7,220 research outputs found
Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms
We propose a scalable method for forward stochastic reachability analysis for
uncontrolled linear systems with affine disturbance. Our method uses Fourier
transforms to efficiently compute the forward stochastic reach probability
measure (density) and the forward stochastic reach set. This method is
applicable to systems with bounded or unbounded disturbance sets. We also
examine the convexity properties of the forward stochastic reach set and its
probability density. Motivated by the problem of a robot attempting to capture
a stochastically moving, non-adversarial target, we demonstrate our method on
two simple examples. Where traditional approaches provide approximations, our
method provides exact analytical expressions for the densities and probability
of capture.Comment: V3: HSCC 2017 (camera-ready copy), DOI updated, minor changes | V2:
Review comments included | V1: 10 pages, 12 figure
A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
The ability to perform classically intractable electronic structure
calculations is often cited as one of the principal applications of quantum
computing. A great deal of theoretical algorithmic development has been
performed in support of this goal. Most techniques require a scheme for mapping
electronic states and operations to states of and operations upon qubits. The
two most commonly used techniques for this are the Jordan-Wigner transformation
and the Bravyi-Kitaev transformation. However, comparisons of these schemes
have previously been limited to individual small molecules. In this paper we
discuss resource implications for the use of the Bravyi-Kitaev mapping scheme,
specifically with regard to the number of quantum gates required for
simulation. We consider both small systems which may be simulatable on
near-future quantum devices, and systems sufficiently large for classical
simulation to be intractable. We use 86 molecular systems to demonstrate that
the use of the Bravyi-Kitaev transformation is typically at least approximately
as efficient as the canonical Jordan-Wigner transformation, and results in
substantially reduced gate count estimates when performing limited circuit
optimisations.Comment: 46 pages, 11 figure
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