Interference effects in computation

The law of addition of probabilities by means of complex probability amplitudes with its powerful interference consequences, unique to quantum mechanics, is shown to apply elsewhere. The two parts of quantum mechanics: an unvisualizable dynamics and a visualizable concretization (the latter corresponding to reduction of the state vector when a measurement is made) are shown to have a correspondence in computation. Namely, a conceptual structure called a field (of the real numbers, say), its operations, and the concretization of that structure is done by means of a (digital) computer (the latter is interpreted as playing the role of a measuring apparatus). The probabilistic state-reduction operator of quantum mechanics is replaced by a deterministic operation, an extension of rounding. State, wave function, dynamics, observation, uncertainty, and nonlocality are shown to have their counterparts in the new model. The algorithmic counterpart of the double slit experiment to validate the existence of interference in the new framework is defined and performed. A notion of spin in computation is introduced. In an appendix, we comment on how this model impacts a speculative theory of the mind by Penrose.