4,375 research outputs found
Witnessing eigenstates for quantum simulation of Hamiltonian spectra
The efficient calculation of Hamiltonian spectra, a problem often intractable
on classical machines, can find application in many fields, from physics to
chemistry. Here, we introduce the concept of an "eigenstate witness" and
through it provide a new quantum approach which combines variational methods
and phase estimation to approximate eigenvalues for both ground and excited
states. This protocol is experimentally verified on a programmable silicon
quantum photonic chip, a mass-manufacturable platform, which embeds entangled
state generation, arbitrary controlled-unitary operations, and projective
measurements. Both ground and excited states are experimentally found with
fidelities >99%, and their eigenvalues are estimated with 32-bits of precision.
We also investigate and discuss the scalability of the approach and study its
performance through numerical simulations of more complex Hamiltonians. This
result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with
minor typos corrected.
Statistical and Computational Tradeoff in Genetic Algorithm-Based Estimation
When a Genetic Algorithm (GA), or a stochastic algorithm in general, is
employed in a statistical problem, the obtained result is affected by both
variability due to sampling, that refers to the fact that only a sample is
observed, and variability due to the stochastic elements of the algorithm. This
topic can be easily set in a framework of statistical and computational
tradeoff question, crucial in recent problems, for which statisticians must
carefully set statistical and computational part of the analysis, taking
account of some resource or time constraints. In the present work we analyze
estimation problems tackled by GAs, for which variability of estimates can be
decomposed in the two sources of variability, considering some constraints in
the form of cost functions, related to both data acquisition and runtime of the
algorithm. Simulation studies will be presented to discuss the statistical and
computational tradeoff question.Comment: 17 pages, 5 figure
Constructive Preference Elicitation over Hybrid Combinatorial Spaces
Preference elicitation is the task of suggesting a highly preferred
configuration to a decision maker. The preferences are typically learned by
querying the user for choice feedback over pairs or sets of objects. In its
constructive variant, new objects are synthesized "from scratch" by maximizing
an estimate of the user utility over a combinatorial (possibly infinite) space
of candidates. In the constructive setting, most existing elicitation
techniques fail because they rely on exhaustive enumeration of the candidates.
A previous solution explicitly designed for constructive tasks comes with no
formal performance guarantees, and can be very expensive in (or unapplicable
to) problems with non-Boolean attributes. We propose the Choice Perceptron, a
Perceptron-like algorithm for learning user preferences from set-wise choice
feedback over constructive domains and hybrid Boolean-numeric feature spaces.
We provide a theoretical analysis on the attained regret that holds for a large
class of query selection strategies, and devise a heuristic strategy that aims
at optimizing the regret in practice. Finally, we demonstrate its effectiveness
by empirical evaluation against existing competitors on constructive scenarios
of increasing complexity.Comment: AAAI 2018, computing methodologies, machine learning, learning
paradigms, supervised learning, structured output
Learning Large-Scale Bayesian Networks with the sparsebn Package
Learning graphical models from data is an important problem with wide
applications, ranging from genomics to the social sciences. Nowadays datasets
often have upwards of thousands---sometimes tens or hundreds of thousands---of
variables and far fewer samples. To meet this challenge, we have developed a
new R package called sparsebn for learning the structure of large, sparse
graphical models with a focus on Bayesian networks. While there are many
existing software packages for this task, this package focuses on the unique
setting of learning large networks from high-dimensional data, possibly with
interventions. As such, the methods provided place a premium on scalability and
consistency in a high-dimensional setting. Furthermore, in the presence of
interventions, the methods implemented here achieve the goal of learning a
causal network from data. Additionally, the sparsebn package is fully
compatible with existing software packages for network analysis.Comment: To appear in the Journal of Statistical Software, 39 pages, 7 figure
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