Grover's search algorithm is the optimal quantum algorithm that can search an unstructured database quadratically faster than any known classical algorithm. The role of entanglement and correlations in the search algorithm have been studied in great detail and it is known that entanglement between the qubits is necessary to gain a quadratic speedup, for pure state implementation of the Grover search algorithm. Here, we systematically investigate the behavior of quantum coherence and monogamy of entanglement in the discrete analogue of the
analog analogue of Grover search algorithm. The analog analogue of Grover search is a continuous time quantum algorithm based on the adiabatic Hamiltonian evolution that gives a quadratic speedup, similar to the original Grover search algorithm. We show that the decrease of quantum coherence, quantified using various coherence monotones, is a clear signature of attaining the maximum success probability in the analog Grover search. We also show that for any two qubit reduced density matrix of the system, the concurrence evolves in close vicinity to the increasing rate of success probability. Furthermore, we show that the system satisfies a
n-party monogamy inequality for arbitrary times, hence bounding the amount of
n-qubit entanglement during the quantum search.
Evolution of entanglement with the processing of quantum algorithms affects the outcome of the algorithm. Particularly, the performance of Grover's search algorithm gets worsened if the initial state of the algorithm is an entangled one. Biham et al [14] have shown that the success probability of search algorithm can be seen as an operational measure of entanglement. Following the same line of thought, analytical expressions for entanglement measure for three and five qubit system have been derived, which reveals that entanglement measure based on Grover's search algorithm is valid for any state with real coefficients for even number of qubits.
Many metaheuristic algorithms have been proposed to solve combinatorial and numerical optimization problems. Most optimization problems have high dependence, meaning that variables are strongly dependent on one another. If a method were to attempt to optimize each variable independently, its performance would suffer significantly. When traditional optimization techniques are applied to highdependence problems, they experience difficulty in finding the global optimum. To address this problem, this paper proposes a novel metaheuristic algorithm, the entanglement-enhanced quantum-inspired tabu search algorithm (Entanglement-QTS), which is based on the quantum-inspired tabu search (QTS) algorithm and the feature of quantum entanglement. Entanglement-QTS differs from other quantum-inspired evolutionary algorithms in that its Q-bits have entangled states, which can express a high degree of correlation, rendering the variables more intertwined. Entangled Q-bits represent a state-of-the-art idea that can significantly improve the treatment of multimodal and high-dependence problems. Entanglement-QTS can discover optimal solutions, balance diversification and intensification, escape numerous local optimal solutions by using the quantum not gate, reinforce the intensification effect by local search and entanglement local search, and manage strong-dependence problems and accelerate the optimization process by using entangled states. This paper uses nine benchmark functions to test the search ability of the entanglement-QTS algorithm. The results demonstrate that Entanglement-QTS outperforms QTS and other metaheuristic algorithms in both its effectiveness at finding the global optimum and its computational efficiency.