Static Quantum Computation

TL;DR

This paper introduces a model of static quantum computation where the ground state of a quantum system encodes solutions to P and NP problems, linking computational complexity with physical system dynamics.

Contribution

It proves two theorems demonstrating that universal static quantum computers can encode any P or NP problem into their ground states using polynomial resources.

Findings

Universal static quantum computers can encode P and NP problems.

Ground states of such systems represent solutions to complex problems.

Relaxation dynamics can be used to read out solutions.

Abstract

Tailoring many-body interactions among a proper quantum system endows it with computing ability by means of static quantum computation in the sense that some of the physical degrees of freedom can be used to store binary information and the corresponding binary variables satisfy some given logic relations if and only if the system is in the ground state. Two theorems are proved showing that the universal static quantum computer can encode the solutions for any P and NP problem into its ground state using only polynomial number (in the problem input size) of logic gates. The second step is to read out the solutions by relaxing the system. The time complexity is relevant when one tries to read out the solution by relaxing the system, therefore our model of static quantum computation provides a new connection between the computational complexity and the dynamics of a complex system.