Grover search algorithm with Rydberg-blockaded atoms: Quantum Monte Carlo simulations

We consider the Grover search algorithm implementation for a quantum register of size $N=2^k$ using k (or k +1) microwave- and laser-driven Rydberg-blockaded atoms, following the proposal by M{\o}lmer, Isenhower, and Saffman [J. Phys. B 44, 184016 (2011)]. We suggest some simplifications for the microwave and laser couplings, and analyze the performance of the algorithm for up to k = 4 multilevel atoms under realistic experimental conditions using quantum stochastic (Monte-Carlo) wavefunction simulations.