We numerically implement quantum algorithms in hyperfine levels of ultracold polar molecules. Logical operations are driven by pulses optimized by optimal control theory. All implementations take place in the lowest two rotational levels of the ground vibrational state of the ground (1)Σ(+) electronic state, exploiting the richness of the hyperfine energy structure and state mixing in static external fields. We show that it is possible to realize high fidelity complex logical operations with microsecond pulses. The possibility to run algorithms implemented on two interacting molecules is also demonstrated. (41)K(85)Rb and (41)K(87)Rb molecules are considered for the numerical simulations but the results are general and can be extended to other species.
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