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Related papers: The Topology of Grover Algorithm

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Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…

Quantum Physics · Physics 2024-11-14 E. M. Stoudenmire , Xavier Waintal

L. K. Grover's search algorithm in quantum computing gives an optimal, square-root speedup in the search for a single object in a large unsorted database. In this paper, we expound Grover's algorithm in a Hilbert-space framework that…

Quantum Physics · Physics 2007-05-23 G. Chen , S. A. Fulling , M. O. Scully

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

In this paper we discuss how we can design Hamiltonians to implement quantum algorithms, in particular we focus in Deutsch and Grover algorithms. As main result of this paper, we show how Hamiltonian inverse quantum engineering method allow…

Quantum Physics · Physics 2018-04-25 Alan C Santos

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…

Quantum Physics · Physics 2019-03-08 Ye-Chao Liu , Jiangwei Shang , Xiangdong Zhang

Distributed quantum computing can give substantial noise reduction due to shallower circuits. An experiment illustrates the advantages in the case of Grover search. This motivates studying the quantum advantage of the distributed version of…

Quantum Physics · Physics 2021-11-08 J. Avron , Ofer Casper , Ilan Rozen

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

We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…

Quantum Physics · Physics 2015-06-26 Michel Boyer , Gilles Brassard , Peter Hoeyer , Alain Tapp

The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is of significant interest to describe it in the most efficient mathematical formalism. We show firstly, that Clifford's formalism…

Quantum Physics · Physics 2012-01-10 James M. Chappell , M. A. Lohe , Lorenz von Smekal , Azhar Iqbal , Derek Abbot

There are major advantages in a newer version of Grover's quantum algorithm utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject…

Quantum Physics · Physics 2007-05-23 Goong Chen , Shunhua Sun

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…

Quantum Physics · Physics 2015-09-17 A. H. Homid , Mahmoud Abdel-Aty , A. -S. F. Obada

This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…

Quantum Physics · Physics 2008-08-05 Michele Mosca

Grover's algorithm achieves a quadratic speedup over classical algorithms, but it is considered necessary to know the value of $\lambda$ exactly [Phys. Rev. Lett. 95, 150501 (2005); Phys. Rev. Lett. 113, 210501 (2014)], where $\lambda$ is…

Quantum Physics · Physics 2018-12-12 Tan Li , Wan-Su Bao , He-Liang Huang , Feng-Guang Li , Xiang-Qun Fu , Shuo Zhang , Chu Guo , Yu-Tao Du , Xiang Wang , Jie Lin

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This…

Quantum Physics · Physics 2026-02-13 Yudai Suzuki , Marek Gluza , Jeongrak Son , Bi Hong Tiang , Nelly H. Y. Ng , Zoë Holmes

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…

Quantum Physics · Physics 2007-07-10 Arti Chamoli , C. M. Bhandari

One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…

Quantum Physics · Physics 2017-11-22 Yan Wang

This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to $n$-valued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguish between constant and balanced Boolean…

Quantum Physics · Physics 2025-02-18 Yale Fan

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…

Quantum Physics · Physics 2007-05-23 J. J. Alvarez , C. Gomez

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.

Quantum Physics · Physics 2007-05-23 Manoj K. Samal , Partha Ghose

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…

Mathematical Physics · Physics 2015-06-03 Carlo Cafaro , Stefano Mancini