We describe a plausible-speculative form of quantum computation which exploits particle (fermionic, bosonic) statistics, under a generalized, counterfactual interpretation thereof. In the idealized situation of an isolated system, it seems that this form of computation yields to NP-complete=P.
The topical quantum computation paradigm is a transposition of the Turing machine into the quantum framework. Implementations based on this paradigm have limitations as to the number of: qubits, computation steps, efficient quantum algorithms (found so far). A new exclusively quantum paradigm (with no classical counterpart) is propounded, based on the speculative notion of continuous uncomplete von Neumann measurement. Under such a notion, NP-complete is equal to P. This can provide a mathematical framework for the search of implementable paradigms, possibly exploiting particle statistics.
In the diakoptic approach, mechanisms are divided into simpler parts interconnected in some standard way (say by a "mechanical connection''). We explore the possibility of applying this approach to quantum mechanisms: the specialties of the quantum domain seem to yield a richer result. First parts are made independent of each other by assuming that connections are removed. The overall state would thus become a superposition of tensor products of the eigenstates of the independent parts. Connections are restored by projecting off all the tensor products which violate them. This would be performed by particle statistics, under a special interpretation thereof. The NP-complete problem of testing the satisfiability of a Boolean network is approached in this way. The diakoptic approach appears to be able of taming the quantum whole without clipping its richness.