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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

In the Grover-type quantum search process a search operator is iteratively applied, say, k times, on the initial database state. We present an additive decomposition scheme such that the iteration process is expressed, in the computational…

Quantum Physics · Physics 2017-06-07 F. M. Toyama , W. van Dijk

We propose a methodology for implementing Grover's algorithm in the digital quantum simulation of disordered Ising models. The core concept revolves around using the evolution operator for the Ising model as the quantum oracle within…

Quantum Physics · Physics 2025-04-28 Andrey Zhukov , Andrey Lebedev , Walter Pogosov

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 search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design.…

Quantum Physics · Physics 2023-02-02 Bin Yan , Nikolai A. Sinitsyn

The improved quantum scheduling algorithm proposed by Grover has been generalized using the generalized quantum search algorithm, in which a unitary operator replaces the Walsh-Hadamard transform, and $\pi/2$ phase rotations replace the…

Quantum Physics · Physics 2007-05-23 Jingfu Zhang , Zhiheng Lu , Zhiwei Deng , Hui Wang

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

Phase matching has been studied for the Grover algorithm as a way of enhancing the efficiency of the quantum search. Recently Li and Li found that a particular form of phase matching yields, with a single Grover operation, a success…

Quantum Physics · Physics 2009-11-13 F. M. Toyama , W. van Dijk , Y. Nogami , M. Tabuchi , Y. Kimura

The execution of Grover's quantum search algorithm needs rather limited resources without much fine tuning. Consequently, the algorithm can be implemented in a variety of physical set-ups, which involve wave dynamics but may not need other…

Quantum Physics · Physics 2021-07-08 Apoorva D. Patel

Grover's algorithm is usually described in terms of the iteration of a compound operator of the form $Q = - H I_{0} H I_{x_0}$. Although it is quite straightforward to verify the algebra of the iteration, this gives little insight into why…

Quantum Physics · Physics 2007-05-23 Richard Jozsa

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

Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…

Quantum Physics · Physics 2020-03-31 Kun Zhang , Vladimir E. Korepin

In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding…

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

Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…

Quantum Physics · Physics 2019-08-20 Rituparna Maji , Bikash K. Behera , Prasanta K. Panigrahi

Grover's search algorithm is the cornerstone of many applications of quantum computing, providing a quadratic speed-up over classical methods. One limitation of the algorithm is that it requires knowledge of the number of solutions to…

Quantum Physics · Physics 2025-12-18 Samuel Cogan , Jonathan Raghoonanan , Tim Byrnes

Multi-objective search means searching for any one of several objectives in an unstructured database. Grover's algorithm has quadratic acceleration in multi-objection search than classical ones. Iterated operator in Grover's algorithm is a…

Quantum Physics · Physics 2024-09-10 Hao Li , Daowen Qiu , Le Luo

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

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

Grover's search algorithm searches a database of $N$ unsorted items in $O(\sqrt{N/M})$ steps where $M$ represents the number of solutions to the search problem. This paper proposes a scheme for searching a database of $N$ unsorted items in…

Quantum Physics · Physics 2007-05-23 A. S. Gupta , M. Gupta , A. Pathak

As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model,…

Data Structures and Algorithms · Computer Science 2020-01-20 Samuel Hunt , Maximilien Gadouleau