Related papers: The Topology of Grover Algorithm
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
We show that iteration of a few ( $\sim N^{1/4}$) unitary steps of Grover's algorithm suffices to perfectly prepare a Dicke state of $N$ atoms in a cavity. We also show that a few subsequent Grover steps can be employed to generate GHZ and…
The quantum circuit model essentially treats every quantum algorithm as a straight-line program. While this view is universal, recent work has shown that it is inconvenient for using different-length quantum subroutines in superposition.…
The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum…
Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any physical system that allows superposition of states. A physical realization of this algorithm is described using…
The Grover search algorithm is a pivotal advancement in quantum computing, promising a remarkable speedup over classical algorithms in searching unstructured large databases. Here, we report results for the implementation and…
Amplitude Amplification -- a key component of Grover's Search algorithm -- uses an iterative approach to systematically increase the probability of one or multiple target states. We present novel strategies to enhance the amplification…
Conditions on sure-success decidability of weights of Boolean functions are presented for a given number of generalized Grover iterations. It is shown that the decidability problem reduces to a system of algebraic equations of a single…
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…
Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required…
The implementation of a quantum computer requires the realization of a large number of N-qubit unitary operations which represent the possible oracles or which are part of the quantum algorithm. Until now there are no standard ways to…
We report the experimental implementation of Grover's quantum search algorithm on a quantum computer with three quantum bits. The computer consists of molecules of $^{13}$C-labeled CHFBr$_2$, in which the three weakly coupled spin-1/2…
We question whether the measurement based quantum computing algorithm is in fact Grover's algorithm or simply a similar oracular search method. The two algorithms share several qualitative features especially in the case of the trivial 4…
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.…
Grover search is one of the most important quantum algorithms. In this paper, we consider a kind of search that the conditions of satisfaction $T$ can be rewritten as $T=T_1\bigcap T_2$. Then we present a new Grover search with smaller…
This article highlights some of the key operating principles of Grover algorithm. These principles were used to develop a new oracle function, that illustrates the possibility of using Grover algorithm for solving more realistic and…
Control and characterization of networks is a paramount step for the development of many quantum technologies. Even for moderate-sized networks, this amounts to explore an extremely vast parameters space in search for the couplings defining…
We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the…
Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known…
There are important algorithms built upon a mixture of basic techniques described; for example, the Fast Fourier Transform (FFT) employs both Divide-and-Conquer and Transform-and-Conquer techniques. In this article, the evolution of a…