13,835 research outputs found
Importance Sampling and its Optimality for Stochastic Simulation Models
We consider the problem of estimating an expected outcome from a stochastic
simulation model. Our goal is to develop a theoretical framework on importance
sampling for such estimation. By investigating the variance of an importance
sampling estimator, we propose a two-stage procedure that involves a regression
stage and a sampling stage to construct the final estimator. We introduce a
parametric and a nonparametric regression estimator in the first stage and
study how the allocation between the two stages affects the performance of the
final estimator. We analyze the variance reduction rates and derive oracle
properties of both methods. We evaluate the empirical performances of the
methods using two numerical examples and a case study on wind turbine
reliability evaluation.Comment: 37 pages, 6 figures, 2 tables. Accepted to the Electronic Journal of
Statistic
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
Introduction to Quantum Information Processing
As a result of the capabilities of quantum information, the science of
quantum information processing is now a prospering, interdisciplinary field
focused on better understanding the possibilities and limitations of the
underlying theory, on developing new applications of quantum information and on
physically realizing controllable quantum devices. The purpose of this primer
is to provide an elementary introduction to quantum information processing, and
then to briefly explain how we hope to exploit the advantages of quantum
information. These two sections can be read independently. For reference, we
have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/prhtm
On the robustness of bucket brigade quantum RAM
We study the robustness of the bucket brigade quantum random access memory
model introduced by Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett. 100,
160501 (2008)]. Due to a result of Regev and Schiff [ICALP '08 pp. 773], we
show that for a class of error models the error rate per gate in the bucket
brigade quantum memory has to be of order (where is the
size of the memory) whenever the memory is used as an oracle for the quantum
searching problem. We conjecture that this is the case for any realistic error
model that will be encountered in practice, and that for algorithms with
super-polynomially many oracle queries the error rate must be
super-polynomially small, which further motivates the need for quantum error
correction. By contrast, for algorithms such as matrix inversion [Phys. Rev.
Lett. 103, 150502 (2009)] or quantum machine learning [Phys. Rev. Lett. 113,
130503 (2014)] that only require a polynomial number of queries, the error rate
only needs to be polynomially small and quantum error correction may not be
required. We introduce a circuit model for the quantum bucket brigade
architecture and argue that quantum error correction for the circuit causes the
quantum bucket brigade architecture to lose its primary advantage of a small
number of "active" gates, since all components have to be actively error
corrected.Comment: Replaced with the published version. 13 pages, 9 figure
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