75,714 research outputs found
The Informational Approach to Global Optimization in presence of very noisy evaluation results. Application to the optimization of renewable energy integration strategies
We consider the problem of global optimization of a function f from very
noisy evaluations. We adopt a Bayesian sequential approach: evaluation points
are chosen so as to reduce the uncertainty about the position of the global
optimum of f, as measured by the entropy of the corresponding random variable
(Informational Approach to Global Optimization, Villemonteix et al., 2009).
When evaluations are very noisy, the error coming from the estimation of the
entropy using conditional simulations becomes non negligible compared to its
variations on the input domain. We propose a solution to this problem by
choosing evaluation points as if several evaluations were going to be made at
these points. The method is applied to the optimization of a strategy for the
integration of renewable energies into an electrical distribution network
Classical capacity of a qubit depolarizing channel with memory
The classical product state capacity of a noisy quantum channel with memory
is investigated. A forgetful noise-memory channel is constructed by Markov
switching between two depolarizing channels which introduces non-Markovian
noise correlations between successive channel uses. The computation of the
capacity is reduced to an entropy computation for a function of a Markov
process. A reformulation in terms of algebraic measures then enables its
calculation. The effects of the hidden-Markovian memory on the capacity are
explored. An increase in noise-correlations is found to increase the capacity
Efficient classical simulation of noisy random quantum circuits in one dimension
Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy quantum computers can provide computational advantage over classical computers. Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device. In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via matrix product operators (MPOs) and characterize the computational power of the 1D noisy quantum system by using a metric we call MPO entanglement entropy. The latter metric is chosen because it determines the cost of classical MPO simulation. We numerically demonstrate that for the two-qubit gate error rates we considered, there exists a characteristic system size above which adding more qubits does not bring about an exponential growth of the cost of classical MPO simulation of 1D noisy systems. Specifically, we show that above the characteristic system size, there is an optimal circuit depth, independent of the system size, where the MPO entanglement entropy is maximized. Most importantly, the maximum achievable MPO entanglement entropy is bounded by a constant that depends only on the gate error rate, not on the system size. We also provide a heuristic analysis to get the scaling of the maximum achievable MPO entanglement entropy as a function of the gate error rate. The obtained scaling suggests that although the cost of MPO simulation does not increase exponentially in the system size above a certain characteristic system size, it does increase exponentially as the gate error rate decreases, possibly making classical simulation practically not feasible even with state-of-the-art supercomputers
Efficient classical simulation of noisy random quantum circuits in one dimension
Understanding the computational power of noisy intermediate-scale quantum
(NISQ) devices is of both fundamental and practical importance to quantum
information science. Here, we address the question of whether error-uncorrected
noisy quantum computers can provide computational advantage over classical
computers. Specifically, we study noisy random circuit sampling in one
dimension (or 1D noisy RCS) as a simple model for exploring the effects of
noise on the computational power of a noisy quantum device. In particular, we
simulate the real-time dynamics of 1D noisy random quantum circuits via matrix
product operators (MPOs) and characterize the computational power of the 1D
noisy quantum system by using a metric we call MPO entanglement entropy. The
latter metric is chosen because it determines the cost of classical MPO
simulation. We numerically demonstrate that for the two-qubit gate error rates
we considered, there exists a characteristic system size above which adding
more qubits does not bring about an exponential growth of the cost of classical
MPO simulation of 1D noisy systems. Specifically, we show that above the
characteristic system size, there is an optimal circuit depth, independent of
the system size, where the MPO entanglement entropy is maximized. Most
importantly, the maximum achievable MPO entanglement entropy is bounded by a
constant that depends only on the gate error rate, not on the system size. We
also provide a heuristic analysis to get the scaling of the maximum achievable
MPO entanglement entropy as a function of the gate error rate. The obtained
scaling suggests that although the cost of MPO simulation does not increase
exponentially in the system size above a certain characteristic system size, it
does increase exponentially as the gate error rate decreases, possibly making
classical simulation practically not feasible even with state-of-the-art
supercomputers.Comment: 27 pages, 9 figures, accepted for publication in Quantu
A non-linear VAD for noisy environments
This paper deals with non-linear transformations for improving the
performance of an entropy-based voice activity detector (VAD). The idea to use
a non-linear transformation has already been applied in the field of speech
linear prediction, or linear predictive coding (LPC), based on source separation
techniques, where a score function is added to classical equations in order to
take into account the true distribution of the signal. We explore the possibility
of estimating the entropy of frames after calculating its score function, instead
of using original frames. We observe that if the signal is clean, the estimated
entropy is essentially the same; if the signal is noisy, however, the frames
transformed using the score function may give entropy that is different in
voiced frames as compared to nonvoiced ones. Experimental evidence is given
to show that this fact enables voice activity detection under high noise, where
the simple entropy method fails
Convergence of algorithms for reconstructing convex bodies and directional measures
We investigate algorithms for reconstructing a convex body in from noisy measurements of its support function or its brightness
function in directions . The key idea of these algorithms is
to construct a convex polytope whose support function (or brightness
function) best approximates the given measurements in the directions
(in the least squares sense). The measurement errors are assumed
to be stochastically independent and Gaussian. It is shown that this procedure
is (strongly) consistent, meaning that, almost surely, tends to in
the Hausdorff metric as . Here some mild assumptions on the
sequence of directions are needed. Using results from the theory of
empirical processes, estimates of rates of convergence are derived, which are
first obtained in the metric and then transferred to the Hausdorff
metric. Along the way, a new estimate is obtained for the metric entropy of the
class of origin-symmetric zonoids contained in the unit ball. Similar results
are obtained for the convergence of an algorithm that reconstructs an
approximating measure to the directional measure of a stationary fiber process
from noisy measurements of its rose of intersections in directions
. Here the Dudley and Prohorov metrics are used. The methods are
linked to those employed for the support and brightness function algorithms via
the fact that the rose of intersections is the support function of a projection
body.Comment: Published at http://dx.doi.org/10.1214/009053606000000335 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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