The Universe and The Quantum Computer

TL;DR

This paper explores the mathematical parallels between the universe's histories approach and measurement-based quantum computation, proposing a quantum measure theory that unifies their frameworks and analyzing interference phenomena.

Contribution

It introduces a quantum measure and integration theory for the universe, showing its uniqueness and applying it to quantum computational paths and interference effects.

Findings

Quantum measure is unique under physical principles

Total interference in finite paths sums to zero

Constructive and destructive interference are balanced

Abstract

It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation. Although a rigorous concrete model for the universe has not been completed, a quantum measure and integration theory has been developed which may be useful for future progress. In this work we show that the quantum integral is the unique functional satisfying certain basic physical and mathematical principles. Since the set of paths (or trajectories) for a quantum computer is finite, this theory is easier to treat and more developed. We observe that the sum of the quantum measures of the paths is unity and the total interference vanishes. Thus, constructive interference is always balanced by an equal amount of destructive interference. As an example we consider a simplified two-slit experiment