Simulation Framework and Optimization of Superconducting Transmon-Tunable Coupler-Transmon System for Qudit Gates

Quantum computing offers the potential to surpass classical computing speeds by leveraging quantum entanglement and superposition. However, progress towards fault-tolerant quantum computers is limited by low qubit counts and considerable gate errors. A promising direction involves transitioning from two-level qubits to d-level qudits, expanding the state space beyond conventional qubit-based quantum computers. The superconducting transmon-tunable coupler-transmon (TTT) system has emerged as a key building block of current quantum processors. Recent demonstration has shown its capability to host three-level qudits (qutrits), including the implementation of qutrit controlled-phase (CPhase) gate via an adiabatic scheme. Despite this progress, further modeling or optimization studies for the qudit-based TTT system are still unexplored. In this work, we propose an integrated simulation framework that predicts the cross-Kerr interactions of the TTT system and the fidelities of two-qutrit CPhase gate with the presence of noise effect. We validate the prediction of the cross-Kerr interactions against data from TTT systems reported in the literature. We also identify the conditions for the maximum target frequency in the adiabatic scheme necessary to achieve higher qutrit CPhase gate fidelity. Furthermore, we demonstrate the control-device co-optimization of the system, showing the potential of achieving the highest gate fidelity allowed by the hardware and noise. This work provides valuable insights which can guide the development towards more reliable and powerful superconducting quantum processors.