NP-complete Problems and Physical Reality

TL;DR

This paper surveys various physical proposals for solving NP-complete problems efficiently, analyzing their potential and limitations, and discusses how studying these proposals can deepen our understanding of both computation and physics.

Contribution

It provides a comprehensive review of physical approaches to solving NP-complete problems and discusses their implications for physics and computational complexity.

Findings

Most proposals are unlikely to solve NP-complete problems efficiently.

Studying these proposals offers insights into the relationship between physics and computation.

Some experimental results on soap bubbles demonstrate physical approaches to computation.

Abstract

Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden variables, relativistic time dilation, analog computing, Malament-Hogarth spacetimes, quantum gravity, closed timelike curves, and "anthropic computing." The section on soap bubbles even includes some "experimental" results. While I do not believe that any of the proposals will let us solve NP-complete problems efficiently, I argue that by studying them, we can learn something not only about computation but also about physics.