We firstly investigate the multipartite entanglement features of the quantum states, including the iteration states achieved by repeated application of Grover iteration and the Oracle ones into which the above iteration states evolve by applying single Oracle operation, employed in Grover's search algorithm by means of the separable degree and the entanglement measure. Then we give the quantitative and qualitative descriptions of the entanglement dynamics in Grover's search algorithm. Our results show that for most instances (i) the separable degrees of these states and ranges of their maximum Schmidt numbers are invariable by following the dynamics of Grover's search algorithm; (ii) the dynamics of Grover's search algorithm is almost "filled" by the fully entangled states.We firstly investigate the multipartite entanglement features of the quantum states, including the iteration states achieved by repeated application of Grover iteration and the Oracle ones into which the above iteration states evolve by applying single Oracle operation, employed in Grover's search algorithm by means of the separable degree and the entanglement measure. Then we give the quantitative and qualitative descriptions of the entanglement dynamics in Grover's search algorithm. Our results show that for most instances (i) the separable degrees of these states and ranges of their maximum Schmidt numbers are invariable by following the dynamics of Grover's search algorithm; (ii) the dynamics of Grover's search algorithm is almost "filled" by the fully entangled states.

arXiv:1210.3418Oct 12, 20123 citations

Scale invariance of entanglement dynamics in Grover's quantum search algorithm

Matteo A. C. Rossi, Dagmar Bruß, Chiara Macchiavello

We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present. Remarkably, the dynamics of any type of entanglement as well as of genuine multipartite entanglement is independent of the number $n$ of qubits for large $n$ , thus exhibiting a scale invariance property. We compare this result with the entanglement dynamics induced by a fixed-point quantum search algorithm. We also investigate criteria for efficient simulatability in the context of Grover's algorithm.We calculate the amount of entanglement of the multiqubit quantum states employed in the Grover algorithm, by following its dynamics at each step of the computation. We show that genuine multipartite entanglement is always present. Remarkably, the dynamics of any type of entanglement as well as of genuine multipartite entanglement is independent of the number $n$ of qubits for large $n$, thus exhibiting a scale invariance property. We compare this result with the entanglement dynamics induced by a fixed-point quantum search algorithm. We also investigate criteria for efficient simulatability in the context of Grover's algorithm.

arXiv:1205.3000Physical Review AFeb 21, 201336 citations

n

of qubits for large

n

, thus exhibiting a scale invariance property. We compare this result with the entanglement dynamics induced by a fixed-point quantum search algorithm. We also investigate criteria for efficient simulatability in the context of Grover's algorithm.