Related papers: Similarity between Grover's quantum search algorit…
We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact…
We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity.…
A simple circuit implementation of the oracle for Grover's quantum search of a real unstructured classical database is proposed. The oracle contains a kind of quantumly accessible classical memory, which stores the database.
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
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…
We firstly investigate the multipartite entanglement features of the quantum states, including the iteration states achieved by repeated application of Grover iteration and the Oracle ones into which the above iteration states evolve by…
In the emerging domain of quantum algorithms, the Grover's quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
It was recently shown (quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
We show how to perform a quantum search for a classical object, specifically for a classical object which performs no coherent evolution on the quantum computer being used for the search. We do so by using interaction free measurement as a…
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…
This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…
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…
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…
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…
Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries…
Grover search algorithm drives a quantum system from an initial state to a desired final state by using selective phase inversions of these two states. In (1), we studied a generalization of Grover algorithm which relaxes the assumption of…
A misunderstanding that an arbitrary phase rotation of the marked state together with the inversion about average operation in Grover's search algorithm can be used to construct a (less efficient) quantum search algorithm is cleared. The…
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…