Implementing high fidelity single and entangling two-qubit gates in multi-level systems

A recent experiment introduced a novel multi-level nuclear spin (3/2) of single molecule magnet TbPc₂ as qubit or qudit. Due to the strong coupling of the nuclear spin to the electric field, this system exhibits simultaneously long coherence times and fast controllability. One of the important questions to address is how well one can implement quantum gates in these systems. By using a combination of analytically solvable two level dynamics and the Suzuki-Trotter product formula, we design z-rotations of high fidelity. We also investigate the implementation of two-qubit entangling gates mediated by a superconducting transmission line resonator coupling two TbPc₂ qudits.