FPGA acceleration of a quantum Monte Carlo application

Quantum Monte Carlo methods enable us to determine the ground-state properties of atomic or molecular clusters. Here, we present a reconfigurable computing architecture using Field Programmable Gate Arrays (FPGAs) to accelerate two computationally intensive kernels of a Quantum Monte Carlo (QMC) application applied to N-body systems. We focus on two key kernels of the QMC application: acceleration of potential energy and wave function calculations. We compare the performance of our application on two reconfigurable platforms. Firstly, we use a dual-processor 2.4 GHz Intel Xeon augmented with two reconfigurable development boards consisting of Xilinx Virtex-II Pro FPGAs. Using this platform, we achieve a speedup of 3× over a software-only implementation. Following this, the chemistry application is ported to the Cray XD1 supercomputer equipped with Xilinx Virtex-II Pro and Virtex-4 FPGAs. The hardware-accelerated application on one node of the high performance system equipped with a single Virtex-4 FPGA yields a speedup of approximately 25× over the serial reference code running on one node of the dual-processor dual-core 2.2 GHz AMD Opteron. This speedup is mainly attributed to the use of pipelining, the use of fixed-point arithmetic for all calculations and the fine-grained parallelism using FPGAs. We can further enhance the performance by operating multiple instances of our design in parallel.     

Toward a scalable quantum computing architecture with mixed species ion chains

Quantum Information Processing - We report on progress toward implementing mixed ion species quantum information processing for a scalable ion-trap architecture. Mixed species chains may help solve...     

Global‐view coefficients: a data management solution for parallel quantum Monte Carlo applications

Quantum Monte Carlo (QMC) applications perform simulation with respect to an initial state of the quantum mechanical system, which is often captured by using a cubic B‐spline basis. This representation is stored as a read‐only table of coefficients and accesses to the table are generated at random as part of the Monte Carlo simulation. Current QMC applications, such as QWalk and QMCPACK, replicate this table at every process or node, which limits scalability because increasing the number of processors does not enable larger systems to be run. We present a partitioned global address space approach to transparently managing this data using Global Arrays in a manner that allows the memory of multiple nodes to be aggregated. We develop an automated data management system that significantly reduces communication overheads, enabling new capabilities for QMC codes. Experimental results with QWalk and QMCPACK demonstrate the effectiveness of the data management system. Copyright © 2016 John Wiley & Sons, Ltd.     

QSAR/QSPR模型中的蒙特卡罗交叉效验评价

介绍了用于QSAR或QSPR模型的蒙特卡罗(Monte Carlo)交叉效验模型评价方法。该方法是采用蒙特卡罗随机思想把数据集随机的分成训练集和预测集来对模型进行交叉效验,从模型的预测能力和预测稳定性两个方面评价模型。通过研究不同代表性的3套化学数据的结果表明,与k-折交叉效验相比,Monte Carlo交叉效验,是一种有效且稳定的QSAR或QSPR模型的评价方法。     

Feedback control of quantum entanglement in a two-spin system

A pair of spins is the most simple quantum system that can exhibit entanglement: a nonclassical property that plays an essential role in quantum information technologies. In this paper, feedback control problems of a symmetric two-spin system conditioned on a continuous measurement are investigated. In order to make some useful formulas in stochastic control theory directly applicable, we first derive a two-dimensional representation of the system. We then prove that a feedback controller stabilizes an entangled state of the two spins almost globally with probability one. Furthermore, it is demonstrated that some entangled states, which correspond to nonequilibrium points of the dynamics, are globally stabilized via feedback in the sense that the mean distance from a target can be reduced to an arbitrarily small value.     

Nanodroplets on a solid plane: wetting and spreading in a Monte Carlo simulation

The wetting behavior and spreading dynamics of small polymer melt droplets in the course of transition from partial to complete wetting conditions on a flat structureless solid substrate have been studied by dynamic Monte Carlo simulation. From the density profiles of the drops we determine the contact angles at varying strength of the van der Waals surface forces in the whole interval of partial wetting. The validity of Young's equation is then tested whereby the surface tension of the melt/vapor interface is derived independently from interfacial fluctuation analysis, and the surface free energy of the melt at the substrate—from the anisotropy of the local pressure at the wall. The bending rigidity of the melt/vapor interface turns out negative, as recently predicted for short-range interactions.We carry out computer experiments which show that Tanner's law for the kinetics of drop spreading holds also on nanoscopic scales. The observed density profiles of spreading droplets confirm earlier predictions that the central cap-shaped region of the droplets shrinks at the expense of a transition region (“foot”) surrounded by a precursor film which is roughly one monolayer thick. At later times the precursor film breaks into individual polymer chains and advances in typically diffusive manner as found in laboratory experiments.Eventually we investigate the impact of line tension on nanodroplets behavior at varying strength of adhesion and demonstrate that the Gretz equation which incorporates line tension into Young's rule holds even on nanoscale and predicts important properties of the drops subject to droplet size.     

Parallel Monte Carlo Driver (PMCD)—a software package for Monte Carlo simulations in parallel

Thanks to the dramatic decrease of computer costs and the no less dramatic increase in those same computer's capabilities and also thanks to the availability of specific free software and libraries that allow the set up of small parallel computation installations the scientific community is now in a position where parallel computation is within easy reach even to moderately budgeted research groups. The software package PMCD (Parallel Monte Carlo Driver) was developed to drive the Monte Carlo simulation of a wide range of user supplied models in parallel computation environments. The typical Monte Carlo simulation involves using a software implementation of a function to repeatedly generate function values. Typically these software implementations were developed for sequential runs. Our driver was developed to enable the run in parallel of the Monte Carlo simulation, with minimum changes to the original code that implements the function of interest to the researcher. In this communication we present the main goals and characteristics of our software, together with a simple study its expected performance. Monte Carlo simulations are informally classified as “embarrassingly parallel”, meaning that the gains in parallelizing a Monte Carlo run should be close to ideal, i.e. with speed ups close to linear. In this paper our simple study shows that without compromising the easiness of use and implementation, one can get performances very close to the ideal.     

Pairwise thermal entanglement and quantum discord in a three-ligand spin-star structure

In this work, we perform a comparative study between the pairwise thermal entanglement (PWTE) and thermal quantum discord (TQD) to detect quantum phase transitions (QPT)s in a three-ligand spin-star structure whose magnetic interactions are described by different model Hamiltonians such as pure Dzyaloshinskii–Moriya (DM) interaction, anisotropic Heisenberg model (XXZ), and XXZ model with the different components of the DM interaction. Representing the system’s energy spectrum, we also focus on the critical points of QPTs where the ground-state level crossing happens in such models. Taking advantage of the concurrence as a measure of the PWTE, we found that while the ligand–ligand concurrence in all models is sensitive to the ground-state level crossing, the concurrence between the central qubit and a ligand cannot exhibit a QPT. In contrast, the TQD between any two arbitrary qubits can be a signature of a QPT in a large range of temperature. However, depending on the model studied, the behavior of the TQD at the critical point will be different. In addition, the TQD behaves quite differently than the concurrence. Moreover, in order to confirm the numerical results, we analytically study the entanglement behavior at the low-temperature limit as well as the high-temperature regime. We realized that, at the low-temperature limit, the maximum value of the concurrence is approximately equal to 0.33, independent of the model studied. On the other hand, at high-temperature regime, the concurrence is suppressed down to zero rapidly beyond a critical value of temperature. The dependence of the critical temperature on the DM interaction and the anisotropy parameter is obtained explicitly. Finally we show that there is a perfect agreement between the analytical results and the numerical predictions.     

Monte Carlo modelling of electron beam lithography: a scaling law

The theorem of Dimensional Analysis, usually applied to the inference of physical laws, is for the first time applied to the derivation of interpolation curves of numerical data, leading to a simplified dependence on a reduced number of arguments , dimensionless combination of variables. In particular, Monte Carlo modelling of electron beam lithography is considered and the backscattering coefficient addressed, in case of a general substrate layer, in the elastic regime and in the energy range 5 to 100 keV. The many variables involved (electron energy, substrate physical constants and thickness) are demonstrated to ultimately enter in determining through asingle dimensionless parameter ₀. Thus, a scaling law is determined, an important guide in microsystem designing, indicating, if any part of the configuration is modified, how the other parameters should change (or scale) without affecting the result. Finally, a simple law =83 ₀ is shown to account for all variations of the parameters over all substrates of the periodic table.     

Thermal entanglement of the mixed spin-1/2 and spin-5/2 Heisenberg model under an external magnetic field

We use the concept of negativity to study the entanglement of spin-1/2 and spin-5/2 antiferromagnetic Heisenberg model with an inhomogeneous magnetic field. Analytical conclusions of the model are acquired. It is found that the critical temperature \(T_\mathrm{c}\) goes up, as the increase of anisotropy parameter \(k\) . The temperature \(T_\mathrm{c}\) becomes bigger than the results of spin-1/2 and spin-3/2 Heisenberg XXZ chain for the same value of \(k\) . And we can gain more entanglement at higher temperature by coordinating the value of inhomogeneity \(b\) .     

Robust bandwidth selection in semiparametric partly linear regression models: Monte Carlo study and influential analysis

In this paper, under a semiparametric partly linear regression model with fixed design, we introduce a family of robust procedures to select the bandwidth parameter. The robust plug-in proposal is based on nonparametric robust estimates of the νth derivatives and under mild conditions, it converges to the optimal bandwidth. A robust cross-validation bandwidth is also considered and the performance of the different proposals is compared through a Monte Carlo study. We define an empirical influence measure for data-driven bandwidth selectors and, through it, we study the sensitivity of the data-driven bandwidth selectors. It appears that the robust selector compares favorably to its classical competitor, despite the need to select a pilot bandwidth when considering plug-in bandwidths. Moreover, the plug-in procedure seems to be less sensitive than the cross-validation in particular, when introducing several outliers. When combined with the three-step procedure proposed by Bianco and Boente [2004. Robust estimators in semiparametric partly linear regression models. J. Statist. Plann. Inference 122, 229-252] the robust selectors lead to robust data-driven estimates of both the regression function and the regression parameter.     

Electron-phonon interaction in nanowires: A Monte Carlo study of the effect of the field

The femtosecond dynamics of highly non-equilibrium, confined carriers is analyzed within a Monte Carlo approach. The physical process considered corresponds to a locally excited or injected into a semiconductor nanowire distribution of heated carriers, which evolve under the action of an applied electric field. The carriers are cooled down by dissipation processes caused by phonons. The process is described by a quantum-kinetic equation which generalizes the classical Boltzmann equation with respect to two classical assumptions, namely for temporal and spatial locality of the carrier-phonon interaction. We investigate the effect of the field on the electron-phonon interaction—the intra-collisional field effect (ICFE). A Monte Carlo method for simulation of the considered process has been utilized. Simulation results for carrier evolution in a GaAs nanowire are obtained and analyzed for phenomena related to the ICFE.     

SLOCC orbit of rank-deficient two-qubit states: quantum entanglement,quantum discord and EPR steering

We study selected aspects of non-classical correlations of arbitrary states from the stochastic local operations and classical communication orbit of rank-deficient two-qubit states. In particular, we find explicitly entanglement of formation and quantum discord for these states. Moreover, we determine and analyze the Einstein–Podolsky–Rosen steering ellipsoids corresponding to these states.     

Stochastic iterative dynamic programming: a Monte Carlo approach to dual control

Practical exploitation of optimal dual control (ODC) theory continues to be hindered by the difficulties involved in numerically solving the associated stochastic dynamic programming (SDPs) problems. In particular, high-dimensional hyper-states coupled with the nesting of optimizations and integrations within these SDP problems render their exact numerical solution computationally prohibitive. This paper presents a new stochastic dynamic programming algorithm that uses a Monte Carlo approach to circumvent the need for numerical integration, thereby dramatically reducing computational requirements. Also, being a generalization of iterative dynamic programming (IDP) to the stochastic domain, the new algorithm exhibits reduced sensitivity to the hyper-state dimension and, consequently, is particularly well suited to solution of ODC problems. A convergence analysis of the new algorithm is provided, and its benefits are illustrated on the problem of ODC of an integrator with unknown gain, originally presented by Åström and Helmersson (Computers and Mathematics with Applications 12A (1986) 653-662).     

Tradeoffs in granularity and parallelization for a Monte Carlo shower simulation code

The EGS4 code, developed at Stanford Linear Accelerator Center, simulates electron-photon cascading phenomena. The original code is inherently sequential: processing one particle at a time. This paper reports on a series of experiments in parallelizing different versions of EGS4. Our parallel experiments were run on a 30-processor Sequent Balance B21 and a 6-processor Symmetry S27. We have considered the following approaches for parallel execution of this application code:

1. (1) Original sequential version modified for parallel processing: 1 processor;

2. (2) Version 1 run multiprocessed: 1 to 29 processors;

3. (3) Sequential version modified for large-grain parallel processing: 1 procssor;

4. (4) Version 3 run using the Sequent Microtasking Library: 1 to 29 processors.

For each approach, we discuss the relative advantages and disadvantages in the areas of coding effort, understandability and portability, as well as performance, and outline a new parallelization approach we are currently pursuing based on Large-Grain Data Flow techniques.     

A Monte Carlo study of the primary absorbed energy redistribution in X-ray lithography

The minimum feature size producible by LIGA X-ray lithography is fundamentally limited by the redistribution of primary doses via photoelectrons and the influence of the resulting dose distribution on resist development. Secondary radiation from mask and substrate are well known as source for pattern distortion in deep X-ray lithography. Numerical simulations by means of Monte Carlo simulations using PENELOPE (Salvat et al. in PENELOPE-2008: a code system for Monte Carlo simulation of electron and photon transport. http://www.nea.fr/html/dbprog/penelope-2008.pdf, 2008) are applied to quantify these additional dose values in the resist/substrate interface and the irradiated/shadowed interface. A significant reduction of the additional dose by secondary radiation from the plating base is not observed for Au and Ti layers thicker than 10 nm. The influence of polarized or unpolarized X-rays might be neglected for structure dimensions larger than a few 10 nm. As an example of critical dimension, simulations were used to predict the structure quality of grating structures with a period of 2.4 μm and duty cycle 0.5 in a resist layer of 300 μm.     

Monte Carlo simulations of a single polystyrene chain in spherical confinement

We report on Monte Carlo simulations of a single coarse-grained polystyrene chain in spherical confinement. To this end we employ a variant of the freely rotating chain model, the parameters of which are chosen to mimic polystyrene in good solvent conditions. Entanglements are analyzed as a function of molecular weight and capsid radius to provide an educated guess about the structure of a single polystyrene chain in a miniemulsion droplet. We also show that significant knotting occurs first when the radius of the confining sphere falls below the chain?s radius of gyration.     

Geometric entanglement and quantum phase transition in generalized cluster-XY models

Quantum Information Processing - Based on dynamic analyses on bipartition system, the frozen conditions and the inconsistency of quantum coherence are investigated when one qubit of initial state...     

Adaptation and change detection with a sequential Monte Carlo scheme.

Given the sequential data from an unknown target system with changing parameters, the first part of this paper discusses online algorithms that adapt to smooth as well as abrupt changes. This paper examines four different parameter/ hyperparameter dynamics for online learning and compares their performance within an online Bayesian learning framework. Using the dynamics that performed best in the first part, the second part of this paper attempts to perform change detection in unknown systems in terms of the time dependence of the marginal likelihood. Because of the sequential nature of the algorithms, a sequential Monte Carlo scheme (particle filter) is a natural means for implementation.