Quantum Circuit Optimization by Graph Coloring

TL;DR

This paper demonstrates that optimizing quantum circuit depth for commuting operations can be formulated as a graph coloring problem, enabling the use of graph algorithms for circuit optimization.

Contribution

It introduces a novel reduction of quantum circuit depth minimization to vertex coloring, providing a new framework for circuit optimization using existing graph algorithms.

Findings

Effective reduction of circuit depth to graph coloring problem.

Validation through numerical experiments and real quantum circuits.

Applicable to circuits like finite field multiplication and quantum Fourier transform.

Abstract

This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode non-parallelizability. The reduction leads to algorithms for circuit optimization by adopting any vertex coloring solver as an optimization backend. The approach is validated by numerical experiments as well as applications to known quantum circuits, including finite field multiplication and QFT-based addition.