Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches

We compare pseudopure state ensemble implementations, quantified by their initial polarization and ensemble size, of Grover's search algorithm to probabilistic classical sequential search algorithms in terms of their success and failure probabilities. We propose a criterion for quantifying the resources used by the ensemble implementation via the aggregate number of oracle invocations across the entire ensemble and use this as a basis for comparison with classical search algorithms. We determine bounds for a critical polarization such that the ensemble algorithm succeeds with a greater probability than the probabilistic classical sequential search. Our results indicate that the critical polarization scales as N^(-1/4) where N is the database size and that for typical room temperature solution state NMR, the polarization is such that the ensemble implementation of Grover's algorithm would be advantageous for N > 10^2

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasi-harmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water

Polarization Requirements for Ensemble Implementations of Quantum Algorithms with a Single Bit Output

We compare the failure probabilities of ensemble implementations of quantum algorithms which use pseudo-pure initial states, quantified by their polarization, to those of competing classical probabilistic algorithms. Specifically we consider a class algorithms which require only one bit to output the solution to problems. For large ensemble sizes, we present a general scheme to determine a critical polarization beneath which the quantum algorithm fails with greater probability than its classical competitor. We apply this to the Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%.Comment: 11 pages, 3 figure

Simple computer model for the quantum Zeno effect

This paper presents a simple model for repeated measurement of a quantum system: the evolution of a free particle, simulated by discretising the particle's position. This model is easily simulated by computer and provides a useful arena to investigate the effects of measurement upon dynamics, in particular the slowing of evolution due to measurement (the `quantum Zeno effect'). The results of this simulation are discussed for two rather different sorts of measurement process, both of which are (simplified forms of) measurements used in previous simulations of position measurement. A number of interesting results due to measurement are found, and the investigation casts some light on previous disagreements about the presence or absence of the Zeno effect.Comment: REVTeX; 12 pages including 11 figures; figures reformatted to be more readable; some small changes made to the description of the mode

Efficient stochastic thermostatting of path integral molecular dynamics

The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high-frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently-developed colored-noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nos\'e-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.Comment: Accepted for publication on JC

Transition-Event Durations in One Dimensional Activated Processes

Despite their importance in activated processes, transition-event durations -- which are much shorter than first passage times -- have not received a complete theoretical treatment. We therefore study the distribution of durations of transition events over a barrier in a one-dimensional system undergoing over-damped Langevin dynamics.Comment: 39 pages, 11 figure

Electron-Spin Filters Based on the Rashba Effect

Semiconductor electron-spin filters of a proposed type would be based on the Rashba effect, which is described briefly below. Electron-spin filters more precisely, sources of spin-polarized electron currents have been sought for research on, and development of, the emerging technological discipline of spintronics (spin-based electronics). There have been a number of successful demonstrations of injection of spin-polarized electrons from diluted magnetic semiconductors and from ferromagnetic metals into nonmagnetic semiconductors. In contrast, a device according to the proposal would be made from nonmagnetic semiconductor materials and would function without an applied magnetic field. The Rashba effect, named after one of its discoverers, is an energy splitting, of what would otherwise be degenerate quantum states, caused by a spin-orbit interaction in conjunction with a structural-inversion asymmetry in the presence of interfacial electric fields in a semiconductor heterostructure. The magnitude of the energy split is proportional to the electron wave number. The present proposal evolved from recent theoretical studies that suggested the possibility of devices in which electron energy states would be split by the Rashba effect and spin-polarized currents would be extracted by resonant quantum-mechanical tunneling. Accordingly, a device according to the proposal would be denoted an asymmetric resonant interband tunneling diode [a-RITD]. An a-RITD could be implemented in a variety of forms, the form favored in the proposal being a double-barrier heterostructure containing an asymmetric quantum well. It is envisioned that a-RITDs would be designed and fabricated in the InAs/GaSb/AlSb material system for several reasons: Heterostructures in this material system are strong candidates for pronounced Rashba spin splitting because InAs and GaSb exhibit large spin-orbit interactions and because both InAs and GaSb would be available for the construction of highly asymmetric quantum wells. This mate-rial system affords a variety of energy-band alignments that can be exploited to obtain resonant tunneling and other desired effects. The no-common-atom InAs/GaSb and InAs/AlSb interfaces would present opportunities for engineering interface potentials for optimizing Rashba spin splitting

New tunnel diode for zero-bias direct detection for millimeter-wave imagers

High-resolution passive millimeter wave imaging cameras require per pixel detector circuitry that is simple, has high sensitivity, low noise, and low power. Detector diodes that do not require bias or local oscillator input, and have high cutoff frequencies are strongly preferred. In addition, they must be manufacturable in large quantities with reasonable uniformity and reproducibility. Such diodes have not been obtainable for W-band and above. We are developing zero-bias square-law detector diodes based on InAs/Alsb/GaAlSb heterostructures which for the first time offer a cost-effective solution for large array formats. The diodes have a high frequency response and are relatively insensitive to growth and process variables. The large zero- bias non-linearity in current floor necessary for detection arises from interband tunneling between the InAs and the GaAlSb layers. Video resistance can be controlled by varying an Alsb tunnel barrier layer thickness. Our analysis shows that capacitance can be further decreased and sensitivity increased by shrinking the diode area, as the diode can have very high current density. DC and RF characterization of these devices and an estimate of their ultimate frequency performance in comparison with commercially available diodes are presented

Departures From Axisymmetric Morphology and Dynamics in Spiral Galaxies

New HI synthesis data have been obtained for six face-on galaxies with the Very Large Array. These data and reanalyses of three additional data sets make up a sample of nine face-on galaxies analyzed for deviations from axisymmetry in morphology and dynamics. This sample represents a subsample of galaxies already analyzed for morphological symmetry properties in the R-band. Four quantitative measures of dynamical nonaxisymmetry are compared to one another and to the quantitative measures of morphological asymmetry in HI and R-band to investigate the relationships between nonaxisymmetric morphology and dynamics. We find no significant relationship between asymmetric morphology and most of the dynamical measures in our sample. A possible relationship is found, however, between morphology and dynamical position angle differences between approaching and receding sides of the galaxy.Comment: 24 pages, 19 figures, AASTeX, accepted for publication in AJ, postscript figures available at ftp://culebra.tn.cornell.edu/pub/david/figures.tar.g

Safe Crossover of Neural Networks Through Neuron Alignment

One of the main and largely unexplored challenges in evolving the weights of neural networks using genetic algorithms is to find a sensible crossover operation between parent networks. Indeed, naive crossover leads to functionally damaged offspring that do not retain information from the parents. This is because neural networks are invariant to permutations of neurons, giving rise to multiple ways of representing the same solution. This is often referred to as the competing conventions problem. In this paper, we propose a two-step safe crossover(SC) operator. First, the neurons of the parents are functionally aligned by computing how well they correlate, and only then are the parents recombined. We compare two ways of measuring relationships between neurons: Pairwise Correlation (PwC) and Canonical Correlation Analysis (CCA). We test our safe crossover operators (SC-PwC and SC-CCA) on MNIST and CIFAR-10 by performing arithmetic crossover on the weights of feed-forward neural network pairs. We show that it effectively transmits information from parents to offspring and significantly improves upon naive crossover. Our method is computationally fast,can serve as a way to explore the fitness landscape more efficiently and makes safe crossover a potentially promising operator in future neuroevolution research and applications