop a correspondence between the classical phase space dynamics of a single spin and the quantum dynamics of the infinite-range ferromagnetic Ising model. In particular, we compare the behavior of the equal-time order parameter correlation function both near to and away from the quantum critical point in the presence of a quench or AC transverse field. We explicitly demonstrate that a clear signature of the quantum critical point can be obtained by studying the AC dynamics of the system even in the classical limit. We discuss possible realizations of our model in experimental systems.Comment: Revtex4, 10 pages including 10 figures; corrected a sign error in Eq. 32; this is the final published versio

Ideal-gas like market models with savings: quenched and annealed cases

We analyze the ideal gas like models of markets and review the different cases where a `savings' factor changes the nature and shape of the distribution of wealth. These models can produce similar distribution of wealth as observed across varied economies. We present a more realistic model where the saving factor can vary over time (annealed savings) and yet produces Pareto distribution of wealth in certain cases. We discuss the relevance of such models in the context of wealth distribution, and address some recent issues in the context of these models.Comment: 2-col RevTeX4, 4 pages, 1 eps figure; Proc. APFA5 Conference, Torino, 200

Finding critical points and correlation length exponents using finite size scaling of Gini index

The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality between the values of an order parameter, measured near a critical point, is independent of the system size. Quantification of such inequality through Gini index ($g$), therefore, leads to a scaling form $g=G\left[|F-F_c|N^{1/d\nu}\right]$, where $F$ denotes the driving parameter for the transition (e.g., temperature $T$ for ferro-para transition at $T_c$, or lattice occupation probability $p$ near percolation threshold $p_c$), $N$ is the system size, $d$ is the spatial dimension and $\nu$ is the correlation length exponent. We demonstrate the scaling for the Ising model in two and three dimensions and site percolation on square lattice.Comment: 4 pages, 4 figure

Quantum Annealing and Analog Quantum Computation

We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of such computationally hard problems to the classical spin glass problems. The quantum spin glass problems arise with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a general framework for realizing analog quantum computation.Comment: 22 pages, 7 figs (color online); new References Added. Reviews of Modern Physics (in press

A Deep Learning-Based Framework for Supporting Clinical Diagnosis of Glioblastoma Subtypes

Understanding molecular features that facilitate aggressive phenotypes in glioblastoma multiforme (GBM) remains a major clinical challenge. Accurate diagnosis of GBM subtypes, namely classical, proneural, and mesenchymal, and identification of specific molecular features are crucial for clinicians for systematic treatment. We develop a biologically interpretable and highly efficient deep learning framework based on a convolutional neural network for subtype identification. The classifiers were generated from high-throughput data of different molecular levels, i.e., transcriptome and methylome. Furthermore, an integrated subsystem of transcriptome and methylome data was also used to build the biologically relevant model. Our results show that deep learning model outperforms the traditional machine learning algorithms. Furthermore, to evaluate the biological and clinical applicability of the classification, we performed weighted gene correlation network analysis, gene set enrichment, and survival analysis of the feature genes. We identified the genotype-phenotype relationship of GBM subtypes and the subtype-specific predictive biomarkers for potential diagnosis and treatment