We numerically investigate the possibilities of driving quantum algorithms with laser pulses in a register of ultracold NaCs polar molecules in a static electric field. We focus on the possibilities of performing scalable logical operations by considering circuits that involve intermolecular gates (implemented on adjacent interacting molecules) to enable the transfer of information from one molecule to another during conditional laser-driven population inversions. We study the implementation of an arithmetic operation (the addition of 0 or 1 on a binary digit and a carry in) which requires population inversions only and the Deutsch-Jozsa algorithm which requires a control of the phases. Under typical experimental conditions, our simulations show that high-fidelity logical operations involving several qubits can be performed in a time scale of a few hundreds of microseconds, opening promising perspectives for the manipulation of a large number of qubits in these systems.

Implementation of quantum controlled-NOT ͑CNOT͒ gates in realistic molecular systems is studied using stimulated Raman adiabatic passage ͑STIRAP͒ techniques optimized in the time domain by genetic algorithms or coupled with optimal control theory. In the first case, with an adiabatic solution ͑a series of STIRAP processes͒ as starting point, we optimize in the time domain different parameters of the pulses to obtain a high fidelity in two realistic cases under consideration. A two-qubit CNOT gate constructed from different assignments in rovibrational states is considered in diatomic ͑NaCs͒ or polyatomic ͑SCCl 2 ͒ molecules. The difficulty of encoding logical states in pure rotational states with STIRAP processes is illustrated. In such circumstances, the gate can be implemented by optimal control theory and the STIRAP sequence can then be used as an interesting trial field. We discuss the relative merits of the two methods for rovibrational computing ͑structure of the control field, duration of the control, and efficiency of the optimization͒.