Exploring the Potential of Qutrits for Quantum Optimization of Graph Coloring

TL;DR

This paper investigates using qutrits for quantum graph coloring, demonstrating that qutrit-based QAOA can achieve more accurate solutions with fewer resources compared to qubit-based approaches.

Contribution

It formulates graph 3-coloring with qutrits, constructs corresponding Hamiltonians, and compares performance against qubit-based QAOA through noiseless simulations.

Findings

Qutrit encoding yields more accurate solutions.

Qutrit approach uses half as many qudits.

Qutrit circuits have smaller depth per layer.

Abstract

Recent hardware demonstrations and advances in circuit compilation have made quantum computing with higher-dimensional systems (qudits) on near-term devices an attractive possibility. Some problems have more natural or optimal encodings using qudits over qubits. We explore this potential by formulating graph 3-coloring, a well-known and difficult problem with practical applications, using qutrits, and solve it using the quantum approximate optimization algorithm (QAOA). Qutrit-based cost and mixer Hamiltonians are constructed along with appropriate quantum circuits using qutrit gates. We run noiseless simulations using PennyLane to compare the formulation against qubit-based QAOA, and analyze the solution quality and resources required. Preliminary results show that the qutrit encoding finds more accurate solutions with a comparable set of hyperparameters, uses half as many qudits, and has a notably smaller circuit depth per layer than an efficient qubit encoding. This work suggests that qutrits may be useful in solving some problems on near-term devices, however further work is required to assess their potential in a noisy environment.