Related papers: Quantum Walk Search through Potential Barriers
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
Quantum walks have attracted attention as a promising platform realizing topological phenomena and many physicists have introduced various types of indices to characterize topologically protected bound states that are robust against…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem. We report progress towards its resolution by showing that the oracle complexity for target location can be made optimal, by…
Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…
Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in $\mathcal O(\sqrt n)$ time for $n$…
We study continuous-time quantum walks mimicking the quantum search based on Grover's procedure. This allows us to consider structures, that is, databases, with arbitrary topological arrangements of their entries. We show that the…
This paper describes a quantum algorithm for finding the maximum among N items. The classical method for the same problem takes O(N) steps because we need to compare two numbers in one step. This algorithm takes O(sqrt(N)) steps by…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
We show a simple generalization of the quantum walk algorithm for search in backtracking trees by Montanaro (ToC 2018) to the case where vertices can have different times of computation. If a vertex $v$ in the tree of depth $D$ is computed…
We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is greatly larger than the marked number of vertices we are searching, $N \gg…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
In this work I describe a classical analog of Grover's quantum searching algorithm, explaining why a quantum algorithm should be able to perform search in O(sqrtN) steps and also acting as a useful pedagogic demonstration.
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…
Quantum walks are powerful tools for building quantum search algorithms or quantum sampling algorithms named the construction of quantum stationary state. However, the success probability of those algorithms are all far away from 1.…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
We present a novel methodological framework for quantum spatial search, generalising the Childs & Goldstone ($\mathcal{CG}$) algorithm via alternating applications of marked-vertex phase shifts and continuous-time quantum walks. We…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
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…