Related papers: Comments on quant-ph/0609176
Experimental attempts to implement quantum speedup of computations over the past 30 years have yielded a negative result, despite the absence of physical laws prohibiting such speedup. The article formulates the limitation of quantum…
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 search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…
The previously proposed Heisenberg-type relation $ E_c t_c >> \hbar {\cal C}$ for the energy used by a quantum computer, the total computation time and the logical ("classical") complexity of the problem is verified for the following…
Quantum algorithm is a key tool for cryptanalysis. At present, people are committed to building powerful quantum algorithms and tapping the potential of quantum algorithms, so as to further analyze the security of cryptographic algorithms…
When applying Grover's algorithm to an unordered database, the probability of obtaining correct results usually decreases as the quantity of target increases. To amend the limitation, numbers of improved schemes are proposed. In this paper,…
In this paper, a detrimental mathematical mistake is pointed out in the proof of \textit{Theorem 1} presented in the paper\textit{ [Generalization of the gradient method with fractional order gradient direction, J. Franklin Inst., 357…
Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude…
We show that Grover's algorithm defines a geodesic in quantum Hilbert space with the Fubini-Study metric. From statistical point of view Grover's algorithm is characterized by constant Fisher's function. Quantum algorithms changing…
As the matching condition in Grover search algorithm is transgressed due to inevitable errors in phase inversions, it gives a reduction in maximum probability of success. With a given degree of maximum success, we have derive the…
We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expense of the other components. This leads to a general…
Two indispensable algorithms in an introductory course on Quantum Computing are Grover's search algorithm and quantum phase estimation. Quantum counting is a simple yet beautiful blend of these two algorithms, and it is therefore an…
It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.
We discuss the quantum search algorithm using complex queries that has recently been published by Grover (quant-ph/9706005). We recall the algorithm adding some details showing which complex query has to be evaluated. Based on this version…
Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the…
We prove that it is impossible to built a universal quantum machine that produces reflections about an unknown state. We then point out a connection between this result and the optimality of Grover's search algorithm: if such reflection…
This work tests the performance of Grover's search circuits on some IBM superconducting quantum devices in case of the size of search space $N=2^4$ and $N=2^5$. Ideally, we expect to get an outcome probability distribution that is clearly…
In a recent letter (Phys. Lett. A 377 (2013) 1076, arXiv:0905.3801), the authors presented an impossibility proof of quantum bit commitment, which attempted to cover all possible protocols that involve both quantum and classical…
Recently GM Sofi & SA Shabir [arXive: 1903.01850v2 [math.GM] 6 Mar 2019] made an attempt to prove the Sendov's conjecture. But unfortunately the proof is not correct. In this note, we discuss the fallacy in the proof.
Besides the superior efficiency compared to their classical counterparts, quantum algorithms known so far are basically task-dependent, and scarcely any common features are shared between them. In this work, however, we show that the…