Related papers: Description of the Grover algorithm based on geome…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was…
Some of the secret sharing schemes having unique quantum features like parallelism and entanglement are supposed to be relatively secure. Different schemes proposed by various researchers over the years have features which could be specific…
L. K. Grover's search algorithm in quantum computing gives an optimal, quadratic speedup in the search for a single object in a large unsorted database. In this paper, we generalize Grover's algorithm in a Hilbert-space framework for both…
We present a novel quantum algorithm for solving the unstructured search problem with one marked element. Our algorithm allows generating quantum circuits that use asymptotically fewer additional quantum gates than the famous Grover's…
We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our…
We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This…
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…
We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity.…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
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 present an information geometric characterization of Grover's quantum search algorithm. First, we quantify the notion of quantum distinguishability between parametric density operators by means of the Wigner-Yanase quantum information…
This paper describes a quantum algorithm for proof search in sequent calculus of a subset of Linear Logic using the Grover Search Algorithm. We briefly overview the Grover Search Algorithm and Linear Logic, show the detailed steps of the…
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
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…
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 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.…
Amplitude amplification is a central tool used in Grover's quantum search algorithm and has been used in various forms in numerous quantum algorithms since then. It has been shown to completely eliminate one-sided error of quantum search…
The Grover quantum search algorithm is generalized to deal with an arbitrary mixed initial state. The probability to measure a marked state as a function of time is calculated, and found to depend strongly on the specific initial state. The…
In this article, we discuss the implementation of a quantum recommendation system that uses a quantum variant of the k-nearest neighbours algorithm and the Grover algorithm to search for a specific element in unstructured database. In…