Related papers: Fast quantum search algorithm and Bounds on it
Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the…
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 represented by a basis state in the…
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…
Quantum search algorithms are considered in the context of protein sequence comparison in biocomputing. Given a sample protein sequence of length m (i.e m residues), the problem considered is to find an optimal match in a large database…
Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms…
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…
A generalized quantum search algorithm, where phase inversions for the marked state and the prepared state are replaced by $\pi/2$ phase rotations, is realized in a 2-qubit NMR heteronuclear system. The quantum algorithm searches a marked…
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…
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…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier…
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…
Recently, Andreas de Vries proposed a quantum algorithm that would find an element in an unsorted database exponentially faster than Grover's algorithm. We show that de Vries' algorithm does not work as intended and does not give any clue…
The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time,…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
A framework is presented for the design and analysis of quantum mechanical algorithms, the sqrt(N) step quantum search algorithm is an immediate consequence of this framework. It leads to several other search-type applications - several…
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…
Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…