Implementing the Quantum Fourier Transform on a molecular qudit with full refocusing and state tomography

Molecular spin qudits based on lanthanide complexes offer a promising platform for quantum technologies, combining chemical tunability with multi-level encoding. However, experimental demonstrations of their envisaged capabilities remain scarce, posing the difficulty of achieving precise control over coherences between qudit states in long pulse sequences. Here, we implement in a ¹⁷³Yb(trensal) qudit the Quantum Fourier Transform (QFT), a core component of numerous quantum algorithms, storing quantum information in the phases of coherences. QFT provides an ideal benchmark for coherence manipulation and a challenge for molecular spin qudits. We address this challenge by embedding a full-refocusing protocol for spin qudits in our algorithm, mitigating inhomogeneous broadening and enabling a high-fidelity recovery of the state. Complete state tomography demonstrates the performance of the algorithm, while simulations provide insight into the physical mechanisms behind inhomogeneous broadening. This work shows the feasibility of quantum logic on molecular spin qudits and highlights their potential.