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Related papers: Optimizing Quantum Search Using a Generalized Vers…

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We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…

Quantum Physics · Physics 2017-01-03 Gilles Brassard , Peter Hoyer , Alain Tapp

Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…

Quantum Physics · Physics 2021-03-29 Ji Liu , Huiyang Zhou

We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…

Quantum Physics · Physics 2009-11-11 A. Romanelli , A. Auyuanet , R. Donangelo

The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's…

Quantum Physics · Physics 2015-06-26 P. G. Kwiat , J. R. Mitchell , P. D. D. Schwindt , A. G. White

Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…

Data Structures and Algorithms · Computer Science 2015-02-09 Luís Tarrataca , Andreas Wichert

Each iteration in Grover's original quantum search algorithm contains 4 steps: two Hadamard-Walsh transformations and two amplitudes inversions. When the inversion of the marked state is replaced by arbitrary phase rotation \theta and the…

Quantum Physics · Physics 2009-10-31 Gui Lu Long , Yan Song Li , Wei Lin Zhang , Li Niu

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…

Quantum Physics · Physics 2007-05-23 Goong Chen , Stephen A. Fulling , Jeesen Chen

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…

Quantum Physics · Physics 2007-05-23 Jin-Yuan Hsieh , Che-Ming Li , Der-San Chuu

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…

Quantum Physics · Physics 2007-05-23 Eli Biham , Dan Kenigsberg

Grover's quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a…

Quantum Physics · Physics 2025-05-13 Suryansh Srivastava , Arun K. Pati , Samyadeb Bhattacharya , Indranil Chakrabarty

Grover search is a renowned quantum search algorithm that leverages quantum superposition to find a marked item with quadratic speedup. However, when implemented on Noisy Intermediate-scale Quantum (NISQ) hardware, the required repeated…

Quantum Physics · Physics 2023-04-11 Chen-Yu Liu

Grover's quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is shown that the optimal time to perform the measurement is independent of $| \phi>$,…

Quantum Physics · Physics 2009-11-10 O. Biham , D. Shapira , Y. Shimoni

Grover's database search algorithm is the optimal algorithm for finding a desired object from an unsorted collection of items. Although it was discovered in the context of quantum computation, it is simple and versatile enough to be…

General Physics · Physics 2007-12-03 Aavishkar A. Patel

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…

Quantum Physics · Physics 2018-01-17 Gui Lu Long , Wei Lin Zhang , Yan Song Li , Li Niu

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…

Quantum Physics · Physics 2023-03-08 Patrick Rall , Bryce Fuller

We investigate the performance of Grover's quantum search algorithm on a register which is subject to loss of the particles that carry the qubit information. Under the assumption that the basic steps of the algorithm are applied correctly…

Quantum Physics · Physics 2012-10-23 D. D. Bhaktavatsala Rao , Klaus Mølmer

This paper introduces a quantum-classical hybrid algorithm for generalized pattern search (GPS) algorithms. We introduce a quantum search step algorithm using amplitude amplification, which reduces the number of oracle calls needed during…

Quantum Physics · Physics 2024-10-02 Colton Mikes , Ismael R. de Farias , David Huckleberry Gutman , Victoria E. Howle

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…

Quantum Physics · Physics 2022-11-15 Tanay Roy , Liang Jiang , David I. Schuster

Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…

Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…

Quantum Physics · Physics 2018-03-08 Anirban Narayan Chowdhury , Yigit Subasi , Rolando D. Somma