Qutrit-ZX Calculus on superconducting transmon qutrits

A qutrit-based quantum computer requires fewer circuit components and provides more efficient ways to compose quantum circuits than a qubit-based quantum computer. Qutrit-ZX Calculus is a powerful tool for ternary quantum logic reasoning and has been shown to be helpful for qutrit logic decomposition. Here, we demonstrate the implementation of Qutrit ZX-Calculus building blocks on a superconducting transmon device. We realize a single qutrit virtual Z gate and the qutrit Hadamard gate.  Finally we present a two-qutrit logic gate that can be synthesized from a differential AC-stark shift interaction. This work bridges the gap between the established theory of qutrit ZX-Calculus and the experimental realization in superconducting quantum circuits.