Implementation of three-qubit Deutsch-Jozsa algorithm with pendular states of polar molecules by optimal control

Ultracold polar molecules have gained much attention as a potential candidate for quantum information processing due to their long coherence time and strong dipole-dipole interaction. In the present study, we explore the dynamics of three polar molecules that are mutually coupled and arranged in an equilateral triangle configuration within a gradient electric field. By employing the pendular states of polar molecules as qubits, we simulate the three-qubit Deutsch-Jozsa algorithm via multi-target optimal control. Through the design of optimal microwave pulses with multiple iterations, our approach can accomplish the operations required to complete the algorithm in a single operational step with high fidelity and large transition probability. Furthermore, we compare and analyze the fidelity and average transition probability with respect to iteration numbers for each unitary operation Uf pulse. It is found that by combining the optimized X, H (R) H (R) H, Uf, and H (R) H gate pulses, the Deutsch-Jozsa algorithm in the three-dipole system can be performed well for distinguishing between constant and balanced functions. Our findings could shed some light on the physical realization of multi-particle quantum algorithm based on polar molecules in external electric fields.