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Related papers: Exact results on Quantum search algorithm

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In this paper, we study decoherence on Grover's quantum searching algorithm using a perturbative method. We assume that each two-state system (qubit) suffers \sigma_{z} error with probability p (0\leq p\leq 1) independently at every step in…

Quantum Physics · Physics 2010-09-03 Hiroo Azuma

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

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…

Quantum Physics · Physics 2023-07-31 Guanzhong Li , Lvzhou Li

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

We study the fully generalized Grover's algorithm to find the optimal phase changes for each step of the iteration to maximize gain in probability of observation of the target, and when phase matching is required. We find that classical…

Quantum Physics · Physics 2026-05-14 Chris Cardullo , Min Kang

This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…

Quantum Physics · Physics 2025-06-06 Alok Shukla , Prakash Vedula

Grover's algorithm solves the unstructured search problem. Grover's algorithm can find the target state with certainty only if searching one out of four. Designing the deterministic search algorithm can avoid any repetition of the…

Quantum Physics · Physics 2025-01-14 Zhen Wang , Kun Zhang , Vladimir Korepin

Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $\lambda$ of…

Quantum Physics · Physics 2014-11-26 Theodore J. Yoder , Guang Hao Low , Isaac L. Chuang

We introduce the concepts of Grover operators and Grover kernels to systematically analyse Grover's searching algorithms. Then, we investigate a one-parameter family of quantum searching algorithms of Grover's type and we show that the…

Quantum Physics · Physics 2009-11-06 Alberto Galindo , Miguel A. Martin-Delgado

We report the implementation of Grover's quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space,…

Quantum Physics · Physics 2009-11-11 K. -A. Brickman , P. C. Haljan , P. J. Lee , M. Acton , L. Deslauriers , C. Monroe

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…

Quantum Physics · Physics 2009-11-13 Avatar Tulsi

Grover's search algorithm is one of the first quantum algorithms to exhibit a provable quantum advantage. It forms the backbone of numerous quantum applications and is widely used in benchmarking efforts. Here, we report…

Quantum Physics · Physics 2022-11-10 Bibek Pokharel , Daniel Lidar

The recursion equation analysis of Grover's quantum search algorithm presented by Biham et al. [PRA 60, 2742 (1999)] is generalized. It is applied to the large class of Grover's type algorithms in which the Hadamard transform is replaced by…

Quantum Physics · Physics 2016-09-08 Eli Biham , Ofer Biham , David Biron , Markus Grassl , Daniel A. Lidar , Daniel Shapira

Grover's quantum search algorithm drives a quantum computer from a prepared initial state to a desired final state by using selective transformations of these states. Here, we analyze a framework when one of the selective trasformations is…

Quantum Physics · Physics 2013-05-30 Avatar Tulsi

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

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…

Quantum Physics · Physics 2021-06-22 Austin Gilliam , Marco Pistoia , Constantin Gonciulea

A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…

Quantum Physics · Physics 2023-08-23 Yutong Huang , Shengshi Pang

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first and second neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations…

Quantum Physics · Physics 2015-05-13 T. Gorin , L. Lara , G. V. Lopez

Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude…

Quantum Physics · Physics 2009-10-31 B. Pablo-Norman , M. Ruiz-Altaba

Grover's algorithm is one of the pioneering demonstrations of the advantages of quantum computing over its classical counterpart, providing - at most - a quadratic speed-up over the classical solution for unstructured database search. The…