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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

We have developed a non-unitary extension of Grover's search algorithm by changing the hidden geometry of Hilbert space carried by diffusion operator. Our algorithm finds the solution for search problem by performing a unique bigger…

Quantum Physics · Physics 2026-04-28 V. N. A. Lula-Rocha , M. A. S. Trindade

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

Recent studies have been spurred on by the promise of advanced quantum computing technology, which has led to the development of quantum computer simulations on classical hardware. Grover's quantum search algorithm is one of the well-known…

Grover's algorithm is a fundamental quantum algorithm that offers a quadratic speedup for the unstructured search problem by alternately applying physically implementable oracle and diffusion operators. In this paper, we reformulate the…

Quantum Physics · Physics 2025-12-15 Zhijian Lai , Dong An , Jiang Hu , Zaiwen Wen

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 present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…

Quantum Physics · Physics 2025-12-10 Sören Wilkening

Continuous time quantum walks provide an important framework for designing new algorithms and modelling quantum transport and state transfer problems. Often, the graph representing the structure of a problem contains certain symmetries that…

Quantum Physics · Physics 2015-11-03 Leonardo Novo , Shantanav Chakraborty , Masoud Mohseni , Hartmut Neven , Yasser Omar

This paper examines the performance of spatial search where the Grover diffusion operator is replaced by continuous-time quantum walks on a class of interdependent networks. We prove that for a set of optimal quantum walk times and marked…

Quantum Physics · Physics 2021-08-26 S. Marsh , J. B. Wang

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 algorithm is a crucial solution for addressing unstructured search problems and has emerged as an essential quantum subroutine in various complex algorithms. By using a different approach with previous studies, this research…

Quantum Physics · Physics 2024-12-04 Yifan Sun , Lian-Ao Wu

Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…

Data Structures and Algorithms · Computer Science 2015-02-09 Luís Tarrataca , Andreas Wichert

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

One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…

Quantum Physics · Physics 2022-02-01 Catalin Dohotaru , Peter Hoyer

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

An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers,…

Quantum Physics · Physics 2016-11-10 Thomas G. Wong

Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…

We introduce a new framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights…

Quantum Physics · Physics 2018-01-16 Stefan Boettcher , Shanshan Li

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

We mainly study exceptional configuration for coined quantum walk search. For searching on a two-dimensional grid by AKR algorithm, we find some new classes of exceptional configurations that cannot be found by the AKR algorithm effectively…

Quantum Physics · Physics 2021-02-03 Meng Li , Yun Shang