Quantum problem solving as simultaneous computation

TL;DR

This paper presents a novel interpretation of quantum computation as a form of simultaneous problem solving, where solutions emerge through a reversible, many-body interaction influenced by all constraints at once, akin to a physical, time-symmetric process.

Contribution

It introduces an alternative view of quantum algorithms as a physical, reversible process involving many-body interactions, extending classical problem solving models to quantum systems.

Findings

Quantum speed-up interpreted as 'precognition' via time-symmetric state reduction.

Reversible, nondeterministic problem solving modeled through many-body interactions.

Bounded by an entropic inequality related to state vector reduction.

Abstract

I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem under the simultaneous influence of all the problem constraints. This requires a perfectly accurate, rigid, and reversible relation between the coordinates of the machine parts - the machine can be considered the many body generalization of another perfect machine, the bounching ball model of reversible computation. The mathematical description of the machine, as it is, is applicable to quantum problem solving, an extension of the quantum algorithms that comprises the physical representation of the problem-solution interdependence. The perfect relation between the coordinates of the machine parts is transferred to the populations of the reduced density operators of the parts of the computer register. The solution of the problem is reversibly and nondeterministically produced under the simultaneous influence of the state before measurement and the quantum principle. At the light of the present notion of simultaneous computation, the quantum speed up turns out to be "precognition" of the solution, namely the reduction of the initial ignorance of the solution due to backdating, to before running the algorithm, a time-symmetric part of the state vector reduction on the solution; as such, it is bounded by state vector reduction through an entropic inequality. PACS numbers: 03.67.Lx, 01.55.+b, 01.70.+w