The Non-mechanistic Character of Quantum Computation

TL;DR

This paper argues that quantum computational efficiency arises from its non-mechanistic nature, where measurement constraints influence the entire reversible process, potentially collapsing complexity classes like NP and P.

Contribution

It introduces a novel perspective linking entanglement, measurement, and non-mechanistic evolution to explain quantum speedup and explores implications for computational complexity.

Findings

Quantum efficiency linked to measurement constraints

Wave function collapse modeled as non-mechanistic process

Potential collapse of NP and P classes under complete constraints

Abstract

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.