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I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to…

Quantum Physics · Physics 2009-10-30 Christof Zalka

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

Grover's search algorithm is one of the basic building block in the world of quantum algorithms. Successfully applying it to combinatorial optimization problems is a subtle challenge. As a quadratic speedup is not enough to naively search…

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

We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…

Quantum Physics · Physics 2019-12-25 Francesco Campaioli , William Sloan , Kavan Modi , Felix Alexander Pollock

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

Partial search has been proposed recently for finding the target block containing a target element with fewer queries than the full Grover search algorithm which can locate the target precisely. Since such partial searches will likely be…

Quantum Physics · Physics 2010-05-24 Byung-Soo Choi , Thomas A. Walker , Samuel L. Braunstein

Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…

Quantum Physics · Physics 2024-01-10 Gayathree M. Vinod , Anil Shaji

We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…

Statistical Mechanics · Physics 2018-07-19 Stefan Boettcher , Shanshan Li , Tharso D. Fernandes , Renato Portugal

Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…

Quantum Physics · Physics 2007-05-23 Rubens Viana Ramos , Paulo Benicio de Sousa , David Sena Oliveira

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…

Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries…

Quantum Physics · Physics 2017-12-05 C. Figgatt , D. Maslov , K. A. Landsman , N. M. Linke , S. Debnath , C. Monroe

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 partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…

Quantum Physics · Physics 2026-04-24 Fintan M. Bolton

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

Optimizing high-degree of freedom robotic manipulators requires searching complex, high-dimensional configuration spaces, a task that is computationally challenging for classical methods. This paper introduces a quantum native framework…

Robotics · Computer Science 2025-10-30 Hassen Nigatu , Shi Gaokun , Li Jituo , Wang Jin , Lu Guodong , Howard Li

Grover's algorithm is a well-known unstructured quantum search algorithm run on quantum computers. It constructs an oracle and calls the oracle O($\sqrt N$) times to locate specific data out of N unsorted data. This represents a quadratic…

Computational Complexity · Computer Science 2023-12-18 Jehn-Ruey Jiang , Qiao-Yi Lin

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

We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…

Quantum Physics · Physics 2012-08-02 Ashley Montanaro

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