Efficient estimation of perturbative error with cellular automata

Understand

From celestial mechanics to quantum theory of atoms and molecules, perturbation theory has played a central role in natural sciences.

• Particularly in quantum mechanics, the amount of information needed for specifying the state of a many-body system commonly scales exponentially as the system size.
• This poses a fundamental difficulty in using perturbation theory at arbitrary order.
• As one computes the terms in the perturbation series at increasingly higher orders, it is often important to determine whether the series converges and if so, what is an accurate estimation of the total error that comes from the next order of perturbation up to infinity.