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Related papers: Spatial search by quantum walk

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Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…

Quantum Physics · Physics 2017-10-12 Nikolajs Nahimovs , Raqueline A. M. Santos

Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…

Quantum Physics · Physics 2022-07-25 Umut Çalıkyılmaz , Sadi Turgut

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

Grover's algorithm is one of the most important quantum algorithms, which performs the task of searching an unsorted database without a priori probability. Recently the adiabatic evolution has been used to design and reproduce quantum…

Quantum Physics · Physics 2007-05-23 Zhaohui Wei , Mingsheng Ying

Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk…

Quantum Physics · Physics 2017-05-03 Renato Portugal , Tharso D. Fernandes

In this work I describe a classical analog of Grover's quantum searching algorithm, explaining why a quantum algorithm should be able to perform search in O(sqrtN) steps and also acting as a useful pedagogic demonstration.

Quantum Physics · Physics 2014-11-25 Shayak Bhattacharjee

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

The present letter proposes a modification in the well known Grover's search algorithm, which searches a database of $N$ unsorted items in $O(\sqrt{N/M})$ steps, where $M$ represents the number of solutions to the search problem.…

Quantum Physics · Physics 2014-07-11 A. S. Gupta , A. Pathak

This paper presents a deterministic search algorithm on complete bipartite graphs. Our algorithm adopts the simple form of alternating iterations of an oracle and a continuous-time quantum walk operator, which is a generalization of…

Quantum Physics · Physics 2024-05-13 Honghong Lin , Yun Shang

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

For a graph $G$ on $n$ vertices, naively sampling the position of a random walk of at time $t$ requires work $\Omega(t)$. We desire local access algorithms supporting $\text{position}(G,s,t)$ queries, which return the position of a random…

Data Structures and Algorithms · Computer Science 2021-02-16 Amartya Shankha Biswas , Edward Pyne , Ronitt Rubinfeld

We develop a general theory for a quantum-walk search on a star graph. A star graph has N edges each of which is attached to a central vertex. A graph G is attached to one of these edges, and we would like to find out to which edge it is…

Quantum Physics · Physics 2015-06-17 Seth Cottrell , Mark Hillery

We propose a new adiabatic algorithm for the unsorted database search problem. This algorithm saves two thirds of qubits than Grover's algorithm in realizations. Meanwhile, we analyze the time complexity of the algorithm by both…

Quantum Physics · Physics 2008-11-06 Nanyang Xu , Xinhua Peng , Mingjun Shi , Jiangfeng Du

Quantum search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This has been proved to be the best possible algorithm for the exhuastive search problem in the sense the number of queries it requires…

Quantum Physics · Physics 2009-11-07 Lov K. Grover

We propose a simpler and more efficient scheme for the implementation of the multi-valued Grover's quantum search. The multi-valued search generalizes the original Grover's search by replacing qubits with qudits --- quantum systems of $d$…

Quantum Physics · Physics 2012-09-21 S. S. Ivanov , H. S. Tonchev , N. V. Vitanov

In this paper, we propose an extension of quantum searches on graphs driven by quantum walks to simplicial complexes. To this end, we newly define a quantum walk on simplicial complex which is an alternative of preceding studies by authors.…

Mathematical Physics · Physics 2017-12-06 Kaname Matsue , Osamu Ogurisu , Etsuo Segawa

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…

Quantum Physics · Physics 2007-05-23 Andrew M. Childs , Andrew J. Landahl , Pablo A. Parrilo

We report on an experiment on Grover's quantum search algorithm showing that {\em classical waves} can search a $N$-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed…

Quantum Physics · Physics 2016-09-08 N. Bhattacharya , H. B. van Linden van den Heuvell , R. J. C. Spreeuw

The "abstract search algorithm" is a well known quantum method to find a marked vertex in a graph. It has been applied with success to searching algorithms for the hypercube and the two-dimensional grid. In this work we provide an example…

Quantum Physics · Physics 2012-05-18 F. L. Marquezino , R. Portugal , S. Boettcher

It is questionable that Grover algorithm may be more valuable than a classical one, when a partial information is given in a unstructured database. In this letter, to consider quantum search when a partial information is given, we replace…

Quantum Physics · Physics 2007-05-23 Sangwoong Park , Joonwoo Bae , Younghun Kwon