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Precise measurements of parameters in the PMNS framework might lead to new physics beyond the Standard Model. However, they are incredibly challenging to determine in neutrino oscillation experiments. Quantum simulations can be a powerful supplementary tool to study these phenomenologies. In today's noisy quantum hardware, encoding neutrinos in a multi-qubit system requires a redundant basis and tricky entangling gates. We encode a three-flavor neutrino in a superconducting qutrit and study its oscillations using PMNS theory with time evolution expressed in terms of single qutrit gates. The qutrit is engineered from the multi-level structure of IBM transmon devices. High-fidelity gate control and readout are fine-tuned using programming microwave pulses using a high-level language. Our quantum simulations on real hardware match well to analytical calculations in three oscillation cases: vacuum, interaction with matter, and CP-violation.