Quantum error correction with molecular spin qudits

Thanks to the large number of levels which can be coherently manipulated, molecular spin systems constitute a very promising platform for quantum computing. Indeed, they can embed quantum error correction within single molecular objects, thus greatly simplifying its actual realization in the short term. We consider a recent proposal, which exploits a spin qudit to encode the protected unit, and is tailored to fight pure dephasing. Here we compare the implementation of this code on different molecules, in which the qudit is provided by either an electronic or a nuclear spin (S, I > 1), coupled to a spin-1/2 electronic ancilla for error detection. By thorough numerical simulations we show that a significant gain in the effective phase memory time can be achieved. This is further enhanced by exploiting pulse-shaping techniques to reduce the leakage and/or the impact of decoherence during correction. Moreover, we simulate the implementation of single-qubit operations on the encoded states.