2016/11/14 by Namit Anand, Arun Kumar Pati, Anand, Namit +1 · 5 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Neural Networks and Applications #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1611.04542
9 pages, 5 figures, comments welcome
arxiv created 2016/11/14 · openalex publication_date 2016/11/14 · arxiv updated 2016/11/15 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28
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.