9,083 research outputs found
Superior memory efficiency of quantum devices for the simulation of continuous-time stochastic processes
Continuous-time stochastic processes pervade everyday experience, and the
simulation of models of these processes is of great utility. Classical models
of systems operating in continuous-time must typically track an unbounded
amount of information about past behaviour, even for relatively simple models,
enforcing limits on precision due to the finite memory of the machine. However,
quantum machines can require less information about the past than even their
optimal classical counterparts to simulate the future of discrete-time
processes, and we demonstrate that this advantage extends to the
continuous-time regime. Moreover, we show that this reduction in the memory
requirement can be unboundedly large, allowing for arbitrary precision even
with a finite quantum memory. We provide a systematic method for finding
superior quantum constructions, and a protocol for analogue simulation of
continuous-time renewal processes with a quantum machine.Comment: 13 pages, 8 figures, title changed from original versio
The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications
The principle goal of computational mechanics is to define pattern and
structure so that the organization of complex systems can be detected and
quantified. Computational mechanics developed from efforts in the 1970s and
early 1980s to identify strange attractors as the mechanism driving weak fluid
turbulence via the method of reconstructing attractor geometry from measurement
time series and in the mid-1980s to estimate equations of motion directly from
complex time series. In providing a mathematical and operational definition of
structure it addressed weaknesses of these early approaches to discovering
patterns in natural systems.
Since then, computational mechanics has led to a range of results from
theoretical physics and nonlinear mathematics to diverse applications---from
closed-form analysis of Markov and non-Markov stochastic processes that are
ergodic or nonergodic and their measures of information and intrinsic
computation to complex materials and deterministic chaos and intelligence in
Maxwellian demons to quantum compression of classical processes and the
evolution of computation and language.
This brief review clarifies several misunderstandings and addresses concerns
recently raised regarding early works in the field (1980s). We show that
misguided evaluations of the contributions of computational mechanics are
groundless and stem from a lack of familiarity with its basic goals and from a
failure to consider its historical context. For all practical purposes, its
modern methods and results largely supersede the early works. This not only
renders recent criticism moot and shows the solid ground on which computational
mechanics stands but, most importantly, shows the significant progress achieved
over three decades and points to the many intriguing and outstanding challenges
in understanding the computational nature of complex dynamic systems.Comment: 11 pages, 123 citations;
http://csc.ucdavis.edu/~cmg/compmech/pubs/cmr.ht
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