Arbitrary phase rotation of the marked state can not be used for Grover's quantum search algorithm

A misunderstanding that an arbitrary phase rotation of the marked state together with the inversion about average operation in Grover's search algorithm can be used to construct a (less efficient) quantum search algorithm is cleared. The $\pi$ rotation of the phase of the marked state is not only the choice for efficiency, but also vital in Grover's quantum search algorithm. The results also show that Grover's quantum search algorithm is robust.Comment: 5 pages, 5 figure

Preparation of GHZ states via Grover's quantum searching algorithm

In this paper we propose an approach to prepare GHZ states of an arbitrary multi-particle system in terms of Grover's fast quantum searching algorithm. This approach can be regarded as an extension of the Grover's algorithm to find one or more items in an unsorted database.Comment: 9 pages, Email address: [email protected]

Effects of Noisy Oracle on Search Algorithm Complexity

Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as O(N^(-1/4)), neither the discrete- nor the continuous-time implementation of Grover's algorithm is scalably robust to this error in the absence of error correction.Comment: 16 pages, 4 figures, submitted to Phys. Rev.

Simulated Quantum Computation of Global Minima

Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations $N$ reduced from O(N) in classical simulation to $O(\sqrt{N})$ in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimization to treat larger systems.Comment: 6 figures. Molecular Physics, in pres