Physics – Quantum Physics
Scientific paper
2003-07-20
Phys. Rev. A 68, 022326 (2003)
Physics
Quantum Physics
Scientific paper
10.1103/PhysRevA.68.022326
Grover's quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is shown that the optimal time to perform the measurement is independent of $| \phi>$, namely, it is identical to the optimal time in the original algorithm in which $| \phi > = | 0>$, with the same number of marked states, $r$. The probability of success $P_{\rm s}$ is obtained, in terms of the amplitudes of the state $| \phi>$, and is shown to be independent of $r$. A class of states, which includes fixed points and cycles of the Grover iteration operator is identified. The relevance of these results in the context of using the success probability as an entanglement measure is discussed. In particular, the Groverian entanglement measure, previously limited to a single marked state, is generalized to the case of several marked states.
Biham Ofer
Shapira Dan
Shimoni Yishai
No associations
LandOfFree
Analysis of Grover's quantum search algorithm as a dynamical system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Analysis of Grover's quantum search algorithm as a dynamical system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analysis of Grover's quantum search algorithm as a dynamical system will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-17089