37,410 research outputs found
Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation
We consider a linear stochastic fluid network under Markov modulation, with a
focus on the probability that the joint storage level attains a value in a rare
set at a given point in time. The main objective is to develop efficient
importance sampling algorithms with provable performance guarantees. For linear
stochastic fluid networks without modulation, we prove that the number of runs
needed (so as to obtain an estimate with a given precision) increases
polynomially (whereas the probability under consideration decays essentially
exponentially); for networks operating in the slow modulation regime, our
algorithm is asymptotically efficient. Our techniques are in the tradition of
the rare-event simulation procedures that were developed for the sample-mean of
i.i.d. one-dimensional light-tailed random variables, and intensively use the
idea of exponential twisting. In passing, we also point out how to set up a
recursion to evaluate the (transient and stationary) moments of the joint
storage level in Markov-modulated linear stochastic fluid networks
Reliable quantum certification for photonic quantum technologies
A major roadblock for large-scale photonic quantum technologies is the lack
of practical reliable certification tools. We introduce an experimentally
friendly - yet mathematically rigorous - certification test for experimental
preparations of arbitrary m-mode pure Gaussian states, pure non-Gaussian states
generated by linear-optical circuits with n-boson Fock-basis states as inputs,
and states of these two classes subsequently post-selected with local
measurements on ancillary modes. The protocol is efficient in m and the inverse
post-selection success probability for all Gaussian states and all mentioned
non-Gaussian states with constant n. We follow the mindset of an untrusted
prover, who prepares the state, and a skeptic certifier, with classical
computing and single-mode homodyne-detection capabilities only. No assumptions
are made on the type of noise or capabilities of the prover. Our technique
exploits an extremality-based fidelity bound whose estimation relies on
non-Gaussian state nullifiers, which we introduce on the way as a byproduct
result. The certification of many-mode photonic networks, as those used for
photonic quantum simulations, boson samplers, and quantum metrology, is now
within reach.Comment: 8 pages + 20 pages appendix, 2 figures, results generalized to
scenarios with post-selection, presentation improve
Spectral Methods from Tensor Networks
A tensor network is a diagram that specifies a way to "multiply" a collection
of tensors together to produce another tensor (or matrix). Many existing
algorithms for tensor problems (such as tensor decomposition and tensor PCA),
although they are not presented this way, can be viewed as spectral methods on
matrices built from simple tensor networks. In this work we leverage the full
power of this abstraction to design new algorithms for certain continuous
tensor decomposition problems.
An important and challenging family of tensor problems comes from orbit
recovery, a class of inference problems involving group actions (inspired by
applications such as cryo-electron microscopy). Orbit recovery problems over
finite groups can often be solved via standard tensor methods. However, for
infinite groups, no general algorithms are known. We give a new spectral
algorithm based on tensor networks for one such problem: continuous
multi-reference alignment over the infinite group SO(2). Our algorithm extends
to the more general heterogeneous case.Comment: 30 pages, 8 figure
The chronotron: a neuron that learns to fire temporally-precise spike patterns
In many cases, neurons process information carried by the precise timing of spikes. Here we show how neurons can learn to generate specific temporally-precise output spikes in response to input spike patterns, thus processing and memorizing information that is fully temporally coded, both as input and as output. We introduce two new supervised learning rules for spiking neurons with temporal coding of information (chronotrons), one that is analytically-derived and highly efficient, and one that has a high degree of biological plausibility. We show how chronotrons can learn to classify their inputs and we study their memory capacity
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