Related papers: Nested Grover's Algorithm for Tree Search
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,…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system ({\it Partial Diffusion Operator}) to propose a quantum search algorithm runs in $O(\sqrt N/M})$ for…
Grover's algorithm is one of the most important quantum algorithms, which performs the task of searching an unsorted database without a priori probability. Recently the adiabatic evolution has been used to design and reproduce quantum…
$ $In its usual form, Grover's quantum search algorithm uses $O(\sqrt{N})$ queries and $O(\sqrt{N} \log N)$ other elementary gates to find a solution in an $N$-bit database. Grover in 2002 showed how to reduce the number of other gates to…
We investigate the performance of Grover's quantum search algorithm on a register which is subject to loss of the particles that carry the qubit information. Under the assumption that the basic steps of the algorithm are applied correctly…
Grover adaptive search (GAS) is a quantum exhaustive search algorithm designed to solve binary optimization problems. In this paper, we propose higher-order binary formulations that can simultaneously reduce the numbers of qubits and gates…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
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…
Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
Grover's search algorithm is one of the first quantum algorithms to exhibit a provable quantum advantage. It forms the backbone of numerous quantum applications and is widely used in benchmarking efforts. Here, we report…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
In this research, we investigate the possibility of applying a search strategy to genetic algorithms to explore the entire genetic tree structure. Several methods aid in performing tree searches; however, simpler algorithms such as…
In this summary we discuss two new algorithms for Grover's unsorted database search problem that claimed to have reached exponential speedup over Grover's original algorithm. One is in the quantum setting with "power queries" that allow for…
The research community has been actively working on the realization of quantum computer. But the large scale commercial quantum computers are not a reality yet quantum computing field has become richer by day with the advent of algorithms…
Database search has wide applications and is used as a subroutine in many important algorithms. We shall consider a database with one target item. Quantum algorithm finds the target item in a database faster than any classical algorithm. It…
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of n items and we would like to find a marked item. We consider a new variant of this problem in which…
It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…