arXiv subjects
Publications and source records attributed to Dalida Monti.
We provide a justification of the quantum speed-up based on the complementary roles played by the reversible preparation of an entangled state before measurement and by the final measurement action.
The higher than classical efficiency exhibited by some quantum algorithms is here ascribed to their non-mechanistic character, which becomes evident by joining the notions of entanglement and quantum measurement. Measurement analogically sets a (partial) constraint on the output of the computation of a hard-to-reverse function. This constraint goes back in time along the reversible computation process, computing the reverse function, which yields quantum efficiency. The evolution, comprising wave function collapse (here a revamped notion), is non-mechanistic as it is driven by both an initial condition and a final constraint. It seems that the more the output is constrained by measurement, the higher can be the efficiency. Setting a complete constraint, by means of a special Zeno effect, yields (speculatively) NP-complete=P.
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.
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a particle statistics symmetry cannot affect the course of such an evolution. We try to avoid this possible deadlock by introducing a generalized (counterfactual, blunt) formulation where this type of symmetry becomes a watchdog effect shaping the evolution of a unitary computation process. The work is an exploration.
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.
In the reductionistic approach, mechanisms are divided into simpler parts interconnected in some standard way (e.g. by a mechanical transmission). We explore the possibility of porting reductionism in quantum operations. Conceptually, first parts are made independent of each other by assuming that all ``transmissions'' are removed. The overall state would thus become a superposition of tensor products of the eigenstates of the independent parts. Transmissions are restored by projecting off all the tensor products which violate them. This would be performed by particle statistics; the plausibility of this scheme is based on the interpretation of particle statistics as projection. The problem of the satisfiability of a Boolean network is approached in this way. This form of quantum reductionism appears to be able of taming the quantum whole without clipping its richness.