  Qutrits, three-level quantum systems, have the advantage of potentially
requiring fewer components than the typically used two-level qubits to
construct equivalent quantum circuits. This work investigates the potential of
qutrit parametric circuits in machine learning classification applications. We
propose and evaluate different data-encoding schemes for qutrits, and find that
the classification accuracy varies significantly depending on the used
encoding. We therefore propose a training method for encoding optimization that
allows to consistently achieve high classification accuracy. Our theoretical
analysis and numerical simulations indicate that the qutrit classifier can
achieve high classification accuracy using fewer components than a comparable
qubit system. We showcase the qutrit classification using the optimized
encoding method on superconducting transmon qutrits, demonstrating the
practicality of the proposed method on noisy hardware. Our work demonstrates
high-precision ternary classification using fewer circuit elements,
establishing qutrit parametric quantum circuits as a viable and efficient tool
for quantum machine learning applications.
