We have surveyed various contrasting and sometimes overlapping conceptions of computation: classical computation, connectionist computation, neural computation, formal-syntactic computation, content-involving computation, information-processing computation, functional computation, structuralist computation, and mechanistic computation.
For now, for most computations, classical computers are still a better value per dollar, and it's not clear that quantum computers will ever be able to match them.
We are interested in exploring the subtheory from a computational point of view and especially in restrictions on the assumptions of T that allow us to return from hyper-computation to classical computation.
The encoding shows little more than embeddibility of the rules of computation of classical truth-table logic in λ-calculus.
Moreover, the comparison with a Finite Element simulation presents the same order of magnitude, however, it shows that direct computations using classical FE codes are difficult to perform in terms of computation times and stability if an explicit integration scheme is chosen.
Typical topics of this non-typical field include, but are not limited to physics of computation, non-classical logics, new complexity measures, novel hardware, mechanical, chemical and quantum computing.
Quantum computers are thus capable of performing any computation which a classical deterministic computer can do.
Although some researchers suggest a fundamental opposition between classical computation and neural network computation, it seems more accurate to identify two modeling traditions that overlap in certain cases but not others (cf. Boden 1991; Piccinini 2008b).
This is presented in the context of classically controlled quantum computation where a classical program controls a sequence of quantum operations, i.e. unitary transformations and measurements acting on a quantum memory.
A surprising feature of quantum computing is that it allows computing certain functions much faster than any known classical computation (Shor 1994).
Before attacking this problem, we should first convince ourselves that quantum computers can be harnessed to perform standard, classical, computation without any "speed-up".
