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Grover's unstructured search algorithm is one of the best examples to date for the superiority of quantum algorithms over classical ones. Its applicability, however, has been questioned by many due to its oracular nature. We propose a…

Quantum Physics · Physics 2017-08-21 Itay Hen

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 report the implementation of Grover's quantum search algorithm in the scalable system of trapped atomic ion quantum bits. Any one of four possible states of a two-qubit memory is marked, and following a single query of the search space,…

Quantum Physics · Physics 2009-11-11 K. -A. Brickman , P. C. Haljan , P. J. Lee , M. Acton , L. Deslauriers , C. Monroe

In this work, we present a quantum query algorithm for searching a word of length $m$ in an unsorted dictionary of size $n$. The algorithm uses $O(\sqrt{n})$ queries (Grover operators), like previously known algorithms. What is new is that…

Quantum Physics · Physics 2024-12-17 Farid Ablayev , Nailya Salikhova , Marat Ablayev

The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state which tends to the solution [Farhi et al.,…

Quantum Physics · Physics 2009-11-07 Jeremie Roland , Nicolas J. Cerf

We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's…

Quantum Physics · Physics 2008-12-18 Robert Gingrich , Colin P. Williams , Nicolas Cerf

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 introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…

Quantum Physics · Physics 2025-07-22 Yash Prabhat , Snigdha Thakur , Ankur Raina

A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…

Quantum Physics · Physics 2023-08-23 Yutong Huang , Shengshi Pang

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

One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…

Quantum Physics · Physics 2017-11-22 Yan Wang

We present a full implementation and simulation of a novel quantum reinforcement learning method. Our work is a detailed and formal proof of concept for how quantum algorithms can be used to solve reinforcement learning problems and shows…

Quantum Physics · Physics 2023-11-10 Simon Wiedemann , Daniel Hein , Steffen Udluft , Christian Mendl

We analyze three different quantum search algorithms, the traditional Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and finally the quantum search by local adiabatic evolution. We show that they are closely…

Quantum Physics · Physics 2009-11-10 J. Roland , N. J. Cerf

Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…

Quantum Physics · Physics 2026-05-05 John Burke , Ciaran McGoldrick

Grover's algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked…

Quantum Physics · Physics 2016-09-08 Eli Biham , Ofer Biham , David Biron , Markus Grassl , Daniel A. Lidar

We introduce a novel deterministic quantum search algorithm that provides a practical alternative to conventional probabilistic search approaches. Our scheme eliminates the inherent uncertainty of quantum search without relying on arbitrary…

Quantum Physics · Physics 2025-07-22 John Burke , Ciaran McGoldrick

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

The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…

Quantum Physics · Physics 2009-11-13 Avatar Tulsi

We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on…

Quantum Physics · Physics 2008-05-12 Andris Ambainis

A general quantum search algorithm with arbitrary unitary transformations and an arbitrary initial state is considered in this work. To serach a marked state with certainty, we have derived, using an SU(2) representation: (1) the matching…

Quantum Physics · Physics 2009-11-07 Jin-Yuan Hsieh , Che-Ming Li