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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…

Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…

We formulate Grover's unstructured search algorithm as a chiral quantum walk, where transitioning in one direction has a phase conjugate to transitioning in the opposite direction. For small phases, this breaking of time-reversal symmetry…

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…

I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to…

It is questionable that Grover algorithm may be more valuable than a classical one, when a partial information is given in a unstructured database. In this letter, to consider quantum search when a partial information is given, we replace…

Grover's quantum search algorithm provides a quadratic quantum advantage over classical algorithms across a broad class of unstructured search problems. The original protocol is probabilistic, returning the desired result with significant…

A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase…

We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's…

Partial search has been proposed recently for finding the target block containing a target element with fewer queries than the full Grover search algorithm which can locate the target precisely. Since such partial searches will likely be…

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…

This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm…

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…

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…

The recursion equation analysis of Grover's quantum search algorithm presented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied to the large class of Grover's type algorithms in which the Hadamard transform is replaced by…

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…

We compare pseudopure state ensemble implementations, quantified by their initial polarization and ensemble size, of Grover's search algorithm to probabilistic classical sequential search algorithms in terms of their success and failure…

This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks. We prove that for a set of optimal quantum walk times and marked…

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…

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…