22,207 research outputs found
Interactive Chemical Reactivity Exploration
Elucidating chemical reactivity in complex molecular assemblies of a few
hundred atoms is, despite the remarkable progress in quantum chemistry, still a
major challenge. Black-box search methods to find intermediates and
transition-state structures might fail in such situations because of the
high-dimensionality of the potential energy surface. Here, we propose the
concept of interactive chemical reactivity exploration to effectively introduce
the chemist's intuition into the search process. We employ a haptic pointer
device with force-feedback to allow the operator the direct manipulation of
structures in three dimensions along with simultaneous perception of the
quantum mechanical response upon structure modification as forces. We elaborate
on the details of how such an interactive exploration should proceed and which
technical difficulties need to be overcome. All reactivity-exploration concepts
developed for this purpose have been implemented in the Samson programming
environment.Comment: 36 pages, 14 figure
Physical consequences of PNP and the DMRG-annealing conjecture
Computational complexity theory contains a corpus of theorems and conjectures
regarding the time a Turing machine will need to solve certain types of
problems as a function of the input size. Nature {\em need not} be a Turing
machine and, thus, these theorems do not apply directly to it. But {\em
classical simulations} of physical processes are programs running on Turing
machines and, as such, are subject to them. In this work, computational
complexity theory is applied to classical simulations of systems performing an
adiabatic quantum computation (AQC), based on an annealed extension of the
density matrix renormalization group (DMRG). We conjecture that the
computational time required for those classical simulations is controlled
solely by the {\em maximal entanglement} found during the process. Thus, lower
bounds on the growth of entanglement with the system size can be provided. In
some cases, quantum phase transitions can be predicted to take place in certain
inhomogeneous systems. Concretely, physical conclusions are drawn from the
assumption that the complexity classes {\bf P} and {\bf NP} differ. As a
by-product, an alternative measure of entanglement is proposed which, via
Chebyshev's inequality, allows to establish strict bounds on the required
computational time.Comment: Accepted for publication in JSTA
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