Related papers: An improved phase error tolerance in Quantum searc…
We generalize Grover algorithm with two arbitrary phases in a density matrix set up. We give exact analytic expressions for the success probability after arbitrary number of iteration of the generalized Grover operator as a function of…
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…
This paper researches how the systematic errors in phase inversions affect the success rate and the number of iterations in optimized quantum random-walk search algorithm. Through geometric description of this algorithm, the model of the…
Grover's algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of $\lambda$ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where $\lambda$ is…
Grover's quantum search algorithm, involving a large number of qubits, is highly sensitive to errors in the physical implementation of the unitary operators. This poses an intrinsic limitation to the size of the database that can be…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
Phase matching has been studied for the Grover algorithm as a way of enhancing the efficiency of the quantum search. Recently Li and Li found that a particular form of phase matching yields, with a single Grover operation, a success…
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 \theta and the…
The success probability of a search of $M$ targets from a database of size $N$, using Grover's search algorithm depends critically on the number of iterations of the composite operation of the oracle followed by Grover's diffusion…
This article introduces an enhancement to the Grover search algorithm to speed up computing the probability of finding good states. It suggests incorporating a rotation phase angle determined mathematically from the derivative of the model…
We describe an implementation of Grover's fixed-point quantum search algorithm on a nuclear magnetic resonance (NMR) quantum computer, searching for either one or two matching items in an unsorted database of four items. In this new…
Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with $N$ records in $O(\sqrt{N})$ assuming that the item must exist in the…
We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
In standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this Letter we present a modified version of Grover's algorithm that searches a marked state with full successful rate.…
We study the fully generalized Grover's algorithm to find the optimal phase changes for each step of the iteration to maximize gain in probability of observation of the target, and when phase matching is required. We find that classical…
Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in…
Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator…
In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…