Implementing Quantum Gates and Algorithms in Ultracold Polar Molecules

Abstract

We numerically investigate the implementation of small quantum algorithms,an arithmetic adder and the Grover search algorithm, in registersof ultracold polar molecules trapped in a lattice by concatenatingintramolecular and intermolecular gates. The molecular states aremodulated by the exposition to static electric and magnetic fieldsdifferent for each molecule. The examples are carried out in a two-moleculecase. Qubits are encoded either in rovibrational or in hyperfinestates, and intermolecular gates involve states of neighboring molecules.Here we use pi pulses (i.e., laser pulses such that the integralof the product of the transition dipole moment and their envelopeis equal to pi, thus ensuring a total population inversion betweentwo states) and pulses designed by optimal control theory adaptedto a multi-target problem to drive unitary transformations betweenthe qubit states.