Related papers: A Framework for Structured Quantum Search
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods that allows us to locally determine network…
I propose a "quantum annealing" heuristic for the problem of combinatorial search among a frustrated set of states characterized by a cost function to be minimized. The algorithm is probabilistic, with postselection of the measurement…
A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown…
In general, a quantum algorithm wants to avoid decoherence or perturbation, since such factors may cause errors in the algorithm. In this letter, we will supply the answer to the interesting question: can the factors seemingly harmful to a…
We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the…
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 search is a quantum mechanical technique for searching N possibilities in only sqrt(N) steps. This paper gives a fresh perspective on the algorithm in terms of a resonance phenomenon which is implemented through classical coupled…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
The search operation for a marked state by means of Grover's quantum searching algorithm is shown to be an element of group SU(2) which acts on a 2-dimensional space spanned by the marked state and the unmarked collective state. Based on…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
Grover's quantum algorithm for an unstructured search problem and the Count algorithm by Brassard et al. are generalized to the case when the initial state is arbitrarily and maximally entangled. This ansatz might be relevant with quantum…
The simplest technique for simulating a quantum algorithm - QA described based on the direct matrix representation of the quantum operators. Using this approach, it is relatively simple to simulate the operation of a QA and to perform…
We discuss the quantum search algorithm using complex queries that has recently been published by Grover (quant-ph/9706005). We recall the algorithm adding some details showing which complex query has to be evaluated. Based on this version…
The current era of quantum computing has yielded several algorithms that promise high computational efficiency. While the algorithms are sound in theory and can provide potentially exponential speedup, there is little guidance on how to…
Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density of these…
Quantum algorithm can find target item in a database faster than any classical. One can trade accuracy for speed and find a part of the database (a block) containing the target item even faster: this is partial search. One can think of…
Sorting is a fundamental computational process, which facilitates subsequent searching of a database. It can be thought of as factorisation of the search process. The location of a desired item in a sorted database can be found by classical…
Local search algorithms use the neighborhood relations among search states and often perform well for a variety of NP-hard combinatorial search problems. This paper shows how quantum computers can also use these neighborhood relations. An…