19,830 research outputs found
Measurement cost of metric-aware variational quantum algorithms
Variational quantum algorithms are promising tools for near-term quantum
computers as their shallow circuits are robust to experimental imperfections.
Their practical applicability, however, strongly depends on how many times
their circuits need to be executed for sufficiently reducing shot-noise. We
consider metric-aware quantum algorithms: variational algorithms that use a
quantum computer to efficiently estimate both a matrix and a vector object. For
example, the recently introduced quantum natural gradient approach uses the
quantum Fisher information matrix as a metric tensor to correct the gradient
vector for the co-dependence of the circuit parameters. We rigorously
characterise and upper bound the number of measurements required to determine
an iteration step to a fixed precision, and propose a general approach for
optimally distributing samples between matrix and vector entries. Finally, we
establish that the number of circuit repetitions needed for estimating the
quantum Fisher information matrix is asymptotically negligible for an
increasing number of iterations and qubits.Comment: 17 pages, 3 figure
Monte Carlo techniques for real-time quantum dynamics
The stochastic-gauge representation is a method of mapping the equation of
motion for the quantum mechanical density operator onto a set of equivalent
stochastic differential equations. One of the stochastic variables is termed
the "weight", and its magnitude is related to the importance of the stochastic
trajectory. We investigate the use of Monte Carlo algorithms to improve the
sampling of the weighted trajectories and thus reduce sampling error in a
simulation of quantum dynamics. The method can be applied to calculations in
real time, as well as imaginary time for which Monte Carlo algorithms are
more-commonly used. The method is applicable when the weight is guaranteed to
be real, and we demonstrate how to ensure this is the case. Examples are given
for the anharmonic oscillator, where large improvements over stochastic
sampling are observed.Comment: 28 pages, submitted to J. Comp. Phy
Using growing RBF-nets in rubber industry process control
This paper describes the use of a Radial Basis Function (RBF) neural network in the approximation of process parameters for the extrusion of a rubber profile in tyre production. After introducing the rubber industry problem, the RBF network model and the RBF net learning algorithm are developed, which uses a growing number of RBF units to compensate the approximation error up to the desired error limit. Its performance is shown for simple analytic examples. Then the paper describes the modelling of the industrial problem. Simulations show good results, even when using only a few training samples. The paper is concluded by a discussion of possible systematic error influences, improvements and potential generalisation benefits. Keywords: Adaptive process control; Parameter estimation; RBF-nets; Rubber extrusio
Effects of Destriping Errors on CMB Polarisation Power Spectra and and Pixel Noise Covariances
Low frequency detector noise in CMB experiments must be corrected to produce
faithful maps of the temperature and polarization anisotropies. For a
Planck-type experiment the low frequency noise corrections lead to residual
stripes in the maps. Here I show that for a ring torus and idealised detector
geometry it is possible to calculate analytically the effects of destriping
errors on the temperature and polarization power spectra. It is also possible
to compute the pixel-pixel noise covariances for maps of arbitrary resolution.
The analytic model is compared to numerical simulations using a realistic
detector and scanning geometries. We show that Planck polarization maps at 143
GHz should be signal dominated on large scales. Destriping errors are the
dominant source of noise for the temperature and polarization power spectra at
multipoles ell < 10. A fast Monte-Carlo method for characterising noise,
including destriping errors, is described that can be applied to Planck. This
Monte-Carlo method can be used to quantify pixel-pixel noise covariances and to
remove noise biases in power spectrum estimates.Comment: 19 pages submitted to MNRA
A Spatial Quantile Regression Hedonic Model of Agricultural Land Prices
Abstract Land price studies typically employ hedonic analysis to identify the impact of land characteristics on price. Owing to the spatial fixity of land, however, the question of possible spatial dependence in agricultural land prices arises. The presence of spatial dependence in agricultural land prices can have serious consequences for the hedonic model analysis. Ignoring spatial autocorrelation can lead to biased estimates in land price hedonic models. We propose using a flexible quantile regression-based estimation of the spatial lag hedonic model allowing for varying effects of the characteristics and, more importantly, varying degrees of spatial autocorrelation. In applying this approach to a sample of agricultural land sales in Northern Ireland we find that the market effectively consists of two relatively separate segments. The larger of these two segments conforms to the conventional hedonic model with no spatial lag dependence, while the smaller, much thinner market segment exhibits considerable spatial lag dependence. Un mod�le h�donique � r�gression quantile spatiale des prix des terrains agricoles R�sum� Les �tudes sur le prix des terrains font g�n�ralement usage d'une analyse h�donique pour identifier l'impact des caract�ristiques des terrains sur le prix. Toutefois, du fait de la fixit� spatiale des terrains, la question d'une �ventuelle d�pendance spatiale sur la valeur des terrains agricoles se pose. L'existence d'une d�pendance spatiale dans le prix des terrains agricoles peut avoir des cons�quences importantes sur l'analyse du mod�le h�donique. En ignorant cette corr�lation s�rielle, on s'expose au risque d'�valuations biais�es des mod�les h�doniques du prix des terrains. Nous proposons l'emploi d'une estimation � base de r�gression flexible du mod�le h�donique � d�calage spatial, tenant compte de diff�rents effets des caract�ristiques, et surtout de diff�rents degr�s de corr�lations s�rielles spatiales. En appliquant ce principe � un �chantillon de ventes de terrains agricoles en Irlande du Nord, nous d�couvrons que le march� se compose de deux segments relativement distincts. Le plus important de ces deux segments est conforme au mod�le h�donique traditionnel, sans d�pendance du d�calage spatial, tandis que le deuxi�me segment du march�, plus petit et beaucoup plus �troit, pr�sente une d�pendance consid�rable du d�calage spatial. Un modelo hed�nico de regresi�n cuantil espacial de los precios del terreno agr�cola Resumen T�picamente, los estudios del precio de la tierra emplean un an�lisis hed�nico para identificar el impacto de las caracter�sticas de la tierra sobre el precio. No obstante, debido a la fijeza espacial de la tierra, surge la cuesti�n de una posible dependencia espacial en los precios del terreno agr�cola. La presencia de dependencia espacial en los precios del terreno agr�cola puede tener consecuencias graves para el modelo de an�lisis hed�nico. Ignorar la autocorrelaci�n espacial puede conducir a estimados parciales en los modelos hed�nicos del precio de la tierra. Proponemos el uso de una valoraci�n basada en una regresi�n cuantil flexible del modelo hed�nico del lapso espacial que tenga en cuenta los diversos efectos de las caracter�sticas y, particularmente, los diversos grados de autocorrelaci�n espacial. Al aplicar este planteamiento a una muestra de ventas de terreno agr�cola en Irlanda del Norte, descubrimos que el mercado consiste efectivamente de dos segmento relativamente separados. El m�s grande de estos dos segmentos se ajusta al modelo hed�nico convencional sin dependencia del lapso espacial, mientras que el segmento m�s peque�o, y mucho m�s fino, muestra una dependencia considerable del lapso espacial.Spatial lag, quantile regression, hedonic model, C13, C14, C21, Q24,
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
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