Experimental implementation of Grover's search algorithm with neutral atom qubits

Grover's algorithm for searching an unsorted data base provides a provable speedup over the best possible classical search and is therefore a test bed for demonstrating the power of quantum computation. The algorithm has been demonstrated with NMR, trapped ion, photonic, and superconducting hardware, but only with two qubits encoding a four element database. We report on progress towards experimental demonstration of Grover's algorithm using two and three neutral atom qubits encoding a database with up to eight elements. Our approach uses a Rydberg blockade C$_k$NOT gate for efficient implementation of the Grover iterations[1]. Quantum Monte Carlo simulations of the algorithm performance[2] that account for gate errors and decoherence rates are compared with experimental results. [1] K. M\o{}lmer, L. Isenhower, and M. Saffman, J. Phys. B {\bf 44}, 184016 (2011). [2] D. Petrosyan, M. Saffman, and K. M\o{}lmer, arXiv: 1512.05588.