The P versus NP Problem in Quantum Physics

TL;DR

This paper explores the P versus NP problem within quantum physics, analyzing how physical processes relate to computational complexity classes and highlighting a quantum process that exemplifies NP but not P.

Contribution

It introduces a physical interpretation of P and NP classes and discusses a quantum process that exemplifies the separation between them.

Findings

Identifies a quantum process in NP not contained in P.

Provides a physical perspective on computational complexity classes.

Highlights implications for quantum information processing.

Abstract

Motivated by the fact that information is encoded and processed by physical systems, the P versus NP problem is examined in terms of physical processes. In particular, we consider P as a class of deterministic, and NP as nondeterministic, polynomial-time physical processes. Based on these identifications, we review a self-reference physical process in quantum theory, which belongs to NP but cannot be contained in P.