arXiv subjects

Wei Lin Zhang

Publications and source records attributed to Wei Lin Zhang.

4 recordsLinked to original sources

arXiv1999

A novel SO(3) picture for quantum searching

An SO(3) picture of the generalized Grover's quantum searching algorithm,with arbitrary unitary transformation and with arbitrary phase rotations, is constructed. In this picture, any quantum search operation is a rotation in a 3 dimensional space. Exact formulas for the rotation angle and rotational axis are given. The probability of finding the marked state is just $(z+1)/2$, where z is the z-component of the state vector. Exact formulas for this probability is easily obtained. The phase matching requirement and the failure of algorithm when phase mismatches are clearly explained.

quant-ph↗

arXiv1999

An intrinsic limitation on the size of quantum database

It is found that Grover's quantum search algorithm is not robust against phase inversion and Hadmard transformation inaccuracies. Imperfect phase inversions and Hadmard-Walsh transformations in Grover's quantum search algorithm lead to reductions in the maximum probability of the marked state and affect the efficiency of the algorithm. even in the absence of decoherence. Given the degrees of inaccuracies, we find that to guarantee half rate of success, the size of the database should be in the order of $O({1 \over δ^2})$, where $δ$ is the uncertainty.

quant-ph↗

arXiv1999

Phase matching in quantum searching

Each iteration in Grover's original quantum search algorithm contains 4 steps: two Hadamard-Walsh transformations and two amplitudes inversions. When the inversion of the marked state is replaced by arbitrary phase rotation θand the inversion for the prepared state |γ> is replaced by rotation through ϕ, we found that these phase rotations must satisfy a matching condition θ=ϕ. Approximate formula for the amplitude of the marked state after an arbitrary number of iterations are also derived. We give also a simple explanation of the phase matching requirement.

quant-ph↗

arXiv1999

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 $π$ 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.

quant-ph↗