Related papers: Quantum spatial search with multiple excitations
We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…
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…
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…
We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…
The hardness to solve an unstructured quantum search problem by a standard quantum search algorithm mainly originates from the low efficiency to amplify the amplitude of the marked state by the oracle unitary operation associated with other…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…
In this work we use the wave equation to obtain a classical analog of the quantum search algorithm and we verify that the essence of search algorithms resides in the establishment of resonances between the initial and the serched states. In…
The lackadaisical quantum walk, which is a quantum walk with a weighted self-loop at each vertex, has been shown to speed up dispersion on the line and improve spatial search on the complete graph and periodic square lattice. In these…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for finding L equal numbers. We point out that this algorithm actually solves a much more…
We give a quantum algorithm for a novel type of black-box problem: identifying a hidden $d$-regular base graph $G$ on $n$ vertices from oracle access to an obfuscated version of it, rather than traversing it. From $G$ we build the spired…
We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an $n$-node tree of height $h$ under the assumption that a node can…
Subexponential parameterized algorithms are known for a wide range of natural problems on planar graphs, but the techniques are usually highly problem specific. The goal of this paper is to introduce a framework for obtaining…
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…
When classically searching a database, having additional correct answers makes the search easier. For a discrete-time quantum walk searching a graph for a marked vertex, however, additional marked vertices can make the search harder by…
Executing quantum circuits on currently available quantum computers requires compiling them to a representation that conforms to all restrictions imposed by the targeted architecture. Due to the limited connectivity of the devices' physical…
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.
The lackadaisical quantum walk is a discrete-time, coined quantum walk on a graph with a weighted self-loop at each vertex. It uses a generalized Grover coin and the flip-flop shift, which makes it equivalent to Szegedy's quantum Markov…
We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk…