Implementing Quantum Gates and Algorithms in Ultracold Polar Molecules

We numerically investigate the implementation of small quantum algorithms, an arithmetic adder and the Grover search algorithm, in registers of ultracold polar molecules trapped in a lattice by concatenating intramolecular and intermolecular gates. The molecular states are modulated by the exposition to static electric and magnetic fields different for each molecule. The examples are carried out in a two-molecule case. Qubits are encoded either in rovibrational or in hyperfine states, and intermolecular gates involve states of neighboring molecules. Here we use π pulses (i.e., laser pulses such that the integral of the product of the transition dipole moment and their envelope is equal to π, thus ensuring a total population inversion between two states) and pulses designed by optimal control theory adapted to a multi-target problem to drive unitary transformations between the qubit states.