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Recent hardware demonstrations and advances in circuit compilation have madequantum computing with higher-dimensional systems (qudits) on near-term devicesan attractive possibility. Some problems have more natural or optimal encodingsusing qudits over qubits. We explore this potential by formulating graph3-coloring, a well-known and difficult problem with practical applications,using qutrits, and solve it using the quantum approximate optimizationalgorithm (QAOA). Qutrit-based cost and mixer Hamiltonians are constructedalong with appropriate quantum circuits using qutrit gates. We run noiselesssimulations using PennyLane to compare the formulation against qubit-basedQAOA, and analyze the solution quality and resources required. Preliminaryresults show that the qutrit encoding finds more accurate solutions with acomparable set of hyperparameters, uses half as many qudits, and has a notablysmaller circuit depth per layer than an efficient qubit encoding. This worksuggests that qutrits may be useful in solving some problems on near-termdevices, however further work is required to assess their potential in a noisyenvironment.

Exploring the Potential of Qutrits for Quantum Optimization of Graph Coloring