Related papers: Grover's Algorithm and Many-Valued Quantum Logic
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…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process,…
We apply majorization theory to study the quantum algorithms known so far and find that there is a majorization principle underlying the way they operate. Grover's algorithm is a neat instance of this principle where majorization works step…
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…
We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on…
Grover's algorithm provides a quadratic speedup over classical algorithms to search for marked elements in an unstructured database. The original algorithm is probabilistic, returning a marked element with bounded error. There are several…
Time evolution of quantum systems is of interest in physics, in chemistry, and, more recently, in computer science. Quantum computers are suggested as one route to propagating quantum systems far more efficiently than ordinary numerical…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
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…
This paper highlights a practical research of the possibility of forming quantum circuits for training neural networks. The demonstrated quantum circuits were based on the principles of Grover's Search Algorithm. The perceptron was chosen…
One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…
In recent decades, the field of quantum computing has experienced remarkable progress. This progress is marked by the superior performance of many quantum algorithms compared to their classical counterparts, with Shor's algorithm serving as…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by…
Grover's search algorithm provides a quadratic speedup over classical brute-force search in terms of query complexity and is widely used as a versatile subroutine in numerous quantum algorithms, including those for combinatorial problems…
Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In…
We present quantum algorithms for routing concentration assignments on full capacity fat-and-slim concentrators, bounded fat-and-slim concentrators, and regular fat-and-slim concentrators. Classically, the concentration assignment takes…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
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…