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The Grover search algorithm performs an unstructured search of a marked item in a database quadratically faster than classical algorithms and is shown to be optimal. Here, we show that if the search space is divided into two blocks with the…

Quantum Physics · Physics 2023-12-12 Akankshya Dash , Biswaranjan Panda , Arun K Pati

The search operation for a marked state by means of Grover's quantum searching algorithm is shown to be an element of group SU(2) which acts on a 2-dimensional space spanned by the marked state and the unmarked collective state. Based on…

Quantum Physics · Physics 2007-05-23 Sixia Yu , Chang-Pu Sun

Grover presented the phase-shift search by replacing the selective inversions by selective phase shifts of $\pi /3$. In this paper, we investigate the phase-shift search with general equal phase shifts. We show that for small uncertainties,…

Quantum Physics · Physics 2009-12-16 D. Li , J. P. Chen , X. Li , H. Huang , X. Li

Logic entailment is essential to reasoning, but entailment checking has the worst-case complexity of an exponential of the variable size. With recent development, quantum computing when mature may allow an effective approach for various…

Quantum Physics · Physics 2025-06-05 Tatpong Katanyukul

Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…

Quantum Physics · Physics 2019-01-02 Mauro E. S. Morales , Timur Tlyachev , Jacob Biamonte

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…

Quantum Physics · Physics 2009-11-11 Shahar Dolev , Itamar Pitowsky , Boaz Tamir

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

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

Grover's algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems of size $N$. Recent studies have reformulated this task as a maximization problem on the unitary manifold and solved it…

Quantum Physics · Physics 2026-04-06 Zhijian Lai , Dong An , Jiang Hu , Zaiwen Wen

Here we suggest a modification of Grover's algorithm, based on a multiphase oracle which marks each solution with a different phase when there is more than one solution. Such a modification can be used to maintain a high probability of…

Quantum Physics · Physics 2025-09-03 Hristo Tonchev , Rosen Bahtev

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

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

Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…

Quantum Physics · Physics 2020-09-21 Xiaoyu He , Jialin Zhang , Xiaoming Sun

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,…

Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with $N$ records in $O(\sqrt{N})$ assuming that the item must exist in the…

Quantum Physics · Physics 2008-12-01 Ahmed Younes

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

Grover recently presented the fixed-point search algorithm. In this letter, we study the fixed-point search algorithm obtained by replacing equal phase shifts of $\pi /3$ by different phase shifts.

Quantum Physics · Physics 2012-05-08 D. Li , X. Li , H. Huang , X. Li

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

Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity. Thus, upon measurement, there is a…

Information Theory · Computer Science 2012-03-15 Ashish Mani , C. Patvardhan

Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time…