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Abstract

Variational Quantum Algorithms (VQAs) are a noise-resilient class of algorithms that have potential real-world applications for Noisy Intermediate Scale Quantum (NISQ) devices. Some NISQ devices are based on physical systems with more than two distinct measurable states, which can be utilized as qudits. VQAs have been developed using qudits, but it is unclear if they will outperform qubit-based VQAs. We study the performance of one VQA, the Quantum Approximate Optimization Algorithm (QAOA), to solve graph three colouring, an NP-complete problem with applications in scheduling, using both qubits and qutrits, three-dimensional quantum states. Qutrits efficiently encode the three colouring problem, and we find that the qutrit QAOA circuit requires fewer resources; however, physical implementations of qutrits have increased error. To understand the effect of this noise, we develop a noise model for both qubits and qutrits, building on previously developed noise models and basing each source of error on experimentally verified metrics of superconducting transmon qubit and qutrit devices. To implement our qutrit noise model, we developed a noisy qutrit simulator, DefaultQutritMixed [1], adding it to PennyLane, an open-source quantum software framework. Simulations of our circuits with pretrained parameters showed that the current qutrit transmon device’s entangling gate’s execution time and infidelity are too high for the qutrit’s efficient encoding and advantage in circuit resources to account for. It would take approximately a 3 − 3.5× increase in damping (T₁ ) and decoherence (T₂ ) times and a 3 − 3.5× reduction in entangling gate error for the qutrit circuit’s noise to be comparable to that of the qubits. We do not find strong evidence to suggest that this can be achieved through qutrit device specific optimizations. An alternative two-qutrit gate, the state-controlled subspace X gate, which is implementable on qutrit transmon devices, may have high enough fidelity for a qutrit circuit’s noise to be equivalent to that of a qubit. Finally, we find that the qubit’s noise is much more disruptive to training the QAOA parameters. Therefore, a qutrit system would be a better candidate for solving larger problems that classical methods struggle with if it were equivalently noisy to a qubit system.