Practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. 88, 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

The stochastic Gross-Pitaevskii equation: II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a 'high temperature' master equation for a Bose gas, which includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.

Integrating spatial optimization and cellular automata for evaluating urban change

Urban growth and change presents numerous challenges for planners and policy makers. Effective and appropriate strategies for managing growth and change must address issues of social, environmental and economic sustainability. Doing so in practical terms is a difficult task given the uncertainty associated with likely growth trends not to mention the uncertainty associated with how social and environmental structures will respond to such change. An optimization based approach is developed for evaluating growth and change based upon spatial restrictions and impact thresholds. The spatial optimization model is integrated with a cellular automata growth simulation process. Application results are presented and discussed with respect to possible growth scenarios in south east Queensland, Australia.

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.

Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

High-pressure adsorption capacity and structure of CO2 in carbon slit pores: Theory and simulation

We present new simulation results for the packing of single-center and three-center models of carbon dioxide at high pressure in carbon slit pores. The former shows a series of packing transitions that are well described by our density functional theory model developed earlier. In contrast, these transitions are absent for the three-center model. Analysis of the simulation results shows that alternations of flat-lying molecules and rotated molecules can occur as the pore width is increased. The presence or absence of quadrupoles has negligible effect on these high-density structures.

Transition-state-theory calculations for reactions of O(3P) with halogenated olefins

The potential energy surfaces for the reactions of atomic oxygen in its ground electronic state, O(P-3), with the olefins: CF2=CCl2 and CF2=CF - CF3, have been characterized using ab initio molecular orbital calculations. Geometry optimization and vibrational frequency calculations were performed for reactants, transition states and products at the MP2 and QCISD levels of theory using the 6-31G(d) basis set. This database was then used to calculate the rate constants by means of Transition-State-Theory. To obtain a better reference and to test the reliability of the activation barriers we have also carried out computations using the CCSD(T)(fc)/6-311Gdagger, MP4(SDQ)(fc)/CBSB4 and MP2(fc)/CBSB3 single point energy calculations at both of the above levels of theory, as well as with the composite CBS-RAD procedure ( P. M. Mayer, C. J. Parkinson, D. M. Smith and L. Radom, J. Chem. Phys., 1998, 108, 604) and a modi. cation of this approach, called: CBS-RAD( MP2, MP2). It was found that the kinetic parameters obtained in this work particularly with the CBS-RAD ( MP2, MP2) procedure are in reasonable agreement with the experimental values. For both reactions it is found that the channels leading to the olefin double-bond addition predominates with respect to any other reaction pathway. However, on account of the different substituents in the alkenes we have located, at all levels of theory, two transition states for each reaction. Moreover, we have found that, for the reactions studied, a correlation exists between the activation energies and the electronic structure of the transition states which can explain the influence of the substituent effect on the reactivity of the halo-olefins.

Implications of seasonal climate forecasts on world wheat trade: a stochastic, dynamic analysis

Improvements in seasonal climate forecasts have potential economic implications for international agriculture. A stochastic, dynamic simulation model of the international wheat economy is developed to estimate the potential effects of seasonal climate forecasts for various countries' wheat production, exports and world trade. Previous studies have generally ignored the stochastic and dynamic aspects of the effects associated with the use of climate forecasts. This study shows the importance of these aspects. In particular with free trade, the use of seasonal forecasts results in increased producer surplus across all exporting countries. In fact, producers appear to capture a large share of the economic surplus created by using the forecasts. Further, the stochastic dimensions suggest that while the expected long-run benefits of seasonal forecasts are positive, considerable year-to-year variation in the distribution of benefits between producers and consumers should be expected. The possibility exists for an economic measure to increase or decrease over a 20-year horizon, depending on the particular sequence of years.

Fast simulation of a quantum phase transition in an ion-trap realizable unitary map

We show that a specific implementation of a unitary map on multiple qubits in an ion trap is physically equivalent to a Hamiltonian evolution that belongs to the same universality class as the transverse Ising Hamiltonian. We suggest experimental signatures, and present numerical simulations for the case of four qubits.

Evaluation of 1-site and 5-site models of methane on its adsorption on graphite and in graphitic slit pores

In this paper, we evaluate the performance of the 1- and 5-site models of methane on the description of adsorption on graphite surfaces and in graphitic slit pores. These models have been known to perform well in the description of the fluid-phase behavior and vapor-liquid equilibria. Their performance in adsorption is evaluated in this work for nonporous graphitized thermal carbon black, and simulation results are compared with the experimental data of Avgul and Kiselev (Chemistry and Physics of Carbon; Dekker: New York, 1970; Vol. 6, p 1). On this nonporous surface, it is found that these models perform as well on isotherms at various temperatures as they do on the experimental isosteric heat for adsorption on a graphite surface. They are then tested for their performance in predicting the adsorption isotherms in graphitic slit pores, in which we would like to explore the effect of confinement on the molecule packing. Pore widths of 10 and 20 angstrom are chosen in this investigation, and we also study the effects of temperature by choosing 90.7, 113, and 273 K. The first two are for subcritical conditions, with 90.7 K being the triple point of methane and 113 K being its boiling point. The last temperature is chosen to represent the supercritical condition so that we can investigate the performance of these models at extremely high pressures. We have found that for the case of slit pores investigated in this paper, although the two models yield comparable pore densities (provided the accessible pore width is used in the calculation of pore density), the number of particles predicted by the I-site model is always greater than that predicted by the 5-site model, regardless of whether temperature is subcritical or supercritical. This is due to the packing effect in the confined space such that a methane molecule modeled as a spherical particle in the I-site model would pack better than the fused five-sphere model in the case of the 5-site model. Because the 5-site model better describes the liquid- and solid-phase behavior, we would argue that the packing density in small pores is better described with a more detailed 5-site model, and care should be exercised when using the 1-site model to study adsorption in small pores.

A simulation analysis of the market effect of the Australian Broadcasting Corporation

In this paper we utilise a stochastic address model of broadcast oligopoly markets to analyse the Australian broadcast television market. In particular, we examine the effect of the presence of a single government market participant in this market. An examination of the dynamics of the simulations demonstrates that the presence of a government market participant can simultaneously generate positive outcomes for viewers as well as for other market suppliers. Further examination of simulation dynamics indicates that privatisation of the government market participant results in reduced viewer choice and diversity. We also demonstrate that additional private market participants would not result in significant benefits to viewers.

Geometric phases of scattering states in a ring geometry: adiabatic pumping in mesoscopic devices

Geometric phases of scattering states in a ring geometry are studied on the basis of a variant of the adiabatic theorem. Three timescales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a ring geometry play a crucial role in determining geometric phases, in contrast to only two timescales, i.e., the adiabatic period and the dwell time, in an open system. We derive a formula connecting the gauge invariant geometric phases acquired by time-reversed scattering states and the circulating (pumping) current. A numerical calculation shows that the effect of the geometric phases is observable in a nanoscale electronic device.