Optimal control of quantum permutation algorithm with a molecular ququart

Quantum algorithms can afford greater computational efficiency compared to their classical counterparts when addressing specific computing tasks. We describe here the implementation, using a polar molecule in an external electric field, of the single-qudit cyclic permutation identification algorithm proposed by Gedik et al. [Sci. Rep. 5, 14671 (2015).]. A molecular ququart is realized through the field-dressed states generated as the pendular modes of BaI. By employing multi-target optimal control theory, we design microwave pulses for ququart-based operations such as the Fourier transformation and its inverse, as well as the oracle U_f operation. Specifically, we design an optimized pulse sequence that realizes a quantum algorithm on a single BaI molecule identifying the parity of a member of a set of cyclic permutations with high fidelity. This demonstrates the applicability of optimal control theory to polar molecules for quantum computation.