ENTANGLEMENT IN ADIABATIC QUANTUM SEARCHING ALGORITHMS

Quantum entanglement is widely considered as one of the key resources for quantum-computational power. However, present interpretations of entanglement in speeding up of quantum algorithms remain far from complete. We analyze and compare the behaviors of entanglement during the adiabatic evolution of Grover's quantum search algorithms with complexity $O(\sqrt{N})$ and O(1), respectively. Our results show that entanglement has a significant impact on the computational efficiency of both algorithms. That is, the greater the entanglement, the higher is the quantum computation, and vice versa. Furthermore, the correlations between entanglement and energy are discussed. It is observed that for the algorithm with complexity O(1), its entanglement degree becomes larger when the energy input into the quantum system increases, thus making the algorithm more efficient.