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Related papers: Tight bounds on quantum searching

200 papers

The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of…

Other Computer Science · Computer Science 2010-03-10 D. K. Ningtyas , A. B. Mutiara

Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identification of a base-pairing with a quantum query gives a natural (and first ever) explanation of why living organisms have 4…

Quantum Physics · Physics 2009-11-06 Apoorva Patel

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

Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…

Quantum Physics · Physics 2023-06-21 Jian Leng , Fan Yang , Xiang-Bin Wang

Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by…

Quantum Physics · Physics 2018-07-13 Avinash Dash , Deepankar Sarmah , Bikash K. Behera , Prasanta K. Panigrahi

This paper is a written version of a one hour lecture given on Lov Grover's database search algorithm. Table Of Contents 1 ... Problem Definition 2 ... The quantum mechanical perspective 3 ... Properties of the inversion I_|psi> 4 ... The…

Quantum Physics · Physics 2007-05-23 Samuel J. Lomonaco

Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…

Quantum Physics · Physics 2016-10-11 Ciarán M. Lee , John H. Selby

In this paper we will present a quantum algorithm which works very efficiently in case of multiple matches within the search space and in the case of few matches, the algorithm performs classically. This allows us to propose a hybrid…

Quantum Physics · Physics 2008-08-06 Ahmed Younes , Jon Rowe , Julian Miller

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

We present an extension of Adiabatic Quantum Computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a small counting…

Mathematical Physics · Physics 2015-03-17 Zhenwei Cao , Alexander Elgart

A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…

Data Structures and Algorithms · Computer Science 2007-05-30 Eva Borbely

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

This paper discusses an improvement to Grover's algorithm for searches where target states are Hamming weight eigenstates and search space is not ordered. It is shown that under these conditions search efficiency depends on the smaller…

Quantum Physics · Physics 2020-10-09 Jiang Liu

This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm…

Quantum Physics · Physics 2009-11-07 Dafa Li , Xinxin Li

We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits. With this processor, we run the Grover…

Quantum Physics · Physics 2011-10-25 A. Dewes , R. Lauro , F. R. Ong , V. Schmitt , P. Milman , P. Bertet , D. Vion , D. Esteve

We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only…

Quantum Physics · Physics 2007-05-23 Andris Ambainis

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

Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this…

Quantum Physics · Physics 2024-10-16 Xiang Li , Hanxiang Shen , Weiguo Gao , Yingzhou Li

This article highlights some of the key operating principles of Grover algorithm. These principles were used to develop a new oracle function, that illustrates the possibility of using Grover algorithm for solving more realistic and…

Quantum Physics · Physics 2021-09-14 Cesar Borisovich Pronin , Andrey Vladimirovich Ostroukh

It is found that Grover's quantum search algorithm is not robust against phase inversion and Hadmard transformation inaccuracies. Imperfect phase inversions and Hadmard-Walsh transformations in Grover's quantum search algorithm lead to…

Quantum Physics · Physics 2007-05-23 Gui Lu Long , Yan Song Li , Wei Lin Zhang , Chang Cun Tu