Constrained quantum annealing of graph coloring

TL;DR

This paper explores a quantum annealing method for graph coloring that naturally enforces constraints, reduces Hilbert space size, and leverages degeneracy, with simulations providing insights into its effectiveness.

Contribution

It introduces a constraint-preserving quantum annealing approach with a reduced Hilbert space and explores the role of degeneracy in solving graph coloring problems.

Findings

Simulations show promising results for small systems.

The approach naturally satisfies constraints without penalty terms.

Degeneracy in the ground state is beneficial for the method.

Abstract

We investigate a quantum annealing approach based on real-time quantum dynamics for graph coloring. In this approach, a driving Hamiltonian is chosen so that constraints are naturally satisfied without penalty terms, and the dimension of the Hilbert space is considerably reduced. The total Hamiltonian, which consists of driving and problem Hamiltonians, resembles a disordered quantum spin chain. The ground state of the problem Hamiltonian for graph coloring is degenerate. This degeneracy is advantageous and is characteristic of this approach. Real-time quantum simulations in a small system demonstrate interesting results and provide some insight into quantum annealing.